nuclear power (negative): Hi, Another debate? If you are to defend anti-nuclear side there is nothing I can do to help you guys! :( The two accidents are very similar as far as the sequence of the accidents but very different in the consequences of the accidents. Chernobyl is...

Nuclear Power: nuclear energy, nuclear power pros and cons

nuclear power pros and cons: Nuclear energy provides Navy ships and submarines with enough power to operate for long periods without refueling. The trade-off is that it is extremely expensive, and produces lots of radiation that must be handled carefully. Exposure to radiation causes...

Nuclear Power: nuclear question, nuclear power plant, maine lobster

nuclear power plant, maine lobster, public affairs offices: A chemical engineer could help by sampling and recording the harsh chemicals that are used in nuclear plants. Then the chemical engineer could help the nuclear plant keep these harsh chemicals out of the cooling water that returns to the environment. Also,...

Nuclear Power: 400 nm laser pumped by aneutronic fusion -- possible?, charged particles, laser medium

charged particles, laser medium, nm laser: When you re talking about laser power of that magnitude, the wavelength doesn t matter as much as the sheer power. A few watts of electricity is relatively harmless, a few watts of laser power is ridiculously dangerous! Going closer to IR would be more useful...

Nuclear Power: Career vs. Compensation, doing a phd, northeastern school

doing a phd, northeastern school, nuclear field: I would always suggest the PhD. Not for the pay, but for the experience. Getting a PhD involves a different level of understanding of a subject. A different level of critical thinking. The biggest thing I learned when I got my PhD was when I don t know anything...

Nuclear Power: Gas fuelled electricity vs other resources, cost per kwh, carbon emissions

cost per kwh, carbon emissions, windpower: Windpower is the cheapest to operate because the fuel source is free. Once the machinery is in place, only minimal investment is needed to keep the windmill spinning. Gas will always require drilling, storage, and a per-unit expense. Windpower is about the...

Nuclear Power: the sodium coolant of the Super Phneix fast reactor, pressurized water reactor, water storage tank

pressurized water reactor, water storage tank, commercial nuclear plants: I can t say with certainty because I can t seem to find more detailed information, but they probably use the same general set-up as most commercial nuclear plants. There is a huge tank used to hold the coolant while a plant is refueled or otherwise drained....

Nuclear Power: coal vs. gas vs. nuclear, generating electricity, uranium fuel

generating electricity, uranium fuel, cost per kilowatt hour: Yes. Coal has the lowest heat capacity, followed by natural gas. Nuclear fuel has the highest heat capacity. Bear in mind that there are different grades of coal, some have higher heat capacities than others. But in any case, you get more energy per...

Nuclear Power: Nuclear Chemistry, nuclear fission, nuclear chemistry

nuclear fission, nuclear chemistry, release heat: There are a couple of differences. Chemical reaction is a very broad term. Chemical reactions can be exothermic (releasing heat) or endothermic (absorbing heat), or neither. Nuclear reactions always release heat. Chemical reactions can bond molecules...

Nuclear Power: nuclear reactions, nuclear particles, elementary particles

nuclear particles, elementary particles, radioactive decay: From wikipedia... A chemical reaction is a process that always results in the interconversion of chemical substances. The substance or substances initially involved in a chemical reaction are called reactants. Chemical reactions are usually characterized...

Nuclear Power: purpose of a reflector in a nuclear reactor, fission chain reaction, uranium fission

fission chain reaction, uranium fission, uranium atoms: In order to sustain a fission chain reaction, neutrons must be reflected back into the reactor core. Otherwise, the neutrons would just leak out and the fission reaction would cease. Basically, a uranium fission reaction is maintained using uranium-235....

Nuclear Power: alpha and beta decay, nuclear fission and fusion, protons and neutrons

nuclear fission and fusion, protons and neutrons, beta decay: Hi Seyda, Presently I am in South Africa heading for Turkey in few days. I had limited access to internet and no access to my library so my reply is delayed. What you ask is rather extensive so I would recommend that you do a Google or Wikipedia search...

Nuclear Power: nuclear eactors, nuclear power plants, kyoto protocol

nuclear power plants, kyoto protocol, harmful gases: Hi, I was in NWU at Potchefstroom for a week long lectures on nuclear engineering and had no Internet connection so I just saw your mail. Sorry for the delay. Yes definitely! ESKOM should build more reactor. When coal is burned a lot of harmful gases...

Nuclear Power: radioactive source, radiation measurements, radiation expert

radiation measurements, radiation expert, radiation source: Hi, I would like to apologize for replying so late. I live in Turkey and presently I am in South Africa for a lecture tour. I did not have a proper Internet connection for the past week, so I just read your e-mail. Sorry for the delay. First of all,...

Nuclear Power: Nuclear Power Plants, capital investment costs, nuclear power plants

capital investment costs, nuclear power plants, world nuclear association: This article from the world nuclear association gives a good overview of where the major contributors of cost are: http://www.world-nuclear.org/info/inf02.html. Recently, costs for building new nuclear power plants in the US has tripled from previous estimates...

Nuclear Power: nuclear fusion, electric energy production, helium nucleus

electric energy production, helium nucleus, deuterium and tritium: Hi, I have small problem with your question, so I will try to answer it the way I understand it. Fusion process is the combination of two light nuclei to form a heavier nuclei thus producing energy out of it. Usually, deuterium and tritium kept in a...

Nuclear Power: nuclear power, nuclear power plants, reactor vendors

nuclear power plants, reactor vendors, nuclear power development: Hi Ross, The question is bit vague but I will try to answer it the way I understand it. Nuclear power is a rather interdisciplinary undertaking. Starting from the fuel, mining companies, fuel manufacturing companies, companies that supply metals like...

Nuclear Power: Questions about aneutronic laser fusion., bremsstrahlung radiation, radioactive byproducts

bremsstrahlung radiation, radioactive byproducts, national ignition facility: The National Ignition Facility uses lasers of close to that wavelength (350 nm), 192 of them, with a total of 2 MJ of power. It s estimated that you need approximately 10-45 times that much power (depending on the laser quality and confinement of the plasma)...

Nuclear Power: Canned reactor cooling pumps for AP 1000, canned motor pumps, reactor coolant

canned motor pumps, reactor coolant, coolant pumps: The AP1000 reactor coolant pumps are high-inertia, high-reliability, low-maintenance, hermetically sealed canned motor pumps that circulate the reactor coolant through the reactor vessel, loop piping, and steam generators. The pumps are integrated into the...

Nuclear Power: Chemistry, radioactive properties, google

radioactive properties, google, obscure references: I had to Google this one, since it has nothing directly to do with nuclear power. In many cases curie plot refers to the plotting the radioactive properties (measured in curies) of a material as the temperature is lowered or against time. I found quite...

Nuclear Power: what happens.., atomic mass units, nucleus of an atom

atomic mass units, nucleus of an atom, beta particle: When a nucleus emits a beta particle, it loses one of its neutrons and gains one proton. Hence,its mass and atomic number remain the same but its charge increases by +1. When an alpha particle is emitted, the atomic mass of an element goes down by about...

Nuclear Power: characterictic of Simplified BWR and BWR, convection heat transfer, boiling water reactor

convection heat transfer, boiling water reactor, core geometries: Hi, Since I have no knowledge of the extend of nuclear engineering knowledge you have I tried to be as non-technical as I could be. ABWR or the earlier versions of BWRs use forced convection heat transfer mode and SEBWR uses natural convection heat transfer...

Nuclear Power: Difference of BWR and Simplified BWR, reactor pressure vessel, boiling water reactor

reactor pressure vessel, boiling water reactor, reactor coolant: Hi Yudha, BWR is Boiling Water Reactor, where high pressure (7.5 MPa) water is allowed to boil within the core. Other alternative is the PWR where water is kept at higher pressure (15 MPa) and boiling is not allowed within the core. In BWR s steam produced...

Nuclear Power: nuclear power, thermal power plants, coal gas

thermal power plants, coal gas, mwe: Hi Travis, MWe is a power unit. W stands for Watt which is Joule/sec. M stands for million, so MW is million Watts. e is a subscript which indicates that it is electric power. All thermal power plants (Nuclear, coal, gas and oil fired) produce certain amount...

Nuclear Power: Nuclear plant, megatons to megawatts, fallout radiation

megatons to megawatts, fallout radiation, nuclear warheads: There s no easy answer to that. You have several things to think about: how big is the nuclear bomb? How big is the nuclear plant? How long will the nuclear plant run? Are talking about all of the energy released or just the blast energy and thermal energy?...

Nuclear Power: Coal Energy Vs. Nuclear Energy, sustainable energy source, sustainable energy supply

sustainable energy source, sustainable energy supply, coal plants: Thank you for the question! This does seem to be the most popular one I get. I personally believe in what is called a diverse energy portfolio moving towards more sustainable technologies. In other words, I believe we need to rely on all forms of energy (coal,...

Nuclear Power: Nuclear Energy V. Coal Energy, nuclear, environment

nuclear, environment, health: First it is important to point out that we have many options for generating energy. We do not, and should not, assume that we have to choose between coal and nuclear. Both options have serious drawbacks, and in general I would recommend an energy strategy...

Nuclear Power: Other forms of energy other than nuclear or coal, nuclear, Fukushima

nuclear, Fukushima, environment: Bobo, Sorry not to get back to you before. You may have already gotten an answer to your question, but in any event, I ll reply now. Alternative energy includes solar, wind, biomass, hydro, and conservation. In the last year, these renewable forms of...

Nuclear Power: nuclear power, homework question, nuclear power stations

homework question, nuclear power stations, reply: Hi Chloe, Is this a homework question? If so I did answered many questions of this sort through out the years. If you be a bit more specific, I could be much more helpful to you. Please tell me your level of education and why do you ask this question. Based...

Nuclear Power: Alternative Energy, nuclear power, alternative energies

nuclear power, alternative energies: Hi Greg, Alternative to what? Nuclear energy is one of the backbones of electricity production systems. If you mean alternative to fossil fired plants or renewable energy systems yes you can talk about it. With nuclear power you can produce very large amounts...

Nuclear Power: low and medium voltage magnetics, high voltage transformers, reactor coolant

high voltage transformers, reactor coolant, coolant pumps: Hey, if you re getting any money from this I want a cut! grin The engineering company (Stone & Webster, Westinghouse, Areva, et al)that designs and constructs the plant does the original specs, which will include the manufacturer of each component. Usually...

Nuclear Power: nuclear energy, nuclear power

nuclear power: The long term viability for nuclear power is nil. The costs of new construction alone are so high that no investor would ever get their money back. Setting aside, for the moment, the costs of waste storage, safety, decommissioning, health and environmental...

Nuclear Power: nuclear power, nuclear power plants, cold war days

nuclear power plants, cold war days, coal fired power plants: Well, you get far more radiation from coal-fired power plants (radon released from burning the coal goes straight into the air) than you do from nuclear power plants, so you might want to start with those first. Since I m a physicist and a university professor,...

Nuclear Power: nuclear reactor waste, nuclear reactor, critera

nuclear reactor, critera, nuclear fuel: The short answer is no. The long answer is that there is no clear criteria for long term disposal of spent nuclear fuel from a reactor. Notice I used the term spent nuclear fuel instead of waste, since in the strictest sense it is not waste and could be reprocessed...

Nuclear Power: Aneutronic fusion -- is a turbine better than direct-conversion?, electrostatic repulsion, fusion reactor

electrostatic repulsion, fusion reactor, direct conversion: Hydrogen-boron fusion is at least 30 years away as a power source, in my opinion. D-T fusion will happen first, but only maybe in that timescale. It s all for practical reasons of engineering, this isn t going to happen overnight in anyone s wildest dreams....

Nuclear Power: nuclear fusion, fission reactor, fusion reactors

fission reactor, fusion reactors, animal habitats: There are few compared to other power sources. Fusion produces minimal nuclear waste compared to fission plants and certainly to what s released by coal (radon into the atmosphere). The standard power issue of heat pollution might be lower with fusion because...

Nuclear Power: research homework, fission product, fission products

fission product, fission products, nuclear power station: A typical nuclear power station in the U.S. is fueled with uranium (U235 and U238). During the fission process, which generates heat, the fuel is burned . This results in the creation of additional radioactive materials of smaller quantities. These fission...

Nuclear Power: robot, boiling water reactor, reactor vessel

boiling water reactor, reactor vessel, occasional repair: This is very interesting. There are no pipes inside the reactor vessel itself. It is basically a big pot that the fuel sits in, with large pipes attached to the side for the water to enter and leave the vessel (or for steam to leave the vessel if it is a...

Nuclear Power: earth sciences, nuclear power, climate change

nuclear power, climate change, global warming: Nuclear energy has limited advantages due to its cost and environmental problems. In navy ships and submarines, it allows dramatically longer range than fossil fuels. In these applications, the mission is national defense, not cost effectiveness, so nuclear...

Nuclear Power: reuse of nuclear waste fuel, steam leaks, moscow ohio

steam leaks, moscow ohio, hat supply: I like your thinking, but it still won t work :( For effective heat transfer, you would need a fluid medium around the fuel. Placing a pipe near warm fuel rods would be so incredibly inefficient. In addition, you would have to postulated or safety analysis...

Nuclear Power: nuclear power, uranium thorium, petrochemical industries

uranium thorium, petrochemical industries, world coal: Hi Kristin, Nuclear energy and language Arts!? You got me. :)) Your question is very very broad. I will answer it the way I understand it. 1) Nuclear power is an alternative to limited resources like hydro and fossil, and so called alternative resources...

Nuclear Power: nuclear waste storage, nuclear waste storage, chemistry class

nuclear waste storage, chemistry class, precautionary measures: Whooops! I just discovered this question when I answered another question. I was away from home and lecturing in South Africa when you asked me this question. I did not have an Internet connection there and also I did not have spare time then to answer...

Nuclear Power: question about power plant generators and wiring to our homes, nuclear power plant, phase conductors

nuclear power plant, phase conductors, static discharges: Generators make electricity by spinning copper wire inside magnets. Nuclear plants accomplish this by using heat to create steam. The steam pressure is then used to turn a turbine, like a large pinwheel. The turbine has a long shaft which has copper wire...

Nuclear Power: Modular Gas Reactor, pebble bed reactor, light water reactors

pebble bed reactor, light water reactors, nuclear power plants: Hi, Pebble bed nuclear reactors are not new. There were two important pebble bed nuclear reactors operated in Germany in the early 70 s. The first was the AVR reactor in Julich, Germany, which operated very successfully for more than 20 years and later...

Nuclear Power: Uranium, grams to pounds, atomic bomb

grams to pounds, atomic bomb, mws: This answer was surprisingly difficult to find. I also had to make some assumptions about the reactor size and other information. First you must know that a nuclear weapon uses a much more highly enriched uranium than a nuclear plant does. The uranium...

Nuclear Power: Uranium, atomic bomb, health costs

atomic bomb, health costs, radioactive waste: The electricity will typically be used instantly, although it could be stored for a short period in a battery- but the radioactive waste used to generate it will be around for thousands of years. There is an ethical question prompted by financial gains for...

Nuclear Power: Uranium, megawatt hours, atomic bomb

megawatt hours, atomic bomb, tajuddin: What is 109 Uranium? By what process are you making electricity, in a reactor? Reactors and bombs both require much higher amounts of uranium (10 s to hundreds of kilograms) than 10 grams. An atom of 235-U fissioning has an energy of 202.5 MeV, which converts...

Nuclear Power: Useful isotopes from fission, uses of radioactive isotopes, uses for radioactive isotopes

uses of radioactive isotopes, uses for radioactive isotopes, useful isotopes: Hi! Sorry for taking so long to answer your question. Swamped at work lately. You bet there are good uses for radioactive isotopes. Here s a fact sheet from the U.S. Nuclear Regulatory Commission on the medical uses of radioactive isotopes: http://www.nrc.gov/reading-rm/doc-collections/fact-sheets/med-use-radactiv-mat-fs.htm...

Nuclear Power: Ph.D research topics, light water reactors, thermal hydraulics

light water reactors, thermal hydraulics, research collaborations: so very sorry for not getting back to you sooner. i love to have the opportunity to suggest research topics. A new hot topic right now is small, integral light-water reactors. I am the Safety Analysis manager for NuScale power and would be interested in exploring...

Nuclear Power: Nuclear Power, nuclear power plants, lesbos greece

nuclear power plants, lesbos greece, green house effect: Dear Basi, I would like to apologize for my delay, I was in Lesbos, Greece for more than a week and did not have Internet connections there. I hope my replay is not too late and useless. Naturally, nuclear power is much more better than the fossil fired...

Nuclear Power: Can the use of nuclear energy be justified?, nuclear power, climate change

nuclear power, climate change, global warming: While the use of nuclear power can be justified in such applications as submarines or aircraft carriers, it cannot be justified for producing electricity, as it is the most expensive way to make electricity. The construction costs alone for new nuclear...

Nuclear Power: Can the use of nuclear energy be justified?, use of nuclear energy, hydrogen production

use of nuclear energy, hydrogen production, nuclear plants: Can you provide me with more information with respect to your basis. For example, nuclear energy for power production? Nuclear energy for hydrogen production? Technically, nuclear energy also includes fusion. The most common question I get is to describe...

Nuclear Power: Can the use of nuclear energy be justified?, use of nuclear energy, nuclear power

use of nuclear energy, nuclear power, wikipedia: Of course it can, or we wouldn t use it. Since you asked a question with such a massive scope, I m just going to point you in the direction of some research. Start with the wiki page, it s pretty accurate: http://en.wikipedia.org/wiki/Nuclear_powe...

Nuclear Power: AP1000, makeup water, pool designs

makeup water, pool designs, supply pipe: I haven t found the answer to this yet, but I ll keep looking and repost this response if I find the answer. But I need clarification: which pipes are you taking about? The spent fuel pool makeup water supply pipe, the cooling water pipe, or something else?...

Nuclear Power: nuclear power plant, nuclear reactors, thermal-hydraulica

nuclear reactors, thermal-hydraulica: Hi Kostas, You have not given me enough information about your level of understanding of engineering so I will try to answer your question in general form. If you need additional information please feel free to ask further. Thermodynamics is the science...

Nuclear Power: Social Studies Project, Nuclear energy, use of

Nuclear energy, use of: Hi Arun, 1- Definitely nuclear energy has changed the world in both ways, good and bad. Nuclear power gives us clean, economical and dependable way of producing electricity and heat. Nuclear research produced radioisotopes and machinery to generate radioactive...

Nuclear Power: thermohydraulic core design, reactor operation, concise question

reactor operation, concise question, core design: Your question involves textbooks worth of explanation and a course or two in upper-level nuclear engineering. It s far beyond the scope of this forum. I suggest you start reading extensively at this site: http://thcentral.com/ You may want to contact them....

Nuclear Power: Control Room Chain of Command, zion nuclear power, nuclear power plant

zion nuclear power, nuclear power plant, nuclear engineer: These titles don t all match up with the ones at the sites where I ve worked. The NSO is the licensed operator who actually manipulates the plant controls (or did, until they were shutdown). The US is his/her supervisor. I haven t heard of a SE or QNE,...

Nuclear Power: Control Room Chain of Command, power plant operations, valve alignments

Nuclear Power: Control Room Chain of Command, power plant operations, valve alignments, operations control room

Nuclear Power: Pros of a Boiling Water Reactor, boiling water reactor, light water reactors

boiling water reactor, light water reactors, naval reactor program: Hi Megan, According to my old students, who are now big shots at GE, BWR is better because it uses more hygienic cooling medium, namely, boiling water! :) First of all I must explain what is a good reactor. A good reactor should use the least amount...

Nuclear Power: nuclear engineering project, retirement benefits, advancement opportunities

retirement benefits, advancement opportunities, specific tools: Hi Ethan, Boy, this looks like pretty personal! I do not think I am the right nuclear engineer to ask these questions. I have spent all my professional life as a Prof. of nuclear engineering and taught courses and did some research. You should try your...

Nuclear Power: nuclear engineering project, thermal hydraulic calculations, nuclear power plant

thermal hydraulic calculations, nuclear power plant, thermal hydraulics: Hi Ethan, What you ask can be answered with a very long list but I will try to answer it as brief as possible. A Nuclear Engineer is a mechanical engineer with good knowledge of nuclear physics. (I am Mech/Nuc. Eng.) Someone will say a nuclear engineer...

Nuclear Power: Reuse of nuclear waste fuel, oklo reactor, fission reaction

oklo reactor, fission reaction, hydrocarbon reserves: The issue is there currently is no licensing process or technical basis that the NRC could rely on to review such an application. R&D would need to be developed within the NRC to prepare the staff to be able to review the safety of such a concept. This would...

Nuclear Power: Nuclear Power Costs and safety., writing an argumentative paper, coal plants

writing an argumentative paper, coal plants, coal gas: Is nuclear power cost effective? Yes. The cost for nuclear fuel is relatively stable and runs around $2 for every kilowatt of power produced. Coal, at it s cheapest, is about the same but typically runs about $5/kw. With more and more states banning or...

Nuclear Power: Nuclear waste, yucca mountain repository, nuclear waste repository

yucca mountain repository, nuclear waste repository, yucca mountains: Only if we continue to act out of fear and do not rationally approach the problem. A nuclear waste repository has been started in the Yucca Mountains that can contain the wastes for hundreds of years. Additionally, we could drastically reduce the amount...

Nuclear Power: Reuse of nuclear waste fuel, oklo reactor, fission reaction

oklo reactor, fission reaction, hydrocarbon reserves: The issue is there currently is no licensing process or technical basis that the NRC could rely on to review such an application. R&D would need to be developed within the NRC to prepare the staff to be able to review the safety of such a concept. This would...

Nuclear Power: Nuclear Energy Careers, nuclear energy industry, hacettepe university

nuclear energy industry, hacettepe university, hacettepe edu tr: Hi Robert, Nice to get a question from down under. I may be the right guy or the wrong guy to answer this question. I live in Turkey and a retired Nuclear Engineering Prof. that still have connections in the States. So, bare with me, I will try to answer...

Nuclear Power: alfa ışımasında fazla elektronlar, radyum, 305 z

radyum, 305 z, itli: Merhaba, Soruyu pek anlamadım, herhalde elektronları kaybeden fizk konusunda fazla bilgili değil. Alfa parçacıkları aslında helyum çekirdeğidir. Yani iki proton ve iki nötrondan oluşur. Elektronlar çekirdeğe...

Nuclear Power: A future for African student, nuclear engineering department, university of cape town

nuclear engineering department, university of cape town, pbmr: Hi Sabatha, I was instrumental in the establishment of the nuclear engineering department at the North-West University in Potchefstroom, and lectured there for around six years. I would recommend you this institution since it is in South Africa. After the...

Nuclear Power: General Inquiry of Fissile Materials and Control Rods + Hypothetical Inquiries of SCW Reactors, efficiency production, uranium fuel

efficiency production, uranium fuel, topical range: Hello, thank you for the opportunity to answer your questions. Please see answers below... 1. About how long after enriched uranium fuel is considered spent does it remain fissile enough to potentially produce meltdown like conditions if improperly handled?...

Nuclear Power: HTTR concentric hot gas duct, test reactor, thermal stresses

test reactor, thermal stresses, central tube: The gas duct is a cross connect to the intermediate heat exchanger. In a sense, the inner tube is the inlet to the IHX and the annular tube around the central tube is the outlet. So you have a tube within a tube where the flows are in the opposite direction....

Nuclear Power: Nuclear(of course!)sodium cooled reactors, boiling water reactor, different types of nuclear reactors

boiling water reactor, different types of nuclear reactors, types of nuclear reactors: I can answer the question about different types of reactors, but nuclear medicine is out of my area of expertise. When you say different types I m assuming that you mean the three basic categories of commercial reactor designs: boiling water, pressurized...

Nuclear Power: Nuclear plant workers, contamination, nuclear power

contamination, nuclear power, radiation: The answer depends on what work they re doing. If they re actually working with radioactive or contaminated components, they will be checked with a hand-held monitor before they leave the immediate work area. They will then go through a very sensitive full...

Nuclear Power: Ph.D.Topic, reactor physics, thermal hydraulics

reactor physics, thermal hydraulics, nuclear instrumentation: I would suggest small modular or scalable modular reactors. There are a lot of areas that are new and emerging with this technology. Cost control, business models, modular construction, multi-module risk, multi-module control and operation, testing, etc...

Nuclear Power: Question about radiation in Japan, radiation emissions, john lyman

radiation emissions, john lyman, freelance journalist: Hello, thank you for the opportunity to answer your questions. Please see responses below... 1. Are there any websites available to the public where you can see just how much radiation is being emitted/released from atomic energy plants like those in Japan?...

Nuclear Power: Radioactive element, alpha beta gamma, alpha beta gamma rays

alpha beta gamma, alpha beta gamma rays, nucleus of an atom: Hi Manuel, Regardless of weather natural or man made, all radioactive isotopes decay to a much stable isotope. Some decay really fast (with very short half-life) some decay very slowly. Half-life is the amount of time required for half of the weight of...

Nuclear Power: Safe to travel?, reactor plants, us aircraft carriers

reactor plants, us aircraft carriers, nuclear reactors: Of course she is. And the meltdown problem in Japan is vastly overblown, though it does highlight the need to replace the really ancient type of nuclear reactors with modern meltdown-proof designs. Why would it not be safe flying to NY via Frankfurt? ...

Nuclear Power: Thoughts on travelling to Japan?, travelling to japan, japanese authorities

travelling to japan, japanese authorities, japan tokyo: Hi Doug, You are planning to go to Japan in six months time and wondering about the effects of the nuclear accident!!!??? This a very good example of how media manipulates us. There is a nuclear accident that is not over yet in Japan. The site is few...

Nuclear Power: Nuclear & other power generation deaths, hydro power generation, nuclear power plants

hydro power generation, nuclear power plants, nuclear power generation: Hi, sorry for the delay in answering your question. Was on a trip to Sandia National Lab and just got back. Please see responses below: 1. Couldn t find a direct comparison with hydro, but here is a good comparison between nuclear, coal, and oil: http://www.geekosystem.com/coal-oil-nuclear-deaths-chart/....

Nuclear Power: science, advantages and disadvantages of nuclear power, disadvantages of nuclear power

advantages and disadvantages of nuclear power, disadvantages of nuclear power, nuclear power plants: Hi Matt, Sorry for the delay. To answer your question, nuclear power for electricity generation is a safe and environmentally benign solution. It is relatively expensive from an initial cost perspective, but is cheap to operate and fuel. For example, fuel...

Nuclear Power: Difference between a Degree in Nuclear Engineering Technology and Nuclear Engineering, nuclear engineering department, nuclear power program

nuclear engineering department, nuclear power program, engineer program: Hi Thomas, May be I should start answering your question by introducing myself. I am a retired nuclear engineering professor living in Turkey. I can help you very little since my knowledge about the US Navy is very limited. Otherwise, I may have trouble...

Nuclear Power: Difference between a Degree in Nuclear Engineering Technology and Nuclear Engineering, nuclear electronics, electronics technician

Nuclear Power: Difference between a Degree in Nuclear Engineering Technology and Nuclear Engineering, nuclear electronics, electronics technician, college credits

Nuclear Power: Efficiency, nuclear, environment

nuclear, environment, health: Coal has always been cheaper than nuclear to produce. Of course, both forms of energy have serious environmental costs associated with them. Coal is a big contributor to climate change, producing nasty chemicals and easily visible black smoke. Nuclear power...

Nuclear Power: industrial accidents, nuclear power plant, coolant system

nuclear power plant, coolant system, reactor core: This is much like your previous question, almost impossible to answer. You never mentioned what kind of accident at all. It s the same as the danger level at any coal-fired plant, but less likely because at those plants people actually handle the fuel and...

Nuclear Power: industrial accidents, nuclear power plants, nuclear power plant

nuclear power plants, nuclear power plant, f4 phantom jet: Hi, Nuclear power plants are build in special sites. When a nuclear site is licensed by the regulatory agency (NRC for USA) certain criteria must be met. Site must be away from population centers, industrial sites, etc. So, it is very improbable to find...

Nuclear Power: industrial accidents, reactor coolant system, nuclear power plant

reactor coolant system, nuclear power plant, reactor core: These would be as dangerous as any industrial accident. Transformers can explode on light poles or anywhere else. About the only thing not related to the reactor or reactor coolant system that would cause an automatic shutdown would be an electrical problem....

Nuclear Power: maintenance, repairs, and safety, nuclear power plants, coolant system

nuclear power plants, coolant system, water reactors: Nuclear power plants adhere to a very strict maintenance rule as part of their license to operate the plant. Defense-in-depth design, construction, operation, and maintenance principles ensure that no single failure of hardware, software, or process will result...

Nuclear Power: maintenance, repairs, and safety, nuclear power plants, reactor head

nuclear power plants, reactor head, nuclear power plant: Hi, Nuclear power plants are very expensive machines and like care given to any very expensive property a lot of care is given. Nuclear power plants when not producing electricity the cost to the company are twofold. Losing revenues from selling electricity...

Nuclear Power: man made or natural disasters, natural background radiation, nuclear disasters

natural background radiation, nuclear disasters, exposure zones: While I am not an engineer, I m a physicist, I can help answer this one to an extent. To an extent means that you never wrote what kind of shock, explosion, or other disaster. Obviously the shock would have to be about 125 times what it was designed for...

Nuclear Power: man made or natural disasters, shock waves, diesel locomotive

shock waves, diesel locomotive, containment wall: Hi, This is a difficult question to answer, since in most of the properties of containment buildings design limits, an upper limit for a shock waves is not mentioned. Nevertheless, all containment building has to withstand severest earthquake at the site,...

Nuclear Power: man made or natural disasters, ground water moves, fuel pools

ground water moves, fuel pools, fuel bundle: The small leaks would be detected quickly and repaired quickly. Uncovering a used fuel bundle isn t an option, the radiation levels would be lethal. However, if leaks persisted over 40 years the tritium would build up. But remember that it is decaying...

Nuclear Power: Nuclear waste, radioactive elements decay, helium nucleus

radioactive elements decay, helium nucleus, beta particles: Hi, You have asked four extensive questions and I will try to answer them as much as I can. So, bare with me. :) In this question there is something fundamentally wrong. Usually nothing leaks from the spend fuel pools. If there is a catastrophic accident,...

Nuclear Power: Nuclear waste, beta radiation, bone surfaces

beta radiation, bone surfaces, paper clothes: First, please understand that these aren t in the groundwater unless there is a major accident in the spent fuel pool. The strontium and nickel are contained within the spent fuel itself, so we don t find these in the spent fuel unless a fuel rod has been...

Nuclear Power: Nuclear waste, city water supply, fuel pools

city water supply, fuel pools, external radiation: That depends on a ridiculous number of factors. Such as: who lives there? What is their water consumption? Is their ground water from the local water table or from a city water supply? How far is the leak from the ground water that supplies their water?...

Nuclear Power: plant maintenance, steam generators, water reactors

steam generators, water reactors, inconel 600: Eli, PWRs need to refuel every 18 months or so. They need constant maintenance, which is expensive because all people, tools and equipment become radioactively contaminated. Further, all steam generators made with inconel 600 have needed to be repaired...

Nuclear Power: plant maintenance, chernobyl accidents, coolant system

chernobyl accidents, coolant system, lifetime extension: Maintenance is ongoing to ensure that the plants remain safe. Major maintenance happens every 18 to 24 months when the core is refueled. The cost is impossible for me to guess, it depends on so many factors like adequacy of preventative maintenance and other...

Nuclear Power: safety, nuclear, Fukushima

nuclear, Fukushima, environment: Any industrial accident at a nuclear power plant which triggers an automatic shutdown is potentially catastrophic. Nuclear plants rely on backup power to keep fuel cool when the plant shuts down. If power from off-site is unavailable or interrupted, the fuel...

Nuclear Power: Radiation, beta emitters, radiation types

beta emitters, radiation types, dryer lint: You re partly confusing (don t worry, most people do) radioactive material with radiation itself, and not distinguishing between the radiation types. Some radiation emitted by radioactive material can be penetrating, but most types are pretty much blocked...

Nuclear Power: Tungsten Conduct Rods, high temperature materials, tungsten rods

high temperature materials, tungsten rods, magma chambers: This is basically what we call geothermal energy. It can be extracted from anywhere in the Earth s core, not just actual magma. However, the corrosive environments and extreme materials costs currently make geothermal energy expensive and problematic as...

Nuclear Power: A world without nuclear fission?, discovery of nuclear fission, j robert oppenheimer

discovery of nuclear fission, j robert oppenheimer, fritz strassman: Hi Tessa, Thanks for waiting for my return to home. If you are writing a novel, may I suggest a title such as Chainsaw Massacre in Physics and the Eternal Damnation of Physicist since this is what you need to postpone fission for seven decades. It...

Nuclear Power: Nuclear Engineering/Nuclear Fusion, nuclear fusion reactors, laser wakefield accelerator

nuclear fusion reactors, laser wakefield accelerator, thermal hydraulics: Many of the issues which engineers will be working on in the first generation of successful nuclear fusion reactors will involve the handling of large amounts of tritium because deuterium-tritium fusion will be much more easily achieved than low-radiation...

Nuclear Power: Reducing CO2 If It Is Still Possible At This Point, alternative energy sources, nucleus of an atom

alternative energy sources, nucleus of an atom, lightning bolt: We don t actually bury the waste, we store it almost entirely above ground at the reactor sites themselves. Large-scale storage underground hasn t been achieved for power plant fuel. However, we could always recycle that fuel, right now a holdover from cold...

Nuclear Power: Nuclear Energy, fight climate change, commercial reactor

fight climate change, commercial reactor, airplane crash: Countries should not create any new nuclear plants. There are two major reasons why not. First, nuclear is the most expensive form of new power. The construction costs alone of new nuclear plants make them more expensive than any other form of power. This...

Nuclear Power: OCD and radioactivity fear, irrational fears, anxiety disorder

irrational fears, anxiety disorder, a1s: Dear Leandro, I hope I can help you but, I am bit astonished why me?. I had a lot of Argentinean nuclear engineer classmates from my MIT years. I am sure Argentinian nuclear engineers could help you much better then I. I will try to do my best. My mother...

Nuclear Power: Power plant tranformers, transformer, transformers

transformer, transformers, solar flare: I found an article in National Geographic that states large transformers could be destroyed by solar flares, but I need to look into the possibility of the further. The article states that a large solar flare hit the earth in the 1800s and caused sparks to...

Nuclear Power: Studying Fusion Energy, universidad central de venezuela, foreing student

universidad central de venezuela, foreing student, plasma physics: 1) Yes, these are crossover fields, but you ll find it slightly more difficult without a bachelor s degree in physics. 2) That depends on where you apply and how much you can bring up your written English, your current question makes it obvious that you re...

Nuclear Power: Is a Nuclear Strike more lethal on Land or in the Sea in the long term Globally?, tactical nukes, lethal consequences

tactical nukes, lethal consequences, water cloud: Then I would focus on a very realistic scenario involving the evaporation of methane hydrates, specifically http://en.wikipedia.org/wiki/Methane_clathrate and see the climate-change scenario. It would lead to one of those desert post-apocalyptic worlds you...

Nuclear Power: radiations, protons neutrons electrons, deuterium nucleus

protons neutrons electrons, deuterium nucleus, hydrogen nucleus: Hi, Matter is composed of atoms whose nucleus have neutrons and protons. Protons are positively charged particles. Since like charges repel each other there cannot be a nucleus composed of only protons. Neutrons are neutral particles very similar to protons...

Nuclear Power: Licensing Engineer, nuclear power plant, nuclear power industry

nuclear power plant, nuclear power industry, degree in electrical engineering: Hi Mark! Thanks for the question. The NRC provides an excellent training program for engineers. It is called the Nuclear Safety Development Program if I remember correctly. They hire ME, CE, and all kinds of engineers to send through the program. Most of the...

Nuclear Power: Nuclear Fusion Propulsion for Aircraft, fusion propulsion, vtol aircraft

fusion propulsion, vtol aircraft, nuclear propulsion: No, VTOL would just make the aircraft extremely more difficult to build and fly. Also, the airports of Paris, Frankfurt, and Dubai are absolutely massive, no need for VTOL in those cities at all (especially Dubai, from the photos I ve seen of it). I also...

Nuclear Power: Fast Breeder Reactors, experimental breeder reactor, global nuclear energy partnership

Nuclear Power: Fast Breeder Reactors, experimental breeder reactor, global nuclear energy partnership, reactor facility

Nuclear Power: Fast Breeder Reactors, nuclear fuel cycle, fast breeder reactors

nuclear fuel cycle, fast breeder reactors, research breakthroughs: Hi Brenden! Thank you for the question. Several countries have prototype FBRs. The U.S. used to have them as well. However, FBRs are current not economical viable and still remain in the research phase. If economical, they could provide a way to reuse spent...

Nuclear Power: Nuclear Power - Optimal method for generating electricity?, pros and cons of nuclear power, cons of nuclear power

pros and cons of nuclear power, cons of nuclear power, nuclear power plant: Hi Tihomir, Nice to hear from Wien, I love your town. My sister lives in Bruck/Mur. First of all how big is your island? You know UK is an island so as Australia! In other words how much power is necessary for the economic life in your island? What...

Nuclear Power: nuclear reactors, coal fired power plant, nuclear reactors

coal fired power plant, nuclear reactors, nuclear reactor: If you mean inside the reactor itself, then almost none. They fill that with ultra-pure water and let it run in a closed and pressurized system, only topping it off occasionally. If you re talking about the cooling pools for the fuel rods, then a lot more...

Nuclear Power: Nuclear Concerns

Seriously, a sinkhole in Japan? The geology is just...all wrong for the usual process...I m not a geologist, but I looked around and that seems true. Anyhow, it also makes no sense to reinforce foundations. The nuclear material needs to be isolated until...

Nuclear Power: RE:

You really need to take a bunch of science classes and put NUMBERS to these things. NUMBERS that provide a sense of scale. For one thing, what you read is wrong about spewing isotopes for decades. All the hottest isotopes will decay away in their characteristic...

Nuclear Power: Nuclear Power vs. Coal Combustion, nuclear power generation, coal combustion

nuclear power generation, coal combustion, potential health risks: Dear Matthew, Sorry for the delay, I was away from home for few days. You are welcome to ask anything nuclear, I hope I can help you. You have not mentioned what kind of research paper that you are preparing, so my answers may be bit underestimating or...

Nuclear Power: interview questions for english paper, nuclear reactors, radiation exposure

nuclear reactors, radiation exposure, military targets: Nuclear reactors in the united states are very safe. They are essentially hardened military targets with 24/7 highly trained security forces. No civilian nuclear accident in the united states has resulted in any deaths due to radiation exposure. Nuclear...

Nuclear Power: Ra226, helium atom, decay equations

helium atom, decay equations, decay scheme: Hi Jo, Alpha particle is the nucleus of Helium atom. ( beta particle is an electron ) We seldom refer alpha particle as Helium in text or verbal communications. When we mention equations we usually use mathematical notations. If you want to know where...

Nuclear Power: Nukes at WTC on 9/11?, radioactive fission products, fission and fusion

radioactive fission products, fission and fusion, wtc towers: Dear Jerry, I would like to ask your forgiveness for my long delay in replying to your question. I have to cope with unplanned health emergencies of my relatives. A 90 year old relative of mine is in ICU for more than a month and I had to travel to places...

Nuclear Power: Nuclear power in Australia, nuclear power plants, disadvantages of nuclear power

nuclear power plants, disadvantages of nuclear power, pros and cons of nuclear power: Jaya, thank you for the question! Nuclear power is a safe way to provide carbon free baseload power to cities. I would recommend the following presentation as an excellent source of pros and cons of nuclear power in Australia. http://www.engineersaustralia.org.au/sites/default/files/shado/Divisions/Sydney%20Division/Southern%20Highlands%20and%20Tablelands%20Regional%20Group/ENERGY/NuclearPower-Pros%26Cons_EATalk-13Jul06.pdf...

Nuclear Power: Nuclear power in Australia, amory lovins, nuclear power plants

amory lovins, nuclear power plants, disadvantages of nuclear power: Hi Jaya, I ve added an article that I wrote a couple of years ago as it might give you a little more material that you may use--it has more scientific information: While the use of nuclear power can be justified in such applications as submarines or...

Nuclear Power: Nuclear power in Australia, westinghouse ap1000, nuclear power plants

westinghouse ap1000, nuclear power plants, self contained units: It was really a fallout from the decision not to mine more uranium in Australia. People were afraid of uranium being shipped across the country (which is silly, natural uranium is rather lower in terms of radiation released. I ve held new fuel rods in my...

Nuclear Power: Nuclear power plant

There s four parts to the startup. First, the plant has to heatup to normal operating temperature. Then the reactor itself has to be started (brought critical). Once the reactor is critical it has to be increased in power until the turbine can be started....

Nuclear Power: RE:

Is this the same person asking about Fukushima again? After I stressed number? NUMBERS! Aside from what s generated via cosmic rays, I assume you re referring to 137Cs which comes from Fukushima. It can enter the oceans and be detected in fish immediately...

Nuclear Power: Follow up

I do not still feel like the US is in serious danger, because I never felt that way in the first place. The article is erroneously representing radioactivity from the headline on down. Just look at it, right next to the 134Cs radioactivity level, smack...

Nuclear Power: Actinides.

Wow, you asked me a relevant nuclear physics question, for a change! Excellent, but the question is a little generalized, so I will clarify a bit. Uranium has two fissile heavy elements which can be used for generating nuclear power. In fact, 233U (92...

Nuclear Power: Actinides.

The only fuels that can be used in a nuclear reactor are U-233, U-235, and Pu-239. Nuclear reactors depend on thermal fission (fission created by neutrons that have slowed to thermal equilibrium in the core). U-238 can undergo fission by fast neutrons ...

Nuclear Power: Actinides.

Hi Prashant, If one checks the stability of Actinides one finds few stable or near stable nuclei within the series. Thorium, Uranium (233,235,238) as well as Pu 239 isotopes are suitable as nuclear fuel for fission reactors used in nuclear power plants....

Nuclear Power: radiation on flights

Pilots aren t just frequent flyers, they fly pretty much several times a day, every day. They are also one of the most studied populations on the planet. Take your antioxidants, they re supposed to be good for you in general. Don t worry about the radiation...

Nuclear Power: Radiation on a plane, radiation, exposure

radiation, exposure, airline: While studies show that there is a small increase in exposure to cosmic radiation, it is only significant for the pilot and crew because of the windshield. See http://www.usnews.com/news/articles/2014/12/17/for-pilots-flying-may-be-just-as-dangerous-as-fake-bake...

Nuclear Power: Nuclear power response time

Hi Ryan, Usually nuclear power plants are built to supply the base load since it is more economical way of electricity production in a grid. The turbine is slave to the reactor which produces the maximum amount of power assigned by the operators. If the...

Nuclear Power: Is it safe to live near nuclear plant or dump site?

Hi Alex, It might be dangerous so, I advise you to ask a constructor to check the old house structurally. As far as the old nuclear plant is concern rest your mind in peace. Joke aside, I do not see any problem living near a nuclear power station, old or...

Nuclear Power: question

My current job is not within the nuclear industry itself. I was a professor for the last seven years at one of the schools within the University of Texas, now my work pertains more to monitoring for nuclear material. Don t listen to people who don t know...

Nuclear Power: Fusion powered VTOL cargo spaceships

Hi Gordon, great question! To be frank I m not an expert on fusion or nuclear space propulsion. However, that doesn t stop me from having an opinion :) Based on recent projects I ve been tangentially a part of, plasma propulsion using fission seems like the...

Nuclear Power: Hypothetical : Nuclear Reactor Meltdown

In general, if the situation warranted abandoning a reactor, it would be SCRAMmed first (emergency shutdown). It would also likely be poisoned, meaning that neutron-absorbent materials would be injected into the cooling water, further stabilizing the reactor...

Nuclear Power: west coast fukushima radiation

OK, I m an expert on this. A real one, with an understanding of what the numbers actually mean and access to all the fanciest weather dispersion models and extensive knowledge of the nuclear physics involved. The numbers in this blog you read are wrong...

Nuclear Power: West Coast Radiation

Thanks for the question Jay! I get this a fair amount. Nothing to worry about at all. I was born on the CA coast and have a lot s of family there. The article you provide is full of false information. There is just absolutely not enough radiation in those...

Nuclear Power: fukushima

I would stop reading news from that site entirely. They re talking about fCi/m^3. The gross alpha standard is actually 15 pCi/liter (http://www.epa.gov/dwreginfo/radionuclides-rule). A pCi is 1000 times higher than a fCi, and there are 1000 liters in...

Nuclear Power: Blueprint error (pipe fitter)

Hi Rylan, If I find an error on a blueprint I would bring it to the attention of the people who is responsible in creating that design and making the drawing. It may be a simple mistake and they would be pleased to correct it. Sometimes there are reasons...

Nuclear Power: Cell phone tower concern, cancer, cell

cancer, cell, phone: This is not my area of expertise but I am relatively knowledgeable about the radiation emitted from cell phones. The controversy of course is that extensive use of a cell phone can cause tumors. So I understand why you would be concerned about living next...

Nuclear Power: Cell phone tower

I get this question quite a bit. While it s a little bit medical, the basic physics agrees with all the medical studies. This is one of the most intensely studied public health topics of recent decades, with the massive uptick in transmitter towers. People...

Nuclear Power: Microsieverts/h of items

Hi Jim and thanks for the question! No safety issues at all. Those are very low readings. May favorite way to discuss radiation is the bannana equivalent dose. Sounds kind of silly but helps out things in perspective. Here is a link to a great Wikipedia article...

Nuclear Power: Our 3rd grade class is learning..., navy recruiter, nuclear power plant

navy recruiter, nuclear power plant, math physics: What is the favorite part of my job? I like working with machinery and understanding how each one helps the other out in the process of making electricity. It is like a baseball team, the whole plant has to work as a team of machines, electricity and people...

Nuclear Power: Advanced Reactors, hydro industry, mainframe computer

hydro industry, mainframe computer, coal industry: Current PWRs are safe! The only major accident in the US industry has been TMI. Of which no release of radioactivity resulted in harm to the public. Second, over the 30 years of operating reactors, not one person has died at a plant other than natural causes!...

Nuclear Power: Affects of radiation, summit west, jlab

summit west, jlab, chernobyl: Thanks Jessica for contacting me. The answer to your question is pretty lengthy. You may like to refer to the following web sites: For general kind of information: http://www.jlab.org/div_dept/train/rad_guide/effects.html For Chernobyl specific information:...

Nuclear Power: Alternative Energy??, nuclear power plants, alternative energy sources

nuclear power plants, alternative energy sources, nuclear power plant: Please do not get involved with the Devil ! Hydraulic power is not an alternative to nuclear or fossil plants. You can build a nuclear power plant of a fossil fired plant in Sahara. Can you build a hydraulic power plant? Consider the power levels of...

Nuclear Power: Alternative Energy??, nuclear power plants, devil s advocate

nuclear power plants, devil s advocate, hydro dams: Let s start by defining some terms, so that we re on the same page. Fuel is a substance that can be transformed (by burning, nuclear reaction, etc) into useful forms of energy through work (turning of a turbine, cylinders in a car, etc), to produce electricity...

Nuclear Power: AP1000, radioactive fission products, steam generators

radioactive fission products, steam generators, natural circulation: As I understand it, the basic reason is cost. First, the design had already been created, engineered and approved as the slightly smaller AP600. Being able to use an existing design saves a lot of money. Second, this design uses far fewer components (valves,...

Nuclear Power: Atom, atom atom, what is an atom

atom atom, what is an atom, fermium: Hello Maya, This is a rather funny question. You must be a student trying to do homework!? Who ever suggested this title must have been a bit confused. What is an atom? Atom is the building block of all matter in the universe. We are made of atoms so...

Nuclear Power: actinides, high temperature gas cooled reactor, coolant temp

high temperature gas cooled reactor, coolant temp, control rods: In theory it is possible under a program such as the Global Nuclear Energy Partnership (http://www.gnep.energy.gov/). GNEP seeks to develop worldwide consensus on enabling expanded use of economical, carbon-free nuclear energy to meet growing electricity demand....

Nuclear Power: More advaned pros and cons of using nuclear power stations, nuclear power plants, nuclear power plant

nuclear power plants, nuclear power plant, nitrogen oxides: Hi, Since I do not know how much you know about nuclear power or electricity production I have difficulty in interpreting what you mean by Advanced pros and cons, Nevertheless, I will try my best. Being a nuclear engineer, I do not see any cons for...

Nuclear Power: More advaned pros and cons of using nuclear power stations, nuclear power plants, nuclear power plant

nuclear power plants, nuclear power plant, nitrogen oxides: Hi, Since I do not know how much you know about nuclear power or electricity production I have difficulty in interpreting what you mean by Advanced pros and cons, Nevertheless, I will try my best. Being a nuclear engineer, I do not see any cons for nuclear...

Nuclear Power: Will aneutronic fusion power ever be possible?, fission reactors, cell phone technology

fission reactors, cell phone technology, plasma temperatures: Slide 63 in this presentation on fusion http://www.slideshare.net/omar/nuclear-fusion-31590/ shows the quality of the plasmas achieved over time. Given the rate of advances in the field, I believe neutron-rich fusion will happen first and then eventually...

Nuclear Power: Will aneutronic fusion power ever be possible?, fission reactors, mirror machine

fission reactors, mirror machine, fusion machines: Hi, I do not know, how long are you planning to stay around? :) When it comes to plasma research it is always 20 years. I am 62 years old and when I was learning about plasmas at MIT in early seventies we were told by researchers in the field of plasma...

Nuclear Power: Breeder Reactors, breeder reactors, product streams

breeder reactors, product streams, breeder reactor: Actually, Jimmy Carter banned reprocessing of spent nuclear fuel, which is part of the breeder reactor life cycle. Reprocessing spent fuel creates two product streams: uranium and plutonium. The fear was that it would be easier for bad people to steal the...

Nuclear Power: BUILDING & FINANCING A PLANT, nuclear power plant, electricity grid

nuclear power plant, electricity grid, economic purposes: A country must have a very well established infrastructure, strong electricity grid, established industry, well educated man power and on top of all these a very strong international financial standing. You can get more information from IAEA web site...

Nuclear Power: Career Path, health physics, nuclear plants

health physics, nuclear plants, radiation protection: Isaiah, The Nuclear Industry has been stagnant for about 8 years. In this I means that very few of the plants were hiring and there hasn t been any new plants built. But the work force is aging and looking forward to retirement in the next few years....

Nuclear Power: Chernobyl accident, chernobyl reactor, nuclear power plants

chernobyl reactor, nuclear power plants, chernobyl incident: Hi Travis, No and Yes! A nuclear reactor of Western design can never have an accident like Chernobyl accident. Yes, there has been an accident that happened in the USA which is very similar to Chernobyl accident. It is the Three Mile Island accident. In...

Nuclear Power: Coal-fired vs. nuclear, fossil fuel plants, mercury emissions

fossil fuel plants, mercury emissions, coal plant: A nuclear plant. Unlike a coal plant, a nuclear plant makes no emissions. Depending on the age of the coal plant you can get fly-ash, carbon monoxide and mercury emissions. Fossil fuel plants also contribute to global warming, which nuclear plants do...

Nuclear Power: Conditions inside the dome in a case of an accident, continuum mechanics, worst case scenario

continuum mechanics, worst case scenario, containment structure: I was way off on my peak pressure number (either I was remembering another plant or just plain braindead). The final safety analysis report shows a peak pressure of 41.5 psig. No number is given for peak temperature, only the statement that it occurs after...

Nuclear Power: Cons of nuclear power, underground storage facility, yucca mountains

underground storage facility, yucca mountains, cons of nuclear power: There are none! Just kidding, like any source of energy there are advantages and disadvantages. The major disadvantage has been created by our government..what to do with the used fuel. It is extremely radioactive and will be deadly for hundreds of thousands...

Nuclear Power: core material, core material, power plants

core material, power plants, reactors: I haven t been able to find much specific information on the fuel bundles planned for the new generation of power plants, but what I have found indicates that most still use Zircalloy, although some apparently use stainless steel. Sorry that I can t find...

Nuclear Power: cost for 5 years, college application essay, nuclear power plant

college application essay, nuclear power plant, mid 80s: First, you need to understand that this is really outside my area of expertise. I ll give you my best guess, but that s all it is. The cost of the Millstone 3 plant, which when operational in the mid 80s (and was one of the last plants to startup in the...

Nuclear Power: Dear Mr. Kadiroglu:I believe..., nuclear power plants, fission fragments

nuclear power plants, fission fragments, national regulatory body: Hi Mr. Pierson, No so. Half life is a measure of how fast a radioactive material decays. When a radiaoactive material decays it emits various particles with different energies. For example, Radium 226 decays by emitting 4.782MeV alpha particles with a half...

Nuclear Power: Debate, safeguards systems, american nuclear society

safeguards systems, american nuclear society, greenhouse gases: I d be glad to help. On the Pro side, nuclear power doesn t contribute to global warming. It emits no greenhouse gases or other pollutants. It doesn t use fossil fuels, which are limited. A small plant can produce a lot of electrical power. The plants...

Nuclear Power: Debate, time in turkey, rebuttals

time in turkey, rebuttals, wonders of the world: Dear Jordan, I am presently in a small summer resort called Bodrum (Halicarnassus, home of one of the wonders of the world, Mossellium) in Turkey. The computer I use is at least ten years old. I would love to help you but you have to wait about a week when...

Nuclear Power: Drawbacks, nuclear plants, public perception

nuclear plants, public perception, nuclear capacity: Sadly, that is completely false. Plants are run at their rated power, which is what their safety analysis is based on. They can safely operate at higher powers, but need to get a new license from the US Nuclear Regulatory Commission if they choose to do so....

Nuclear Power: design, fast breeder reactor, fast reactor

fast breeder reactor, fast reactor, plutonium 238: A fast breeder reactor is designed like any other reactor, except that it uses a liquid metal, usually sodium, as a coolant and moderator. A normal reactor uses water as a coolant/moderator. The moderator not only moves the heat from the reactor core to...

Nuclear Power: dirty bomb, arson investigator, suspense novels

arson investigator, suspense novels, dirty bomb: First, I need to apologize for taking so long to answer. I was on vacation and forgot to update my profile here. My expertise is in nuclear power, not nuclear weapons. However, freezing won t stop a nuclear reaction. The CO2 might stop the battery since...

Nuclear Power: I don't know if this is your expertise but..., steam cycle, nuclear accidents

steam cycle, nuclear accidents, coal gas: Unless there s an accident, the only negative impact is the heat released and the creation of radioactive waste. Any steam-cycle power plant, whether coal, gas, or nuclear powered, needs a source of cooling water. This is used to condense the steam that...

Nuclear Power: Economics of construction and decommisioning nuclear power plant, millstone unit, nuclear power plant

millstone unit, nuclear power plant, harris plant: Additional information: I ve looked on our intranet and internet sites and haven t found where they breakout the operational costs, so I don t know the cost of disposal. I d suggest www.nrc.gov and www.epri.com for more information. Sorry I couldn t help...

Nuclear Power: Equipment for Nuclear Power Plants, nuclear power plants, american nuclear society

nuclear power plants, american nuclear society, water temperatures: Dear Mike, Being an academician I am not good in the commerce of nuclear components. Nevertheless, I can give you an idea about them. The temperatures one encounters in a reactor is around 300-340C water temperatures and lower steam temperatures. The maximum...

Nuclear Power: energy in vs. energy out, hacettepe edu tr, fuel element

hacettepe edu tr, fuel element, burnup: Whoops, that is a good question that I have never thouhgt of. I do not have the numbers but I can guide you to helpful sites. Try: know_nukes@yahoogroups.com and put your question there .I am sure there are a lot of very experienced people from the nuclear...

Nuclear Power: enviormental hazardous, yucca mountains, grade 12 chemistry

yucca mountains, grade 12 chemistry, water reactors: Yes. Burning coal releases toxic gases to the atmosphere. Antipollution devices like scrubbers can remove much, but not all of these gases. Nuclear plants, particularly Pressurized Water Reactors (PWRs) don t releaase anything to the environment. The...

Nuclear Power: Fusion, fusion power plant, fusion and fission

fusion power plant, fusion and fission, what is the difference between fusion and fission: Hi Paul! Thanks for visiting allexperts. Let s get right to your questions... 1. What is your educational background and job title? Reactor System Engineer, United States Nuclear Regulatory Commission. I have a Ph.D. in Nuclear Engineering from Oregon...

Nuclear Power: AP1000, reactor coolant, coolant pumps

Nuclear Power: AP1000, reactor coolant, coolant pumps, steam generators

Nuclear Power: More advaned pros and cons of using nuclear power stations, chernoybl, psycological diseases

Nuclear Power: More advaned pros and cons of using nuclear power stations, chernoybl, psycological diseases, power generators

Nuclear Power: Chernobyl accident, rbmk reactors, smolensk

Nuclear Power: Chernobyl accident, rbmk reactors, smolensk, design changes

Nuclear Power: Cons of nuclear power, freak accidents, dangerous chemicals

Nuclear Power: Cons of nuclear power, freak accidents, dangerous chemicals, target

Nuclear Power: Equipment for Nuclear Power Plants, nuclear power plant, commercial nuclear power

Nuclear Power: Equipment for Nuclear Power Plants, nuclear power plant, commercial nuclear power, fossil power

Nuclear Power: Navy nuke, 6am, section 1

Nuclear Power: Navy nuke, 6am, section 1, extreme attitude

Nuclear Power: Nuclear and Chemical Reactions, nuclear reaction, chemical reactions

Nuclear Power: Nuclear and Chemical Reactions, nuclear reaction, chemical reactions, absorption

Nuclear Power: Nuclear Engineering Security Clearance, obtaining a security clearance, illicit drugs

Nuclear Power: Nuclear Engineering Security Clearance, obtaining a security clearance, illicit drugs, financial situation

Nuclear Power: Nuclear Power Plants, graphite material, harmful radiation

Nuclear Power: Nuclear Power Plants, graphite material, harmful radiation, nuclear reactors

Nuclear Power: Nuclear Power vs. Coal burning, nuclear power, missiles

Nuclear Power: Nuclear Power vs. Coal burning, nuclear power, missiles

Nuclear Power: nuclear power plants, nuclear power plants, solid wastes

Nuclear Power: nuclear power plants, nuclear power plants, solid wastes, fossil fuels

Nuclear Power: nuclear power plants, welter, nuclear energy

Nuclear Power: nuclear power plants, welter, nuclear energy, pollution

Nuclear Power: Pros and Cons of Nuclear Power, nuclear power technology, green energy

Nuclear Power: Pros and Cons of Nuclear Power, nuclear power technology, green energy, green house gases

Nuclear Power: Stop Using Nuclear Power!, source of energy, clean energy

Nuclear Power: Stop Using Nuclear Power!, source of energy, clean energy, nuclear waste

Nuclear Power: fast breeder reactor, fast breeder reactor, deuterium heavy water

fast breeder reactor, deuterium heavy water, thermal reactors: Hi Kunu, I will answer your two questions in this reply. When neutrons are born from fission reaction they have various energies. In other words they have a distribution of energies what we call as the fission spectrum. This spectrum peaks around 1 MeV....

Nuclear Power: Gen IV and Hydrogen Economy, advanced gas cooled reactor, hydrogen economy

advanced gas cooled reactor, hydrogen economy, american nuclear society: Hi! Thanks for the question. This is an interesting one. First let me direct you to the American Nuclear Society s web site on Hydrogen (http://www.ans.org/pi/matters/hydrogen/). I wrote their position statement #60 on nuclear power and hydrogen and so...

Nuclear Power: The general cost and saftey of a plant, nuclear energy institute, nuclear power plants

nuclear energy institute, nuclear power plants, progress energy carolinas: I can t answer most parts of this question, but you should be able to get that information from any number of utility company public relations (Duke Energy, Progress Energy Carolinas, Progress Energy Florida, Florida Power & Light, etc..) You can also check...

Nuclear Power: Alpha/Beta Decay, beta decay, beta particle

beta decay, beta particle, gamma source: Hi Simon, I am back at home and ready to answer your question. I do not know how much physics you know. If my answer is too complicated let me know. When a particle gets into a nucleus, (acutally it does not get into it but gets into the field of...

Nuclear Power: High Level Waste Disposal, nuclear power plants, nuclear power plant

nuclear power plants, nuclear power plant, thermal power plants: Hello, Before answering your question let me state few facts about the cost of electricity production. The cost of electricity production can be divided into three groups. The capital cost part, which is rather large for nuclear and hydraulic power, Operation...

Nuclear Power: HTGR, sun and the sea, uranium enrichment

sun and the sea, uranium enrichment, fuel enrichment: Hi, Sorry for the delay in answering your question. I was away from home and could not get hold of an Internet connection for few days. people in Turkey enjoy sun and the sea more than Internet during the summer time. Your question has a small error...

Nuclear Power: Hydro testing of Reactor Vessels, commercial nuclear plants, overpressure protection

commercial nuclear plants, overpressure protection, asme code: A follow-up to this answer. ASME code requires a passive mechanical device and will not allow a digitally controlled relief valve as the primary overpressure protection. However, a digitally controlled device CAN be used in addition to the mechanical release....

Nuclear Power: hello , i want to know, nuclear power plants, google search

nuclear power plants, google search, framatech: Please see: http://www.nuclear.gov/ http://www.nrc.gov/ http://www.framatech.com/home.htm http://www.gepower.com/businesses/ge_nuclear/en/index.htm http://www.aecl.ca/ http://www.westinghousenuclear.com/ http://www.pbmr.com and do a google search...

Nuclear Power: hi i want to know about worldwide..., nuclear power plants, nuclear power plant

nuclear power plants, nuclear power plant, cost of electricity: Your question about the impact of nuclear power on the worldwide economic, social,environmental and political effect is a rather open ended one. It will take many pages to answer this question. I will be brief and try to answer your question. Nuclear power...

Nuclear Power: THe hisory of nuclear power, introduction to nuclear engineering, theodore rockwell

introduction to nuclear engineering, theodore rockwell, history of nuclear power: I would recommend two books: Richard Rhodes, The Making of the Atomic Bomb QC773.R46 1986 Theodore Rockwell, The Rickover Effect V63.R54R63 1995 The first book is about the early day of nuclear energy and the making of the bomb. The second book...

Nuclear Power: hydrogen atom, hydrogen atom, hydrogen gas

hydrogen atom, hydrogen gas, fire etc: Nice to hear from you. If by explosion, you mean explosion of hydrogen gas by fire etc., then the answer is NO. Explosion is a physical thing; it has nothing to do with the internal structure of matter. Moreover, hydrogen atom can t split. It has only...

Nuclear Power: Incident analysis, incident analysis, electrical circuit

incident analysis, electrical circuit, nuke: Mike, Sorry, I must have missed that lecture. I think that my class got a different version of the incident lecture. So with that said: I can not help in finding a copy of that lecture. You might try searching for chain of events or incidents...

Nuclear Power: getting information, heat convection, natural circulation

heat convection, natural circulation, heat density: Natural circulation cooling is a method for removing core heat sink capacity without the use of pumps. Bouyancy and heat convection drive a natural circultion flow. For instance, if you have a sqaure test loop filled with water, and could heat the bottom...

Nuclear Power: Merge of a reactor core, radioactive fission products, fuel pellets

radioactive fission products, fuel pellets, decay heat: Bear in mind that several things have to happen before a core meltdown would occur. There are multiple and independent sources of cooling water for the core, with different injection paths. All of these sources of cooling would have to interrupted for quite...

Nuclear Power: Modern coal fired generation v nuclear, work stoppage, nuclear power stations

work stoppage, nuclear power stations, nuclear reactor: There are a couple of reasons that nuclear plants have taken so long to build (I don t know the reasons behind Finland s, but they re probably the same). First, nuclear plants have each been unique with many differences between the plants. This means that...

Nuclear Power: Navy Nuclear Power School, nuclear power school, nnps

nuclear power school, nnps, level math: Justin, Yes there are jobs outside the Navy. Take a look for yourself at hotjobs.com. Perform a search for Nuclear or operations. With the rumour that more nuclear plants are in the works it might become a more lucrative job in the future. Good luck...

Nuclear Power: Navy nuke, navy experience, old farts

navy experience, old farts, grunt work: Matt, Yes the Nuclear field is still stagnant. It should be picking up in the next 4 or 5 years with retirements of all the old farts from the industry. As for life on board ship..... Well, back in the 80 s when I was aboard a ship it was like locking...

Nuclear Power: Navy, nuclear power school, navy life

nuclear power school, navy life, nnps: Justin, If I was you I would go to the University and not even think about the Navy. Really if you have the money in place and can go to College do it. I was in the same place as you when I joined. I was in my third year of a Community college (goofed...

Nuclear Power: NUCLEAR FUEL, fast breeder reactor, oxide fuel

fast breeder reactor, oxide fuel, plutonium: Hi Kanu, Please do a Wikipedia search for fast reactors. The fuel for a fast breeder reactor is mixed oxide fuel with 20% Pu. I did not understand the last part of your question but if you want to know if one can buy plutonium the answer is NO! If your...

Nuclear Power: NUCLEAR FUEL, fast breeder reactors, fast breeder reactor

fast breeder reactors, fast breeder reactor, fast reactor: Hi Kanu, Yes Pu is a good nuclear fuel but difficult to purchase. Pu229 is a better fuel for fast breeder reactors since it produces many fission neutrons be absorbed neutron. Plutonium is formed in every reactor that has U238 in it whether it is thermal...

Nuclear Power: NUCLEAR, fission reaction, radioactive isotopes

fission reaction, radioactive isotopes, natural uranium: Hi Kanu, Looks like you are becoming a fan of nuclear power. :) First enrichment. In order to have a continuing chain reaction we need to have a fissioning nuclei, a moderating medium to slowdown the fast fission neutrons to thermal energies so that...

Nuclear Power: Nuclear Ages and future Jobs, local power company, glasgow student

local power company, glasgow student, nuclear power industry: I can only answer this from my point of view in the nuclear power industry. You ll need to look elsewhere for other industries. The American nuclear industry has recently announced plans to build several new reactors. Since the last new plant went online...

Nuclear Power: Nuclear Ages and future Jobs, glasgow student, question concerning technology

glasgow student, question concerning technology, nuclear age: Dear Shirley, At this age of Internet one is bound to make errors. Sorry but I live in Turkey and I do not know the job market in California or in the States. Being a retired prof. of nuclear engineering I am not very much interested in the job market overseas....

Nuclear Power: Nuclear Arms Construction, nuclear power reactors, production reactors

nuclear power reactors, production reactors, nuclear reactors: Hi Manuel, I got hold of a computer and let me try to answer your questions. 1- No! the construction of nuclear weapons have not stopped. USA is very active in designing and producing new weapons. 2- Nuclear weapons are actually the war head on top...

Nuclear Power: Nuclear and Chemical Reactions, electron orbits, nucleus of an atom

electron orbits, nucleus of an atom, electron shells: Chemical reactions are the result of rearrangement of electrons in the orbits of an atom. Nuclear reactions are generated within the nucleus of an atom. If you burn coal you join an atom of carbon from the coal with two atoms of oxygen from the air. What accually...

Nuclear Power: Nuclear Destruction, recommended paper, radioactive environment

recommended paper, radioactive environment, nuclear destruction: Maybe some new form of life which we dont know about yet can exist in that kind of radioactive environment but the known forms (human beings, animals) can t. Gases and atoms would still be there although some of them would become radioative themselves...

Nuclear Power: Nuclear Engineering Security Clearance, nuclear engineering department, utah state university

nuclear engineering department, utah state university, nuclear engineer: Dear Justin, I do not think I can answer your question. I am a citizen of the Republic of Turkey and I have no idea about the US system. I do not think graduate schools look for criminal records but rather look for good academic records. Why don t you ask...

Nuclear Power: Nuclear Equation for Radium-226, irving kaplan, radium 226

irving kaplan, radium 226, mail format: I do not know how much you know about differential equations and with my very limited ability to write equations in this e-mail format, I will try to help you. Ra226 has a half-life of 1620 years. Halflive=0.693/Lambda where Lambda is the decay constant...

Nuclear Power: Nuclear energy, fossil fuel reserves, electron volts

fossil fuel reserves, electron volts, natural gas reserves: Hi tumtum, I did answer your question few hours after I received it but it seems it has never reached to you. Sorry about that. You are right, 1 kg of U is approximately 1/20th of a liter of water. As for coal it is very difficult to give a density....

Nuclear Power: Nuclear Fuel Reserves, light water reactors, fusion reactors

light water reactors, fusion reactors, breeder reactors: Hi, I am away from home and that is why I am late in answering your question. One has to consider the price factor for the reserves of primary energy resources when deciding about their depletion time. Off shore petroleum was uneconomical sometime ago....

Nuclear Power: Nuclear fusion, fission reactors, fusion reactors

fission reactors, fusion reactors, fusion reactor: Well...I m not really on expert on fusion, but I think I can answer your questions. 1. Nuclear fusion is still in the research and development stage. This means that new technologies and techniques are still being developed. It s hard to put a price on...

Nuclear Power: Nuclear fusion, foremost research center, cadarache france

foremost research center, cadarache france, h bombs: Sorry for the delay, but I wasn t exactly sure how to answer this question. So I asked one of my colleagues. Here s his response: As a scientific question, maybe. As a practical engineering problem...extremely difficult and $$$. How are these caves...

Nuclear Power: Nuclear fusion, helium nuclei, hydrogen nuclei

helium nuclei, hydrogen nuclei, hydrogen nucleus: Nuclear fusion is just the opposite nuclear reaction of nucear fission, which is the source of nuclear power at present day. Some atomic nuclei are not stable and they tend to change to other nuclear configurations. Heavy nuclei tend to reduce their masses...

Nuclear Power: Nuclear meltdown, pressurized water reactor, neutron absorber

pressurized water reactor, neutron absorber, neutron absorbers: Dear Eiko Lajcsak, Glad to help you but it seems there is a small misunderstanding of nuclear technology in your question. So if you do not mine I would like to correct it first and then answer your question. Chain reaction is the spliting of U235 nucleus...

Nuclear Power: Nuclear Physics, helium nuclei, fission fusion

helium nuclei, fission fusion, nucleus of an atom: Fission is the breakup of a large atom (mostly Uranium) into two smaller ones. Neutrons and energy are released in this process. Fusion is the combining os two smallet atoms (Dueterium, Tritium, etc.). A larger atom like Helium results and energy is released....

Nuclear Power: Nuclear Power, cons of nuclear energy, pros and cons of nuclear energy

cons of nuclear energy, pros and cons of nuclear energy, storage of nuclear waste: Hi Sierra, I have been answering this question over and over so you will be the last kid I will do it. Your question involves everything under the sun. I recommend that you check Wikipedia, Department of Energy web sites. Also Google will give you tons...

Nuclear Power: Nuclear Power generation, nuclear power generation, cost of natural gas

nuclear power generation, cost of natural gas, nuclear plants: James, The reason that there are not more nuclear plants in the US is public opinion. Back in the 70 s and early 80 s the US was in a fuel crunch and Nuclear power for generation was the way the public wanted to go. They seen a cheap way to generate...

Nuclear Power: Nuclear Power Plants, nuclear power sources, alternate energy sources

nuclear power sources, alternate energy sources, nuclear power plants: I think so. At this point, alternate energy sources can t meet the demand for power. Wind power isn t viable in all parts of the country and has it s own cons (takes a lot of room per power generated, impact on birds, etc.), hydro-electric is also limited...

Nuclear Power: Nuclear Power Plants, nuclear power plants, nuclear energy agency

nuclear power plants, nuclear energy agency, oecd nuclear energy: True nothing is perfect even the nuclear technology. :-) I do not know how much you know about nuclear energy, that is why I asked you to read the sites I mentioned to you. As you might know, nuclear reactors were first build for naval vessels. In ships...

Nuclear Power: Nuclear Power vs. Coal burning, nuclear power plants, nuclear power plant

nuclear power plants, nuclear power plant, nitrogen oxides: Hi Josie, It looks like I am helping your class for a homework. I sent this answer to Amy Cawthorn, whom I suspect is one of your classmates, and you may use it too. Or better work with your friend... Hi, Since I do not know how much you know about...

Nuclear Power: Nuclear Power, uranium fission, chernobyl nuclear disaster

uranium fission, chernobyl nuclear disaster, nuclear reactor: Yes it is true. Both accidents are similar in nature, mainly the core of the reactor melted, but there was no harm done to anybody during the Three Mile Island accident. Nobody got radiation exceeding the allowable limits. Chernobyl accident is a different...

Nuclear Power: Nuclear plants, nuclear power plants, nuclear power plant

nuclear power plants, nuclear power plant, inexpensive electricity: Hi, Like all machines nuclear power plants have two lives. One is the book life the other is the real operational life. Book life is used for economical analysis. We assume that in 20 or 30 years the amount of money paid for the power plant will be amortized...

Nuclear Power: Nuclear power, wind power plants, large diesel engines

wind power plants, large diesel engines, thermal efficiencies: Hi Devin, I am having a bit of a problem in understanding what you mean by graph of effectiveness of all energy sources. Do you want to compare the thermal efficiencies of various forms of electricity production methods that use various energy sources?...

Nuclear Power: Nuclear Waste Storage, light water reactor, nuclear waste technology

light water reactor, nuclear waste technology, nuclear waste storage: Dear Mr. Eric Englund, To explain the nuclear waste technology please let me say few words about the nuclear fuel. Nuclear fuel is made of UO2, an oxide of uranium. It is put into small cyclinderical pellets 1cm x 1cm. Then these pellets are put into zirkonium...

Nuclear Power: Nuclear Waste, nuclear waste disposal, many lifetimes

nuclear waste disposal, many lifetimes, finite probability: Dear Michael, Sorry for the delay, I was upgrading my computer! The nuclear waste is radioactive rather than toxic. Toxic waste, like cadmium from the thrown away batteries, will be toxic at all times, but the activity of nuclear waste will decay as...

Nuclear Power: Nuclear waste, nuclear power plant, gallon barrel

nuclear power plant, gallon barrel, nuclear waste: The volume of spent fuel discharged from a nuclear power plant in one year depends on the power capacity of the plant. It should fit in a normal sized room. This waste is very radioactive and has to be stored under water for a few years. After that it can...

Nuclear Power: Nuclear, nuclear power plants, nuclear power plant

nuclear power plants, nuclear power plant, fuel pools: Dear Karen, First I like to mention that I live in Turkey and I am not a US citizen. So my comment related to matters pertinent to US is just a foreigners ideas. What one means to go nuclear ? Does it include all the fuel cycle and design and construction...

Nuclear Power: necular energy, release pollutants, coolant water

release pollutants, coolant water, steam generator: The cleaner sources such as wind power and solar power don t produce enough electricity to meet our needs. Nuclear energy doesn t release pollutants like coal and gas plants. The radioactive wastes are manageable and can be safely stored. Nuclear power...

Nuclear Power: need t ask, nuclear power industry, nuclear station

nuclear power industry, nuclear station, nuclear plant: I m not sure what you are asking. If you want to know how to get a job in the nuclear power industry, you ll need to contact one of the utility companies in your area that run a nuclear plant. If you want to know how you can do business with a nuclear...

Nuclear Power: Is neutron-neutron fusion easier to facilitate than proton-proton fusion?, neutron beams, cubic centimeter

neutron beams, cubic centimeter, nuclear reactor: Hi Green, I must admit I am bit baffled with your question. I never heard of neutron neutron fusion. One can obtain neutrons from some nuclear reactions but the best and most strong source of neutrons is the nuclear reactor. The amount of neutrons produced...

Nuclear Power: Is neutron-neutron fusion easier to facilitate than proton-proton fusion?, neutron beams, electron neutrino

neutron beams, electron neutrino, proton electron: Easier to fuse, yes, but the dineutron is unbound. Unless you could somehow get one of them to decay into a proton-electron-neutrino at exactly the femtosecond they collide and feel each other s strong nuclear force, neutron-neutron fusion does not actually...

Nuclear Power: Is neutron-neutron fusion easier to facilitate than proton-proton fusion?, neutron beams, nuclear fusion

neutron beams, nuclear fusion, viable choice: Although neutron-neutron fusion is theoretically possible, it produces considerably less energy than proton-proton fusion. Although easier to do, you don t get nearly as much gain or power out. Thus, almost all research has been focused on proton-proton...

Nuclear Power: nnps, navy college fund, nuclear power plants

navy college fund, nuclear power plants, new nuclear power plants: Mo, The NNP program is one tough program. DO not take it lightly. It is like doing a 4 year college program in 6 months. Packed with fun and studying all the time. I had a background in math and physics and spent 3 years in college before I joined. So...

Nuclear Power: nuclear energy, canadian nuclear society, grafton ontario

canadian nuclear society, grafton ontario, american nuclear society: Wow! Excellent initiative! Here s a link to the American Nuclear Society Communication Toolkit (http://www.ans.org/pi/pros/member/comkit/). Although it is geared toward the US, it should work fine in Canada :) Simple ways to get involved are to see if there...

Nuclear Power: nuclear fission, nuclear fission reactor, fission chain reaction

nuclear fission reactor, fission chain reaction, fission reaction: HiCory edds, This looks like a homework question, is it? When an uranium 235 nucleus captures a slow moving neutron it becomes very unstable and splits into two intermediate size nuclie, this process is called fission, and gives out two to three neutrons....

Nuclear Power: nuclear fusion comparison, hydrogen bomb, nuclear fusion

hydrogen bomb, nuclear fusion, tritium: Hi, I am sorry but I am away from home for a while. I would like to answer your question by saying in a bomb deterium - tritium is used as the fuel but in the sun it is mainly hydrogen. If you get in touch with me in a few days I could help you more. ...

Nuclear Power: nuclear meltdown, nuclear fission reaction, heat transfer medium

nuclear fission reaction, heat transfer medium, fission fragments: Nuclear meltdown is actually the core meltdown accident of a nuclear reactor. First let me explain few basics: Nuclear fuel is made of uranium oxide (UO2), which is a very bad heat transfer media just like porcelain we used as tableware. UO2 is stable...

Nuclear Power: nuclear power, construction duration, nuclear reactors

construction duration, nuclear reactors, machinery construction: Hi, One can not say that nuclear power is profitable than any source of power. Nevertheless, producing electricity with nuclear energy is definitely an economical choice. First let us see how we decide which power generation is cheaper. In order to generate...

Nuclear Power: nuclear power, boiling water reactor, pressurized water reactor

boiling water reactor, pressurized water reactor, nuclear power plants: Conventional nuclear power plants rely on nuclear fission to provide power. Uranium atoms are split in the core of the reactor, which is covered with high pressure water in a large steel vessel with pumps. The hot water from the core is pumped to a steam generator...

Nuclear Power: nuclear power, nuclear power reactors, nuclear power plants

nuclear power reactors, nuclear power plants, iaea: As of 2004, nuclear power provided 6.5% of the world s energy and 15.7% of the world s electricity, with the U.S., France, and Japan together accounting for 57% of all nuclear generated electricity. As of 2007, the IAEA reported there are 439 nuclear power...

Nuclear Power: nuclear power in america, pebble bed modular reactor, uranium thorium

pebble bed modular reactor, uranium thorium, pebble bed modular reactor pbmr: Sure by all means. Being a foreigner I have no say in the politics of USA but having spent some time in the States and got my education there I feel that I do have some, though very minor, right to say what I think about the States. USA is the hometown...

Nuclear Power: nuclear power in iran, reactor type, electricity production

reactor type, electricity production, product material: Well, my personal opinion any is that country capable of maintaining safe nuclear power for electricity production should be able to do so. However, depending on the reactor type built, the by product material can be used to make nuclear weapons. I think...

Nuclear Power: nuclear power plants, nuclear power plants, greenhouse gases

nuclear power plants, greenhouse gases, fossil fuel: Nuclear power plants produce no greenhouse gases as fossil fuel ones do. But at the same time nuclear planst produce readioactive waste which remeins radioactive for hundreds of thousands of years and has to be isolated from the environment in some way...

Nuclear Power: nuclear power plants, nuclear power plants, nuclear power plant

nuclear power plants, nuclear power plant, nuclear electricity: Hi Hula, Seems like another debate or homework question! What do you mean by startling? No plant has startling facts. They are just plants that produce electricity. An electricity production plants is valued by its overall generation cost. That...

Nuclear Power: nuclear power plants, nuclear power plants, greenhouse gasses

nuclear power plants, greenhouse gasses, nuclear reactors: Interesting question. Here are some less known facts about nuclear power in the US: -There are 104 nuclear power plants operating in the US, providing over 20% of our electrical power. -These power plants have been operating for over 30 years. -Over these...

Nuclear Power: nuclear power plants, nuclear power plants, nuclear regulatory commission

nuclear power plants, nuclear regulatory commission, nuclear power plant: The 1975 WASH-1400 study conducted by the US Nuclear Regulatory Commission (http://en.wikipedia.org/wiki/WASH-1400) placed risk of being killed by a nuclear power plant accident on the same order of magnitude as being killed by a meteorite. This is pretty...

Nuclear Power: nuclear power plants, westinghouse ap1000, nuclear power plants

westinghouse ap1000, nuclear power plants, nuclear power plant: Sorry for the delay, but I was out of town. The only difference between the Westinghouse AP1000 and any other nuclear plant is the reactor design, so the site size would be the same. That being said, the site sizes vary greatly only because of the size...

Nuclear Power: nuclear power project, nuclear power plants, nuclear power project

nuclear power plants, nuclear power project, reactor operations: There are no false facts, however there are some false nonfacts. One: a nuclear plant can blow up like a nuclear bomb. This is impossible. A nuclear bomb needs to be built in a sphere and an external explosive device that blows the sphere into a small...

Nuclear Power: nuclear power and why it should or shouldn't be banned, underground storage facility, yucca mountains

underground storage facility, yucca mountains, radioactive contaminants: The used fuel from a nuclear reactor is extremely radioactive and will remain dangerous for tens of thousands of years. Direct exposure to used fuel would be fatal and if the radioactive material were to somehow get into the environment, it could cause great...

Nuclear Power: nuclear power in space, radiator system, russian satellite

radiator system, russian satellite, space ships: Yes, as a matter of fact there were (and still may be) a number of satellites that used small reactors as a power source. The US military called them SNAPS for Space Nuclear Auxiliary Power Systems. Several years ago there was a scare because a Russian...

Nuclear Power: nuclear power, advantages of nuclear power, coal plants

advantages of nuclear power, coal plants, splitting the atom: In my personal opinion, comparing the advantages and disadvantage of different energy system isn t easy. Why? Because which yard stick should we use? Environmental? Economic? Social? Safety? Capacity? Political? I believe that the US should rely on a mix...

Nuclear Power: nuclear reactions, hydrogen bomb, fission reaction

hydrogen bomb, fission reaction, chemical explosion: Hi Helina, It looks like I will be solving your homework questions and you will be getting the good grades! Want some of those grades for myself.... 1. An atomic bomb is a supercritical nuclear assambly, meaning that if fission reaction starts it will...

Nuclear Power: nuclear reactor, fast breeder reactor, fission reaction

fast breeder reactor, fission reaction, thermal reactors: Hi Nitin, Neutrons react with nuclei, and the amount of interaction is proportional to the number of neutrons present there and a property of the target nucleus. This property is known as the cross section of the nucleus. Physically you can think of a...

Nuclear Power: nuclear reactor, parts of nuclear reactor, nuclear engineer

parts of nuclear reactor, nuclear engineer, colored photos: Hi Nitin, Either I will make you a nuclear engineer or help you get good grades for your homework. I recommend you search the Wikipedia (http://en.wikipedia.org/wiki/Nuclear_reactor )for better information with colored photos. Your question is a rather...

Nuclear Power: nuclear reactor, nuclear power plants, nuclear power plant

nuclear power plants, nuclear power plant, reactor vessel: Let me provide a little background information before I address your answer. A nuclear reactor can be used to make electricity. Nuclear power plants have a core of radioactive material that is submerged in water. When the right conditions occur the core can...

Nuclear Power: nuclear reactors, what is a nuclear reactor, fission reaction

what is a nuclear reactor, fission reaction, nuclear power plant: Hi Sally, If this a homework question I recommend that you do a Google search (1.15M entries) and a Wikipedia search where you will find better information with pictures and drawings. A nuclear reactor is machine that generates neutrons using nuclear...

Nuclear Power: nuclear safety, nuclear powerplant, reinforcement bar

nuclear powerplant, reinforcement bar, earthquake proof: Although nothing can ever be 100% earthquake proof, nuclear plants are built to withstand earthquakes, hurricanes, tornados, and other natural disasters. If a large enough earthquake did happen that the plant was damaged, we have several backup systems that...

Nuclear Power: nuclear science, plasma state, fusion reactions

plasma state, fusion reactions, iter project: You are corrrect to assume that millions of degrees temperature is needed to start fusion reactions. At such temperatures matter is not only in gaseous form it is in Plasma state. That is in ionized state just like the inside of the Sun or stars. To keep plasma...

Nuclear Power: nuclear war effects, surface water runoff, slow neutrons

surface water runoff, slow neutrons, groundwater studies: Dear Tom, Dr MV Ramana, currently at the Center for International Studies at the Massachusetts Institute of Technology [MIT], Cambridge, USA, has estimated the effects of a nuclear bomb attack on a South Asian city in a paper titled Bombing Bombay? Effects...

Nuclear Power: nuclear weapons recycling, pebble bed modular reactor, thermal reactors

pebble bed modular reactor, thermal reactors, commercial reactors: Dear Jay M., Your subject and your question are two different things. Recycling nuclear weapons has nothing to do with recycling waste. So I will try to answer your question the way I understood it. Nuclear weapons are made of mainly Plutonium 239, which...

Nuclear Power: Going nuclear..., nuclear power plants, united states energy

nuclear power plants, united states energy, production scales: I m thinking that you are asking me how many plants it would take to power all of the US with nuclear power? Well, my personal opinion is that we shouldn t limit our selves to just one type of power generation, but maintain an effective mix of clean coal,...

Nuclear Power: nucler power, exothermic chemical reaction, nucler power

exothermic chemical reaction, nucler power, nuclear bombs: In ordinary bombs, there is no nuclear reaction. There is only an exothermic chemical reaction. In nuclear bombs, energy is released as a result of nuclear reaction. Usually an atom of Uranium or Plutonium splits into fragments and energy is produced...

Nuclear Power: Ph.D. Thesis, reactor physics, thermal hydraulics

reactor physics, thermal hydraulics, instability analysis: Wow, you need a topic for a PhD. I have a couple of friends in the NE department at Florida. I think they ve all graduated though. I met them at a conference in DC. Well, anyway, back to the topic. I m two months away from my PhD and am just finishing...

Nuclear Power: POWER, energy scales, carbon atom

energy scales, carbon atom, engry: If you burn fossil fuels you change the electronic structure of the molecules, in other words it is chemistry. The energy scales are few eV. If a U325 fissions you get around 200MeV. If you compare a carbon atom burning and forming a CO2 molecule and fissioning...

Nuclear Power: Pool entrainment setup, reactor assembly, javalin

reactor assembly, javalin, core barrel: First I would consider the relatistic effects of pool entrainment in high gravitational fields. Consider two galaxies traveling at 10000000 m/s toward each other. Then buy all the books on javalin throwing you can find. Stand on your hand. Play the kazoo....

Nuclear Power: Power Plant, junior deacon, radiation dose

junior deacon, radiation dose, doing laundry: From the details you have given, it is very likely that you will not receive any significant radiation dose. So there is no reason why you would turn infertile. There is nothing to worry about. You can accept and continue this job as long as you desire so...

Nuclear Power: Private or Public, fossil fuel plants, nuclear plants

fossil fuel plants, nuclear plants, baby boomers: The nuclear plants in the U.S. are owned by public utilities. These are publicly traded, private industries. A few large companies such as Excelon and Dominion have been purchasing many of the nuclear plants from the local local utilities, but several are...

Nuclear Power: Pros and Cons of Nuclear Power, pros and cons of nuclear power, cons of nuclear power

pros and cons of nuclear power, cons of nuclear power, nuclear power plant: I can give you pros for nuclear power. It is the cheapest and most clean way of producing electicity. It is a green energy that is it does not polute the atmosphere. No greenhouse gases, no posionous elements like Cd, Pb, etc in ash. No release of radioactive...

Nuclear Power: PWR control, control rods, kulick

control rods, kulick, control groups: Ron, Power rating of the reactor, function and other requirements would determine exactly how the core was controlled. Most cores over about .5MW will be divided into control zones in order to flatten the flux distribution or shape it laterally and vertically...

Nuclear Power: pebble bed reactors, pebble bed reactors, commercial nuclear plants

pebble bed reactors, commercial nuclear plants, chemical carcinogens: I don t know how long the design has been around, I first heard about it about 10 years ago. I haven t been able to find anything referencing anything much earlier. Rickover promised that nuclear ships would be able to go 10 years between refueling and he...

Nuclear Power: power plant technology improvements, hydro electric plants, chernoble disaster

hydro electric plants, chernoble disaster, power plant technology: My days as a twelve year old are long gone - sigh! There are several gases collected, but the predominant ones are Ar-41 (1.8 hrs) and Xe-133 (5.3 days). The tanks are vented once a week, I believe, so the Ar-41 will be gone. In another 20 days, the...

Nuclear Power: why are Reactors Round ?, nuclear reactor analysis, molten salt reactor

nuclear reactor analysis, molten salt reactor, reactor cores: Sorry for the delay, I was moving out of town. Reactors are theoretically round, but in real life they are made of rectangular prisms stacked in a cyclinder. Neutrons are generated within the core and they tend to leak out. Generation is dictated by...

Nuclear Power: Reactors, boiling water reactors, light water reactor

boiling water reactors, light water reactor, ge abwr: For each category of reactor, Pressurized Water Reactors (PWRs), Boiling Water Reactors (BWRs), Pebble Bed Module Reactors (PBMRs), Liquid Metal Fast Reactors (LMFRs), there are different generations. Gen I, II, III, III+, and IV Gen I is what you would...

Nuclear Power: radiation, alpha beta gamma, neutron radiation

alpha beta gamma, neutron radiation, uranium thorium: Well...actually, most people don t know, but humans ARE radioactive. You are made up of chemicals, and it should be of no surprise that some of them are radionuclides (e.g., uranium, thorium, potassium 40, radium, etc.), many of which you ingest daily in your...

Nuclear Power: radiation, green house gases, radioactive gases

green house gases, radioactive gases, will find extensive information: Hi Kunu, I have been answering your questions a lot and this will be the last one. Most the radioactive substances that are produced in the reactor is in the fuel. So if one keeps fuel under control during the operation of the reactor and also takes...

Nuclear Power: SAFETY, oversight organizations, emergency shutdown

oversight organizations, emergency shutdown, safe design: There are three primary methods. One, have a good, safe design with redundant safety features (multiple trains of emergency shutdown and cooling systems that are physically separated so that an accident can t take both out at once and with independent power...

Nuclear Power: Stop Using Nuclear Power!, nuclear power plants, renewable energy sources

nuclear power plants, renewable energy sources, nuclear power plant: Hi Dmitriy, I think you are done for. Not even king s horses or king s men could put you back together. :) If you were to argue for stopping the nuclear power you will lose the argunment for sure. All forms of electricity production harm the nature and...

Nuclear Power: science, yucca mountains, coal plants

yucca mountains, coal plants, radioactive decay: Nuclear energy, as practiced in the United States is indeed safe. Every safety device has multiple backups, no one failure and even 2 or 3 failures can keep us from shutting down the reactor, keeping it cool and preventing the release of radioactivity. ...

Nuclear Power: Thermodynamics of a nuclear reactor, boiling water reactor, pressurized water reactor

boiling water reactor, pressurized water reactor, nuclear energy institute: Will MC delta-T and UA delta-T work? Just kidding. Check out The Nuclear Regulatory Commission at http://www.nrc.gov/reactors/pwrs.html for an overview of a Pressurized Water Reactor (the most common type in the US), http://www.nrc.gov/reactors/bwrs.html...

Nuclear Power: Three Mile Island, chernobyl reactor, core meltdown

chernobyl reactor, core meltdown, ghost towns: John, There was a difference between Chernobyl and TMI reactors. The Chernobyl reactor had no containment (a dome like structure) to stop the realease of radioactivity. While TMI reactor had containment. So even in case of complete core meltdown, there...

Nuclear Power: TRANSPORT OF NUCLEAR FUEL, fast breeder reactor, reactor fuel

fast breeder reactor, reactor fuel, thin rods: Fuel is not pumped into a fast breeder reactor. The fuel is a mix of solid uranium and plutonium in capsule form, arranged in thin rods. For more information, go to http://en.wikipedia.org/wiki/Fast_breeder_reactor or http://library.thinkquest.org/CR0213207/Fast%20Breeder-Scott.ht...

Nuclear Power: thermalengineering, lake temperatures, coal oil

lake temperatures, coal oil, manmade lakes: Thermal waste is simply the heat given off by any industrial or manufacturing process. For power plants (coal, oil, nuclear and others), this is the heat that must be removed to turn the steam that drives the turbine-generator back into water. The effects...

Nuclear Power: treatment of nuclear waste, level alpha, nuclear reactor

level alpha, nuclear reactor, medium level: Nuclear waste can be of many types, low level, medium level, high level, alpha bearing waste, spent fuel, reprocessing waste, etc. It s very problematic and so far no proper disposal technique has been found. For details, see http://en.wikipedia.org/wiki/Nuclear_wast...

Nuclear Power: uranium resourses, helium nucleus, deterium

helium nucleus, deterium, nuclear reactors: Please see http://world-nuclear.org/info/info23.htm for a start. From there on you could find more information. Fusion does not need uranium. Fusion is the combination of two deterium nucleus to produce a helium nucleus. Fission is used in nuclear reactors...

Nuclear Power: water temp, nuclear power plant, containment structure

nuclear power plant, containment structure, lake temperature: Actually, it s not a pool; it s a discharge canal heading back to the lake. I can check it from a computer in the same building I work in, so it s no big deal. There are plans in progress to build several new nuclear plants in the US. The need for power...

Nuclear Power: Zeta potential in high speed flow, e mail address, high speed flow

e mail address, high speed flow, nuclear engineering department: As it is known that GE BWRs with jet pumos are considered as old technology. Nowadays GE along with its Japaneese partner builds BWRs with rotary pumps at the bottom circumference of the pressure vessel, which is a followup to Asea Atom design. Even though...

Nudism: boners, semi erections, females

semi erections, females, stomach: It is natural but people I know said as they were naked more often erections happend less often. However resorts discourage erections in public but understand semi- erections if you get a full erections put a towel across your lap people will understand that....

Nudism: nudist family

Nudism: nudist family

Nudism: nudist family, going through puberty, family question

going through puberty, family question, nudist family: It has been a long time I hope things worked out please let me know. If your parents didn t accept my bed situation suggestions. You could sleep on the couch as a last resort or get an Aero Bed (aerobed.com) which is an inflatable mattress or if you want...

Nudism: any private house for nude?, sunchasers travel club, sandy terraces associates

sunchasers travel club, sandy terraces associates, marstons mills ma: Sorry I can t help you there. But I can give you some clubs up there. Framingham C.M.R. Club (T) 46 Gorman Rd Framingham, MA 01702 Hancock Berkshire Vista Resort PO Box 1177 Hancock, MA 01237 413-738-5154 Ludlow Sunchasers Travel Club...

Nudism: Nudism, clothesfree, nudism

clothesfree, nudism, perfect body: One of the main things about nudism is bot accepting the flaws you have. Everybody has flaws nobodies body is perfect and if you go you will see what I mean. You will see if you go that most people have something about their body they don t necessarily like,...

Nudism: feeling free, nudist clubs, google

nudist clubs, google, couples: Well it is kind of hard to tell it is not something people talk about but some people will openly admit it. You can google the Internet for intrest sites and local nudist clubs or something like that. That is probably the best way also if you decide to go...

Nudism: orange county nudist place jobs, nudist place, naturist clubs

nudist place, naturist clubs, google: There are a lot of places to work so you should go online google resorts or naturist clubs in your area go to there website and find the contact information that would be much easier. Sorry I didn t give you exactly what you are looking for, but people there...

Nudism: erection, nudist place, nudest

nudist place, nudest, erection: First of all if you are planning to go to a nudist place you should start by being comfortable naked. Whenever you are a lone or have time try being naked as much as possible. After doing this for a while it shouldn t be arousing then look at nudist pictures...

Nudism: Insecurity

All right well first off you need to be comfortable being naked by yourself. So when you are alone start being naked as much as possible. Don t worry about your weight your wife is not expecting you do have a full six pack or rock hard abs. Like it is with...

Nudism: erections?, pool pond, erection

pool pond, erection: I can t say for sure at all clubs, but at most of them, they won t be offended by an erection as long as you behave appropriately. If people think you re showing off or acting in a sexual way, they ll probably invite you to leave. Just continue doign...

Nudism: erections?, erection, nudist beaches

Nudism: erections?, erection, nudist beaches, beaches resorts

Nudism: nude beaches, nudist camp, aswell

Nudism: nude beaches, nudist camp, aswell, swinger

Nudism: I want to be a naturist., city of corona ca, city of corona

Nudism: I want to be a naturist., city of corona ca, city of corona, sex discrimination

Nudism: Hi...I have been curious..., nudism, erection

nudism, erection, curiosity: Hi, Sean, thanks for writing. First I d suggest that you check out our web site at http://www.takeoffwithus.com. At the bottom of the home page, there is a list of frequently asked questions. Click on a question and it takes you to a new page, each...

Nudism: kids and nudism, body consciousness, nudist place

body consciousness, nudist place, nudist clubs: Hi, Marg, thanks for writing. Many families consider nudity at home to be OK, as long as it seems natural and uncontrived. I ll assume that s true in your home. From there, the next step would probably be to mention to her, sometime in a quiet moment,...

Nudism: nude beaches, sandy terraces associates, cape cod mass

sandy terraces associates, cape cod mass, marstons mills ma: Dear Robb, I just found out about one more thing. You may try to contact or go to Sandy Terraces Associates Family Nudist Campground P.O. Box 98 Marstons Mills, MA 02648 (508)428-9209 This is located in Cape Cod, they have resort, beach, and other...

Nudism: Question??, informative web, unclothed

informative web, unclothed, nudism: Hello, Shae, that is a _very_ broad question. Nudism is the enjoyment of living or recreating without clothing. Most of us can t live like this all the time, because of jobs, etc., but if I had my choice, I would live in a community where it would be...

Nudism: I want to be a naturist., family nudist club, orange county california

family nudist club, orange county california, nudist camps: Hi, each club is different and their rules are too. Most clubs allow singles; some put restrictions on how many. The better clubs have rules and enforce them on behavior, but if any assume that a single would behave poorly, that s their mistake. Same...

Nudism: I want to be a naturist., orange county california, single females

orange county california, single females, nudist camps: Dear Jovi, Thanks for the questions. Those are good questions. Let me answer your questions one by one as you ask. 1. Single females are allowed to go to nudist camp by themselves. However for men, they are allowed to go to nudist camp only if they...

Number Theory: 0.99999999... = 1 (is it true=? If so help me explain this), little faith, math teacher

little faith, math teacher, exact spot: Hello Haruki Sorry for the delayed response, but we were away for a few days and I forgot to log it as a holiday. I think that when you study anything to do with infinity you need to have a little faith. Your statement :0.0000001=0 is not correct. You...

Number Theory: 0.9r, basic algebra, mathematical terms

basic algebra, mathematical terms, mathematicians: Hello Jon This will have to be the last post on this topic. The limit of the series 0.9 + 0.09 + 0.009 +.... is 1 because we can make its sum as close to 1 as we like by taking enough terms. We do not have to speculate whether it is possible to add an...

Number Theory: 1/2 X 8 & 1/2 = ?/8, inverse operation, solving equations

inverse operation, solving equations, mcauley: Hello anon One of the important ideas in solving equations is that if two quantities are equal, they are still equal if multiplied by the same number. 1/2 X 8 = 4 and ?/8 X 8 = ?. The operation X8 was used as it is the inverse operation to divide by 8....

Number Theory: Why 10?, binary digits, arabic system

binary digits, arabic system, arabic number: Hello Bhaskar. The use of base ten certainly predates the arabic system we use. The Romans used X for ten, C for a hundred and M for a thousand. Probably ten is used because we have ten digits, and it is easy to check you have ten objects in a row by putting...

Number Theory: 2 induction questions, linear differential equation, linear recurrence

linear differential equation, linear recurrence, inductive hypothesis: Hello Scott This question is not really on number theory, but I will answer the first part. The equation is a standard linear recurrence relation and is solved by a similar process to the solution of a linear differential equation with which you may be familiar....

Number Theory: Difference, convex polygon, sided polygon

convex polygon, sided polygon, interior angles: Hello Navya A proposition is a mathematical statement such as 3 is greater than 4, an infinite set exists, or 7 is prime. A proposition may be true or false, or its truth may be unknown. For example, the truth of Fermat s last theorem was unknown...

Number Theory: euclidean, 5t, best wishes

5t, best wishes: Hello Navya The equation can be written; ax = b + km a and m share the factor d =(a,m) so b must also have this factor Divide by d to get a x = b + km/d We now multiply by the inverse of a mod m to get x = (a )^(-1)b + a km/d x = x0 mod m/d where...

Number Theory: fermat, best wishes for the new year, fermat number

best wishes for the new year, fermat number, time note: Hello Navya Here is a copy of a spreadsheet with F(n) worked out( only approximately for n 5), and the number of digits calculated worked out using the formula I gave you. It works every time. Note that an integer in standard form has one more digit than...

Number Theory: infinity, sigma 1, infinite series

sigma 1, infinite series, infinity: Hello Navya Let me explain sum to infinity. No one is suggesting we add an infinite number of terms. But the more terms you take, the closer the sum gets to the sum to infinity. By taking enough terms you can make the sum as close to the sum to infinity...

Number Theory: Number Theory, number theory, best wishes

number theory, best wishes: Hello Darcie n^3 + 1 factorises as (n+1)(n^2 -n + 1) If it is prime, one of these factors must be 1. It is not the first of these because that only happens if n = 0, and we are given n 0. So n^2 -n + 1 = 1 n^2 - n = 0 n(n-1) = 0. n is 0 , so n = 1...

Number Theory: number theory, chinese remainder theorem, lowest common multiple

chinese remainder theorem, lowest common multiple, prrof: Hello Mahima I presume the notation [ ] means lowest common multiple. When we multiply the numbers together, the gcd is included to the power n. In the lcm, we only need it to the power 1, so that [a1,a2,…,an ] = a1.a2…an/gcd^(n-1) But the gcd is 1,...

Number Theory: number theory, unit digits, 77d

unit digits, 77d, positive solution: Hello Mahima 1. Suppose to the contrary Then root(p) = a/b with (a,b) = 1 p = a^2/b^2 a^2 = p*b^2. Since (a,b) = 1, a^2 is a multiple of p, and since p is prime a is a multiple of p. a=cp Substituting c^2p^2 = p*b^2 b^2 = c^2*p, so b is a multiple...

Number Theory: numbertheory, digits

digits: Hello, Achyutha! Here is a primitive way to work out the answer. We are concerned with only the last two digits of the number. Note that: 2^4 = 16 Square this equation: (2^4)^2 = 16^2 and we have: 2^8 = 256 ... which ends in...

Number Theory: Rates, best wishes for a happy new year, happy new year

best wishes for a happy new year, happy new year, amount of time: Hello Kenneth Now I come to read your query again, I realise that there wasn t an original question. If the question was how long will they take if they work together? , the answer is 5 days. 2 jobs in 10 days is 1 job in 5 days. If the question was ...

Number Theory: Sequence, polynomial function, integer sequences

polynomial function, integer sequences, mathematical pattern: Hello BenVitale The easy answer is that it could be any number you can think of. But usually we want the given terms to display some sort of pattern, and assume that that pattern should continue. Sometimes no simple mathematical pattern exists. Eg, the...

Number Theory: Set Theory Formulae, grateful thanks, formulae

grateful thanks, formulae, best wishes: Hello Sushaali I m not going to reinvent the wheel. You should find everything you need to know at: http://www.ces.clemson.edu/~mjs/courses/misc/settheory.pdf If there is something you don t understand, get back to me. There are lots of other tutorials...

Number Theory: How to solve Algebra number theories, system of equations, digit number

system of equations, digit number, digits: Hello, Kathryn! Let T = tens-digit of the number. Let U = unit-digit of the number. We are told that: T + U = 14 [1] The two-digit number is: 10T + U Its reversal is: 10U + T The reversal is 18 less than the original number. ...

Number Theory: Follow up question, chinese remainder theorem, polynomial equation

chinese remainder theorem, polynomial equation, 25u: Hello Bridget x^2 + 5x + 1 = 0 mod 47 5 is even so add 47 to get x^2 + 52x + 1 = 0 mod 47 Now you can complete the square. (x+26)^2 = 26^2-1 = 17 mod 47 You do the other one in the same way. There are thus 8 different combinations of solutions to the...

Number Theory: Fractions, diophantine

diophantine: Hello Kenneth I m sorry to disappoint you, but your method does not give the correct answer in the example. 2/3 of Mary s age and 3/4 of Ruth s age equal 24 which is not Sarah s age. These problems lead to Diophantine equations, and often there is not a...

Number Theory: hard math problem, continued fraction, math problem

continued fraction, math problem, consecutive numbers: Hello socra I don t know that there is a largest one. But let us take an example that works, and see why. 1,2,3,4,5,6,7,8,9. The gcd if the first 6 numbers is 60. The next 3 numbers are 7, prime, 8, a power of 2, and 9, a power of 3. Every three consecutive...

Number Theory: heavyweight, wooly mammoths, fools and horses

wooly mammoths, fools and horses, observable universe: Hello Rodney I wonder if you are the Rodney from All fools and horses . Or should it be elephants? 1E60 is 1 with 60 zeroes after it. So a million is 1E6. The biggest number of estimated counted objects is 1E80, the number of atoms in the observable...

Number Theory: Modular arithmetic, phi phi, modular arithmetic

phi phi, modular arithmetic, theory student: Hello olebile I thought you might have been able to do #1 if you studied the previous answer, because we use the same theorem. Fermat s little theorem or the Euler generalisation. phi(5) = 4, so 2^4 = 1 mod 5. 2^30 = (2^4)^7*2^2 = 1*4 = 4 mod 5. #2...

Number Theory: mathmatics-number theory, odd primes, quadratic residues

odd primes, quadratic residues, final answer: Hello natraj I assume that you can use the quadratic residues theorem. Firstly 2 is a a special case. -3 = 1 mod 2. Now the odd primes (-3/p) = (-1/p)*(3/p). (-1/p) = (-1)^((p-1)/2) so =1 if p = 1 mod 4 and = -1 otherwise. Now we lookat (3/p) p = 12k...

Number Theory: Number Theory, Euler phi, last digits.

Euler phi, last digits.: Hello Eugene First of all, we need 123^456 mod 100. We use Euler s generalisation of Fermat s little theorem. phi(100) = 100(1-1/2)(1-1/5) = 40. 123^456 = 23^456. mod 100. 23^40 = 1 mod 100 (Euler) So 23^440 = 1 mod 100 23^456 = 23^440*23^16 = 23^16...

Number Theory: Number Theory, congruence class, recurring decimals

congruence class, recurring decimals, category number: Hello Bridget I think this is a copy of the answer you need Questioner: Jules Category: Number Theory Private: Yes Subject: Number Theory Question: I am so struggling with this. I have tried it over and over on my own. Can you solve these...

Number Theory: number theory, gcd, irrational

gcd, irrational, congruence: Hello obza I don t normally answer such a lot of questions in one post. Please don t ask more than 3 in any further postings. 1. Suppose to the contrary. Then x = ∛5 is a/b, where a, b are coprime integers. This gives 5 = a^3/b^3 and a^3 = 5 b^3....

Number Theory: recurring decimals, recurring decimals, 6 digits

recurring decimals, 6 digits, rigorous proof: Hello Dan This is a very interesting question, and I hadn t realised that before, so thank you. I will try to explain it, but haven t time to develop a rigorous proof. When we divide 1.000000.. by 7, there is a quotient and a remainder at each stage. The...

Number Theory: Series - Arithmetic or Geometric?, harmonic series

harmonic series: Hello mizoink A series in which each term is the reciprocal of the corresponding term in an arithmetic series is called a harmonic series. You are correct in saying the nth term of the first is 1/(2n). Note you do need the parentheses. The second one s...

Number Theory: absoulte value, absolute value

absolute value: Hello pratap An example |3| = 3, so |3| = 3 |-5| = -(-5) = 5, so |-5| -5 I think maybe you thought -a couldn t be greater than a, but of course when a is negative, -a is positive. The sign alone doesn t tell you if a term is positive or negative. ...

Number Theory: Mersenne primes and perfect numbers, perfect number, mersenne

perfect number, mersenne: Hello Heather First of all, your formula is not correct, it has an incorrect sign. A) Suppose it can, (3^(k+1)-1)/2 = 2*3^k There are a number of ways to proceed, but the method that works in the more difficult cases is to rewrite 3^(k+1) as 3*3^k. On...

Number Theory: maths ask a question, sum of squares, happy christmas

sum of squares, happy christmas, 2n: Hello pramu Amazingly, I have never seen this question before, but it should be easy enough. S(n) = a^2 + (a+d)^2 + (a+2d)^2 + ... (a+(n-1)d)^2 On expanding and collecting terms we have S(n) = na^2 + 2ad(0+1+2+...+n-1) + d^2(0^2+1^2+2^2+3^2....+(n-1)^2)...

Number Theory: Number Theory, divisibility tests

divisibility tests: Hello Andrew 1) If a is even, the we can write a = 2b. Then a^2 = 4b^2 = 0 mod 4. If a is odd, we can write a = 2c + 1. And a^2 = 4c^2 + 4c + 1 = 1 mod 4. 2) If n is even, it factorises as the difference of squares. e.g. 3^(2k) -1 = (3^k -1)(3^k +...

Number Theory: Number theory, factor theorem

factor theorem: Hello Heather I don t think your statement a^n+1=a^m2^p+1=a^2pm+1=b^m+1 is correct. It doesn t include any parentheses. a^n + 1 = a^(m*2^p) + 1 = (a^m)^(2^p) +1 = (a^(2^p))^m +1 Write b = a^(2^p) and m is odd. Then the number is b^m + 1. Now consider...

Number Theory: number theory, Wilson

Wilson: Hello Ashok The converse is. If (n-1)! = -1 mod n, then n is prime. If n is not a prime, then it has a divisor, d with 1 d n. Then d is one of the factors of (n-1)!. But d is also a factor of (n+1)! +1. That is clearly not possible. And that concludes...

Number Theory: Permutations and Number Combinations, combinations, permutations

combinations, permutations: Hello Andrew I m not sure I understand what you mean here. Suppose we represent the 20 objects by the first 20 letters of the alphabet, A to T, then the combinations could start: ABCD, ABCE, ABCF,.....ABCT Then ABDE, ABDF,....ABDT ABEF, ABEG,...ABET and...

Number Theory: day of the week, gregorian calendar, leap year

gregorian calendar, leap year, zoeller: Hello Trenita If you just want an answer, the simplest way is to type the date 1/1/2023 in an excel or open office spreadsheet and change the format to custom ddd. It gives Sun But I suspect you want to work it out for yourself. The method is known as...

Number Theory: A Maths Mindbender..., 2 legs, big cats

2 legs, big cats, mindbender: Hello Shaun Sorry for the delay. I didn t get the email. We will assume that the girls each have 2 legs. Girls 7 14 legs bags 49 0 legs big cats 343 1372 legs small cats 2401 9604 legs Total legs 10990. Nothing has been said about...

Number Theory: Pre Alg, geometric progression, pre alg

geometric progression, pre alg, expresion: Hello Tony Sorrry for the delay. I didn t get the email. You have to notice what the pattern is. Each time the number is being multiplied by 3. So the second is 2*3, the third, 2*3^2, the 4th 2*3^3 and so on, so the nth term is 2*3^(n-1). This is an...

Number Theory: Question on eye color gene, dark brown eyes, genetic model

dark brown eyes, genetic model, blue gene: Hello Jackie There is a problem about which genetic model of eye colour you are expected to use. The actual picture is much more complicated than a simple mathematical model. For example, the occurrence of hazel eyes is not properly understood. For example...

Number Theory: comgurances, long gap, set of numbers

long gap, set of numbers, smallest positive integer: Hello Mahima The first one is just saying that adding or subtrac any multiple of b does not change the value of a mod b. For example 23 mod 5 = 23 = 23+/-5 = 23+/-10 etc. Usually we give the smallest positive integer, so we would say 23 = 23 - 4*5 = 3 mod...

Number Theory: congurance, mahima, integers

mahima, integers, cb: Hello Mahima You already know that you don t change the value of a mod b by adding a multiple of b. But cb is a multiple of b. So you don t change the value of a mod b by adding or subtracting cb or a multiple of cb. Adding (c-1)b is just subtracting b...

Number Theory: inverting fractions, dividing by 2, fractions

dividing by 2, fractions, best wishes: Hello Tatiana This about inverses. How do you do the opposite of dividing by 2. You multiply by 2. It brings you back to where you started. We say that the inverse of multiply by 2 is divide by 2 and vice-versa. Now, how do we multiply by 3/4. One way...

Number Theory: possibilitys, possiblity, digit number

possiblity, digit number, repetition: Hello Danny If repetition is allowed, each digit may be chosen in 10 ways, so there are 10^4 ways. If repetition is not allowed, the first digit may be chosen in 10 ways, the second in 9, the third in 8 and the fourth in 7. So there are 10*9*8*7 = 5040...

Number Theory: Repeating Decimals, repeating decimals, repeating decimal

repeating decimals, repeating decimal, 333333: Hello Kenneth When I was at primary school over 60 years ago, we just learned the rule to put the recurring digits over a number composed of the same number of 9 s as there were recurring digits. So .1231213123.... would be 123/999 = 41/333. Of course,...

Number Theory: in regaurds to your contropositive proof on 9/10/2007, geometric series sum, sum of a geometric series

geometric series sum, sum of a geometric series, regaurds: Hello Mike It is n that has to be a power of 2. If n has any odd factor e.g. n = s*t where s is odd then f(2^t) = (2^t)^s + 1 has the factor 2^t + 1 by the factor theorem because f(-1) = (-1)^s + 1 = 0 because s is odd. The other factor is indeed the sum...

Number Theory: Simple Solution, algebra solutions, retirement age

algebra solutions, retirement age, place of employment: Hello Kenneth Sorry for the delay. I didn t receive an email. My ISP is experimenting with a new method of spam removal. Unfortunately it rejects some genuine ones. I think it inevitable that some bit of algebra is used here, but it is very simple....

Number Theory: sums of 2 addends of same parity, addends, odd pair

addends, odd pair, hello bill: Hello Bill I elected to answer this question, even though I have never come across this before. If I wasn t into a heavy marking week, I would be writing a computer program to try to find a counter-example. So, you need computer power on this to find out...

Number Theory: ZETA(4), full proof, euler

full proof, euler, zeta: Hello Ali You need to know how to calculate Fourier series. Define the function f(x) = -x for -PI =x 0 and f(x) = x for 0 =x =PI The Fourier series is f(x) = PI/2 - 4/PI*SUM(cos((2r-1)PI)/(2r-1)^2,r,1,infinity) You then need to use Parseval s theorem...

Number Theory: Congruences, odd power, fermat

odd power, fermat, best wishes: Hello Kelly We will look at each term separately. 111 = -1 mod 7 and -1 to an odd power is -1 333 = 4 mod 7 By Fermat s little theorem, 4^6 = 1 mod 7. 111 = 18*6 + 3, so 4^111 = ((4^6)^18)*4^3 = 4^3 = 1 mod 7. Putting it together, the expression...

Number Theory: CRT, linear algebra, fundamental solution

linear algebra, fundamental solution, mod 8: Hello Mahima When we say there is one solution to a modulus equation, we mean that all the solutions are congruent to a single number to that modulus. In the example there is only one solution in the set {0,1,2,...104}. Some authors use the term one fundamental...

Number Theory: divisbility, prime factorisation, primes

prime factorisation, primes, q1: Hello Clifton Probably the easiest way to see this is to consider the unique prime factorisation of a and b. The primes are disjoint. So the prime factorisation of c contains each of the primes of each of a and b to at least the same power as in the factorisation...

Number Theory: Euclidean Algorithm, euclidean algorithm, local village

euclidean algorithm, local village, pence: Hello George Sorry for the delay. I didn t get the email. My ISP is sometimes too careful about eliminating spam and deletes proper messages. Yes, of course, a linear diophnatine equation can be solved using the euclidean algorithm, but it isn t usually...

Number Theory: Finding the nth term with no constant increase, arithmetic sequences, geometric sequences

arithmetic sequences, geometric sequences, finding the nth term: Hello Beth Sequences where there is a constant difference are called arithmetic sequences. Sequences where there is a constant ratio are called geometric sequences. The nth term of an arithmetic sequence is a + (n-1)d, where a is the first term and d the...

Number Theory: proof, square root of 2, common factor

square root of 2, common factor, 2c: Hello john k Sorry for the delay. I didn t get the email. My ISP is sometimes too careful about eliminating spam and deletes proper messages. Suppose 1/root2 is rational, then it can be written a/b where a,b have no factor in common. then 1/2 = a^2/b^2...

Number Theory: Recurrene Relations, recurrence relation, initial condition

recurrence relation, initial condition, summations: Hello Ali You could show that the second order equation you have quoted does satisfy the recurrence relation just by substitution. But there is a much easier method. The series a(n+1) - a(n) is telescopic, so we can write a1-a0 = q a2-a1 = p + q...

Number Theory: 6-digit combination, number combinations, digit combination

number combinations, digit combination, excel spreadsheet: Hello Arvind With great difficulty. You would need about 84 million cells. You could use a simple basic program FOR A = 0 TO 44 FOR B = A+1 TO 45 FOR C = B+1 TO 46 FOR D = C+1 TO 47 FOR E = D+1 TO 48 FOR F = E+1 TO 49 PRINT A,B,C,D,E,F NEXT F NEXT...

Number Theory: Can the following problem be solved using the Euclidean Algorithm?, euclidean algorithm, local village

euclidean algorithm, local village, pence: Hello George This has already been done. Here is a copy of my previous answer. We have two equations using pence. m+w+c=500 748m + 712w + 45c = 277500 Eliminating c we get 703m +667w = 277500 703 and 277500 share the factor 37, so w = 37t, then divide...

Number Theory: Last question in my sons homework., number sequences, nth term

number sequences, nth term, sequence 4: Hello Tony Sorry for the delay. I didn t get the email. My ISP is sometimes too careful about eliminating spam and deletes proper messages. Having taught maths for 50 years, I can guess what the next to last question might have been. What is the nth...

Number Theory: number puzzle, prize quiz, gbq

Number Theory: number puzzle, prize quiz, gbq

Number Theory: Hello, please take a look at my question., fundamental theorem of arithmetic, type questions

fundamental theorem of arithmetic, type questions, integers: hello, as you said, a|b. this is nothi9ng but, a=bk for k is some integer. Now, the claim is, a^3|b^2 = (bk)^3/b^2 = b^3k^3/b^2 = bk^3 (again some integer). Mainly, I am not interested to solve home work/home work type questions. I will take up only some...

Number Theory: math, 2w, rectangle

2w, rectangle, square feet: Hello John We need to use some algebra and denote the width of the rectangle by w feet. Then the length of the rectangle is 2w feet. The area is length * width = 2w*w = 2w^2. So we have the equation 2w^2 = 128 w^2 = 64 w = +8 or -8 Since a rectangle...

Number Theory: number puzzle, number puzzle, maths problem

number puzzle, maths problem, hello bill: Hello Bill Something tells me that this is not really a maths problem. Your sequence can be written 1*19, 2*12, 3*20, 4*16, 5*17, 6*11, 7*18, 8*13, 9*15 There is no pattern in the second factors, but they could be rearranged into 11,12,13, 15,16,17,18,19,20...

Number Theory: number theory, proof by contradiction, prime factor

proof by contradiction, prime factor, number theory: Hello Ashley Proofs in number theory are notoriously difficult, but don t despair. As you progress it gets easier. This is an example of a proof by contradiction. Suppose there is not a prime p less than root(n) s.t. p|n Then, since n is composite,...

Number Theory: im bothered!, natural numbers, induction

natural numbers, induction, geometry: Hello Anafe I don t think this is something you can prove. It is one of the properties of the set of natural numbers which is not shared with the sets, Z,Q,R or C. It is logically equivalent to both the principle of induction and the principle of strong...

Number Theory: math, scientific calculators, bonus points

scientific calculators, bonus points, computer program: Hello Rick This is 31C6 as there are 31 to choose from and we need to choose 6. Most scientific calculators will give you the answer. Mine gives 736281 I am sure yours will do the same. In answer to your second question, the margin is too small to contain...

Number Theory: Number Theory, binomial theorem, factorisation

binomial theorem, factorisation, real numbers: Hi Mimi If ab is a power of 2 there is no algebraic factorisation for 2^(ab) + 1 in real numbers. But we can factorise 2^(ab) when ab has an odd factor. I don t know a general formula, but I can explain how to do it with an example 2^15 + 1. 2^15 + 1 has...

Number Theory: odd numbered fractions that dont equal 1, recurring decimal, decimal places

recurring decimal, decimal places, 9999999999: Hello Jeremy Your calculator can t show a recurring decimal. 1/3 is 0.3 recurring. A reasonably modern calculator calculates to at least 2 more decimal places than it displays. Suppose it displays 8 places. Then it calculates to 10 places .9999999999...

Number Theory: Probability, isoceles triangle, isoceles trapezoid

isoceles triangle, isoceles trapezoid, consecutive angles: Hello Abbas There is a subtle difference here, as the consecutive property is now given. Since every pair of sides and angles of the triangle is consecutive, it doesn t make any difference. So (a)(1) 1/3 (b)(1) 1/3 In the general case two consecutive...

Number Theory: plz enlighten me., axiom, geometry

axiom, geometry, brains: Hello Anafe I think I said that the well ordering property is exactly that, a property and is part of the definition of number systems, like the one line exactly through a point parallel to another line of Euclidean geometry which Euclid wracked his brains...

Number Theory: combos, permutation with replacement, word combination

permutation with replacement, word combination, digit combination: Hello Joe Let s put it into a real situation. You are the manager of a team which plays 9 a side martian soccer. You have ten players numbered 0 to 9. How many different team selections can you make? All you have to do is select the player who is not...

Number Theory: Explain" Every number can be written as difference of two squares", difference of two squares, difference of squares

difference of two squares, difference of squares, answer service: Hello Akshay Welcome to my answer service. The difference of two squares is factorisable. x^2 - y^2 = (x+y)(x-y) If the number is odd we choose (x-y) = 1, then x + y is a difference of squares. So, we pick a number at random, say 73, and decompose it...

Number Theory: find the remainder when 7^51 is divided by 144, prime factors, natural numbers

prime factors, natural numbers, fermat: Hello vinodannu We can use Euler s generalisation of Fermat s little theorem: a^phi(n) = 1 mod n if a is prime to n and phi(n) is the number of natural numbers less than n and prime to it. The prime factors of 144 are 2 and 3 so phi(144) = 144(1-1/2)(1-1/3)...

Number Theory: number theory, chinese remainder theorem, dividing by 3

chinese remainder theorem, dividing by 3, 5z: Hello vinod We need to solve x^3 + 4x +8 = 0 mod 3 and also mod 5. The first is true for x=2 mod 3. The second has no solution. So there is no solution to the original congruence. 2. Start by dividing by 3 5x+4y+10z = 8 this shows x is even, so write...

Number Theory: number theory, coprime, integers

coprime, integers, phi: Hello Vinodannu 1. x(x-1) congruent to 0 mod m for every m, can only have the solutions x=0 and x=1. 2. I m pretty sure you mean phi(m) = phi(mn) here, where phi(n) is the number of positive integers less than n and prime to it. If m and n are coprime...

Number Theory: number theory, odd powers, equel

odd powers, equel, number theory: Hello vinodannu 1. 2^10 = 1024 =24 mod 1000 2^20 = 24^2 = 576 = 76 = -24 mod 1000 2^30 = -576 = 24 mod 100 Odd powers of 2^10 = 24 mod 1000 Even powers of 2^10 =76 mod 1000 2^1000 is an even power, so 2^1000 = 76 mod 1000 2. (a,a+k) = (a,k). If...

Number Theory: number theory, consecutive integers, k show

consecutive integers, k show, positive integer: Hello Vinodannu 1. Let the largest of the integers be n. Then nCk, the number of ways to choose k objects from n is n(n-1)...(n-k+1)/k!, the product of k consecutive integers in the numerator. The number of ways of course is integral. 2. Do you mean...

Number Theory: number theory, fermat number, fermat numbers

fermat number, fermat numbers, k show: Hello vinodannu 1. You asked this earlier and I said it was impossible to answer, as you haven t specified a modulus for the congruence. 2. Your definition of Fermat number is not correct, it should be 2^(2^n) + 1. Let d= (Fn,Fn+k) where k 0. The...

Number Theory: number theory, 10y, finite number

10y, finite number, pairwise: Hello vinodannu 4y+3z =1 mod 6 multiply by 2 8y + 6z = 2 mod 6 8y = 2 mod 6 1. Suppose there are only a finite number of primes of the form 4n+3. p1,p2,p3....pk, so that pk is the largest prime of this form. Then consider 4*p1*p2*...pk - 1 It is...

Number Theory: (a,p)=1,(n,p-1)=1 then x^n congruent a mod p has exactly one solution, multiplicative group, fermat

multiplicative group, fermat, phi: Hello Vinodannu I will have to assume that you mean p is prime. The p-1 numbers, 1,2,...p-1 form a multiplicative group mod p. If x is one of these then x^(p-1) = 1 mod p is Fermat s little theorem. x^n = 1 mod p is possible if n is a factor of p-1, but...

Number Theory: prime, prime numbers, pqr

prime numbers, pqr, rq: Hello Dasharath I m afraid I don t have the time at present to do justice to this problem, but I would not be surprised if the only solution was p=q=r=3. You can prove using the identity p^3+q^3+r^3-3pqr = (p+q+r)(p^2+q^2+r^2-pq-qr-rp) that pqr and p^2+q^2+r^2...

Number Theory: Watts & Watt-Hours, watt hours, 1 joule

watt hours, 1 joule, energy consumption: Hello Kenneth Suppose we take the example of a 1 watt indicator lamp. It is using energy at the rate of 1 joule per second, so that in 1 hour it has used 3600 joules of energy, and that is what you would pay for. That is, the number of watt hours = 1, and...

Number Theory: a counting and enumeration problem, combinations repetition

combinations repetition: Hello Dan This is an interesting problem I can help you with. Let us look at an example. How many selections of 5 objects are there from 3 colours? Call the colours A,B,C and write the selection in this order. When all occurrences of a colour have been...

Number Theory: how to find the primes in just a few seconds, prime factors

prime factors: Hello Mark Your number certainly has the factor 555. It is 555*(10^9+10^6+10^3+1) = 5*3*37*(10^6+1)(10^3+1) 10^6 + 1 is the sum of two cubes so factorises as (10^2+1)(10^4-10^2+1) and that gives the complete factorisation as 3*5*7*11*13*37*101*9901....

Number Theory: maths, factorisation

factorisation: Hello Bridget I can only help you with the maths of this question. After that it is up to try different combinations of letters perhaps with a web anagram generator. The prime factorisation of 1 million is 2^6*5^6, so the only letters available are A as...

Number Theory: modular proof, induction, congruence

induction, congruence: Hello Brad This could be proved directly using the binomial theorem, but if you need a proof by induction here goes. To prove something by induction, we need to prove two things. First it must be true at the base of the chain i.e. for n=1. This is obvious...

Number Theory: Number Theory, gcd

gcd: Hello Jill I m not going to do all of these for you. They can all be proved by using the unique prime factorisation of the numbers. For example (a) The prime factorisation of a = a1^e1*a2^e2*... b = b1^f1*b2^f2*... c = c1^g1*c2^g2*... from the given,...

Number Theory: Number Theory, gcd

gcd: Hello Joanna 1) You need to use the Euclidean algorithm property. (a,b) = (a, b-ka) or (a, ka-b). here we use a = n!+1, b = (n+1)!+1 and k = n+1 So (n!+1,(n+1)!+1)= (n!+1, (n+1)(n!+1) - ((n+1)!+1)) and this simplifies to (n!+1,n) because n*(n+1)! = (n+1)!...

Number Theory: Number theory Proof, Euler, phi

Euler, phi: Hello Patrick My most sincere apologies for my horrendous mistake. I ve answered so many questions successfully on Euler phi, I can t understand how I typed what I did. I m pleased you worked out the proof yourself. Each element m and prime to it can...

Number Theory: Odd and Even Multiples, maths coursework, graft

maths coursework, graft, best wishes: Hello Dan This sounds like some Maths coursework where you have to put some graft in. Carefully list your results and then describe any patterns you find. To find the number of multiples of 3 from 1 to 2008, you only have to put 2008 in your calculator...

Number Theory: terms and sequence, sequence, term

sequence, term: Hello Richard A sequence is simply an ordered set of numbers, usually without end. e.g. 1,3,5,7,9,..... 1,4,9,16,25,... Each individual number is called a term of the sequence. So the 4th term of the first sequence is 7. For simple sequences, students...

Number Theory: binomials, binomial expansion

binomial expansion: Hello Craig Not even mathcad can display all 64 terms of this expansion, but I can give you the first few terms, the general term and the last term. (a + x)^63 = a^63 + 63a^62x + 63C2*a^61x^2 + ...63Cr*a^(63-r)x^r +....+x^63. 63Cr is the number of ways...

Number Theory: Calendar Weeks & Days, leap year, paydays

leap year, paydays, calendar weeks: Hello Kenneth Your original assumption that there are 26 paydays in a year is false. If payday is a Friday and payday Friday is the first day of the year, then the last day of the year (or the next to last in a leap year) will also be a Friday payday. So...

Number Theory: euler phi function., euler phi

euler phi: Hello Ashley The first case is when n is odd, so that the factor (1 - 1/2) does not occur in the calculation of phi(n). When n is doubled, there is a new factor (1-1/2) = 1/2. This cancels the 2 in 2n, so that phi(2n) = phi(n). When n is even, the bracketed...

Number Theory: Fermat's Last Theorem, cubic congruence

cubic congruence: Hello Holly I don t know how long this has been in the question pool. I don t usually look there. The question is much easier than it looks. We just need to work out all the cubes, and then make all the possible sums. 1^3 = 1, 2^3 = 3, 3^3 = 2, 4^3...

Number Theory: Number theory/divisibility, if and only if, divisibility

if and only if, divisibility: Hello Kate First if and only if. Propostion A if and only if Proposition B To prove this we have to prove A implies B and B implies A. Another way of saying this is: A is a necessary and sufficient condition for B. So let s start with A. (x,y) = g means...

Number Theory: number theory, FLT pseudoprime

FLT pseudoprime: Hello Ashley I ll start with the second because that is much easier. The FLT assures us that a^(p-1) = 1 mod p for p prime and a prime to p. so if k is a non-negative integer, a^(k(p-1)) = 1 mod p. Now multiply by a a^(1 + k(p-1)) = a mod p. And this...

Number Theory: proof, contradiction, rational

contradiction, rational, irrational: Hello Cassie The idea of a proof by contradiction is to start by supposing the opposite of what we have to prove and showing it leads to an impossibility. Suppose to the contrary. Then both x and y are rational. But the sum of two rational numbers is a...

Number Theory: Set theory, notb, distributive law

notb, distributive law, distributive laws: Hello Mohammed I make a rule not to answer more than 3 questions in one post. That is because i believe the student has to make an effort to learn. In your last post we only needed the distributive laws and the inclusion laws. For some of these we need...

Number Theory: Simple Interest & Multiple Accounts, algebraic solution, simple interest

algebraic solution, simple interest, extra 3: Hello Kenneth It s because you can t have a negative amount of cash in an investment account. Unless you know otherwise. So t has to be less than or equal to 5,000 or the amount in the 2% account would be negative. And it has to be greater than or equal...

Number Theory: Circles, vector approach, euclidean geometry

vector approach, euclidean geometry, dividing by 2: Hello Sneha This certainly isn t number theory, so I should reject it, but I m pretty good at geometry, so I ll answer the question. I can t send you a diagram, but you must draw a large clear one using compasses. When you ve done that, read on. Label...

Number Theory: Circles, arc length, radians

arc length, radians, radii: Hello Sneha You certainly ask some varied questions! The only geometry needed here is arc = rǾ. So Ik has length rǾk^2. The sum of the lengths is rǾ*Sigma(k^2) as k goes from 1 to 2005. To avoid unnecessary arithmetic I will use n for...

Number Theory: Compex Numbers, De Moivre

De Moivre: Hello Mohammad This is not really my expertise, but I ll answer it. Of course it is necessary to redefine sin and cos, not as something geometric like adjacent over hypotenuse, but in analytic terms. cos and sin can be defined in terms of the exponential...

Number Theory: Math, inverse function graph, transcendental equation

inverse function graph, transcendental equation, real solutions: Hello Ron The given information says |x-2| δ, so multiply by 2 to get |2x-4| 2δ. then δ = ε/2. So for (a) 0.05 and for (b) 0.005. 2) swap x and y. This is because the inverse function graph is a reflection of the function in...

Number Theory: math, real solutions, two answers

real solutions, two answers, decimal places: 1) If |x-2| δ, then |2x-4| ε, ε = 0.01. Looking at |x-2| and |2x-4|, it can be seen that |2x-4| = |2(x-2)|, so the 2nd is twice the 1st. If ε = 0.01, δ is the is half of ε, so δ is 0.05. b) If ε = 0.01, then δ...

Number Theory: math, sequence

sequence: Hello Suli Recognising a sequence is a matter of knowing the rules of basic sequences and trying to see if you can find a fit. Clearly this sequence is not an AP or GP, nor is it a poynomial function. However, the numbers should be recognisable as factorials....

Number Theory: math -sequencing-arithmetic/geometric, AP, GP

AP, GP: Hello Jackie With the usual notation for an AP, a + d = 1 and a + 4d = 125 Subtracting gives 3d = 124 and d = 41 1/3 So the sequence goes -40 1/3, 1, 42 1/3, 83 2/3, 125, 166 1/3. For a GP, ar = 1 ar^4 = 125 Dividing gives r^3 = 125, so r...

Number Theory: mobius inversion, mobius function, asap thanks

mobius function, asap thanks, d show: g(n) = summation (over d|n) (mew(d)f(n|d)); show f(n) summartion(over d|n) of g(d) questions: what is the mobius function? Suppose n is 10; does this mean that d is taken as 1, 2, 5, and 10? In other words, g(10) = f(1) + f(2) + f(5) + f(10)? ...

Number Theory: mobius inversion, Mobius

Mobius: Hello Timeth This is a standard theorem in the theory of arithmetic functions and the proof will be found in most text books. For example Jones and Jones ISBN 3540761977. theorem 8.6 page 150 is the converse of what you have to prove. Sorry, I m not prepared...

Number Theory: Number Theory, chinese remainder theorem, prime factorisation

chinese remainder theorem, prime factorisation, arithmetic progression: Hello Skrosun 1. It is easily proved that the φ(n) integers less than n and prime to it form a multiplicative group (mod n). The subgroup generated by a has order a factor of φ(n) by Lagrange s theorem, so the result follows. This is just Euler...

Number Theory: Number Theory, FLT carmichael number

FLT carmichael number: Hello Surya A composite number n such as 561 with a^n = a (mod n) for all a is called a Carmichael number, and 561 is the smallest. It is easily proved using Fermat s little theorem or FLT. By the FLT a^2 = 1 (mod 3) for a not a multiple of 3, so a^560...

Number Theory: Number Theory, FLT

FLT: Hello Surya This is another that can be done using FLT. Let n = 2k + 1. Then a^2 = 1 (mod 3) if a is not a multiple of 3. Then, raising to power k, a^(2k) = 1 (mod 3) and a^(2k + 1) = a (mod k), so that a^n = a (mod 3). If a is a multiple of 3 both sides...

Number Theory: Number Theory, Wilson, congruence

Wilson, congruence: Hello Surya Sometimes substituting in an answer you are asked to prove helps, so you were right to try that. However, here, the clue is in the fact that on the right hand side you have ((p-1)/2)!. So we must split up the left hand side into a product of...

Number Theory: Number Theory, composite number, number theory

composite number, number theory, surya: Hello Surya Unless n is a square, it can be factorised, and both of these factors are less than n, and can be found as factors of (n-1)!. So what happens when n is a square. n = 4 is an exception. But for any other square, k^2, both k and 2k are factors...

Number Theory: Number theory, 4 digit numbers, consecutive integers

4 digit numbers, consecutive integers, negative integers: Hello Sneha 1) Call the two numbers A and B. They are not equal since that would involve carrying. Number A has 3 choices for units digit, 10 for tens digit, 5 for hundreds digit and 2 for thousands. So there are 3*10*5*2 choices. But this must be halved...

Number Theory: number theory, congruence

congruence: Q1 1999 = 1 (mod 9) So 1999^1999 = 1 mod 9. log(A) = 19998log(1999) = 6598.3.... This means A has 6599 digits, so the digit sum 9*6599 So B 59391 C = sum of digits of B 5 + 4*9 = 41 D = sum of digits of C = 12 sum of digits of D = 9 The...

Number Theory: number theory, odd terms, even position

odd terms, even position, odd note: So, you mean to keep counting. I was wondering why it started out with a 1,2,3,4,5,6,7,8,9, but now I see why. The first 9 terms are 1 digit, 1 thru 9. The next 90 numbers generate 180 terms, 1,0,1,1,1,2,1,3,1,4.....9,7,9,8,9,9. That makes for a total...

Number Theory: numerical sequences, numerical sequences, time scott

numerical sequences, time scott, scott andrew: Take n(i) to be the ith term. The formula is then n(i) = 5*n(i-1) + 3. If we re looking for a specific formula to say the value at year i without knowing that value at year i-1, I don t know if there is one. We could say that n(i) = 5(5*n(i-2) + 3)...

Number Theory: proof, advanced calculus, divergent series, xn

divergent series, xn, absolute value: It almost looked like |xn| was the absolute value of |xn|, but this can easily be disproved. What is really meant, I belive is the function of the limit as n- ∞ of the terms is the same as the limit as n- ∞ of the function of terms of the...

Number Theory: One more question, advanced calculus, numerator, epsilon

numerator, epsilon, fractions: For xn- a, for n=k large enough, this means that for n =k, all |xn - a| ε for any ε however close to 0. At this point, 1/x is between 1/(x-ε) and 1/(x+ε). Take |1/(x-ε) - 1/x|. Combining the fractions gives |(x - (x-ε)/((x-ε)x)|....

Number Theory: Riemann Hypothesis and Prime Numbers, Riemann Hypothesis

Riemann Hypothesis: Hello Anon The answer is a very firm NO. I have the book Prime Obsession by John Derbyshire, which I think is the best book for attempting to explain the Riemann Hypothesis for anyone not well up to date with analytic number theory. The zeta function could...

Number Theory: theory used to estimate pumkin seeds, pumkin seeds, teaching math

pumkin seeds, teaching math, rabbits: No, I don t know what the thing to look at would be. Maybe you could use how far the rabbit runs in a day. Maybe it could be how long each one stays in the barn. Those both sound like good approaches, but I don t think either on is really correct....

Number Theory: trigonometry, c cos, tanc

c cos, tanc, tana: Hello Sneha This is not my expertise, but I will help you with some of them. cos(2B) = 2 cos^2(B) - 1 = 2/sec^2(B) -1 = (1-tan^2(B))/(1+tan^2(B)) Then, clearing the fraction: cos(A-C) -cos(A-C)tan^2(B) = cos(A+C) +cos(A+C)tan^2(B) tan^2(B)(cos(A+C)+cos(A-C))...

Number Theory: urgent math, trig function, transcendental function

trig function, transcendental function, limit x: Hello Rajeev Don t worry over this. You aren t going to be asked to do something impossible. Trust me. Inverse of such a function where x occurs in more than one place is not possible analytically. Numerically yes. Draw a graph or do a spreadsheet. ...

Number Theory: ap calculus ab, ap calculus ab, tangents

ap calculus ab, tangents, serpentine: Hello Asad These aren t problems but routine examples. I suspect you haven t studied worked examples of the techniques. OK that s the lecture over. 2. The method here is to divide N and D by x^2. This gives (4/x^2 -1)/(1 - 1/x^2). Since 1/x^2 tends...

Number Theory: ap calculus ab, ap calculus ab, quotient rule

ap calculus ab, quotient rule, homework problems: Hello Asad I hope these aren t homework problems. It s OK if you have managed to do 1 to 18 yourself. 19. You need to multiply out N and D to get (x^2+3x+2)/(x^2-3x+2) Then use the quotient rule to get ((2x+3)(x^2-3x+2)-(x^2+3x+2)-((x^2+3x+2)(2x-3))/(x^2-3x+2)^2....

Number Theory: ap calculus ab, ap calculus ab, common denominator

ap calculus ab, common denominator, derivative: Hello Asad You don t say what to differentiate with respect to, but I shall assume it is x. 9. (1/a)(2x/b - 2/a + d/x^2). It is arguable what the simplest expression is here. It may be 2x/(ab) - 2/a^2 + d/(ax^2), or an expression with common denominator....

Number Theory: Number Theory - Mersenne Primes, factor theorem, mersenne

factor theorem, mersenne: Hello Kevin This question is really about the factor theorem. Do you remember it? A polynomial p(x) has the factor (x-a) iff p(x) = 0 has a root x = a. Now, a polynomial of the form p(x) = a^(2k+1) + 1 has a root of the equation p(x) = 0: a = -1 So...

Number Theory: need asap help, dx dt, revolutions per minute

dx dt, revolutions per minute, arctan: Hello George Call A the angle the beam makes with LP and x the distance of the beam on the shoreline from P. Then x = 3tan(A) so dx/dA = 3(sec(A))^2 and dA/dt = 8PI. Multiplying gives dx/dt = 24PI(sec(A))^2. When x = 1, tan(A) = 1/3 so (sec(A))^2 = 4/3....

Number Theory: Question, infinite sequence, divisors

infinite sequence, divisors, natural numbers: Hello Awais a(2010) = 2009(1 + 10^4 + 10^8 + ...10^(4*2009) =2009(10^(4*2010) - 1)/9999 using rule for sum of a GP. Then this is a factor of 2009(10^(4*2010k) - 1)/9999 for all positive intrgral k. But this is just a(k), so the theorem is proved. The...

Number Theory: urgent math

Hello George You have left it late. Why didn t you query days ago. It is past midnight here in the UK and though I can answer all your questions, I don t have time. So I ll give you half an hour. That s till 12:50 here. 1.Call the distance from first...

Number Theory: Derivative Fibonacci Sequence, distinct numbers, geometrical interpretation

distinct numbers, geometrical interpretation, graph paper: Hello Richard Your sequence certainly isn t Fibonacci. Google found Fibonacci because terms 4,5,6,7 and 8 are part of a Fibonacci sequence. Your sequence appears to have nth term the number of partitions of n + 1 into 3 distinct numbers from the set {1,9}...

Number Theory: Derivative Fibonacci Sequence, spiral, snake

Number Theory: Derivative Fibonacci Sequence, spiral, snake

Number Theory: how do you find several primes in a small gap?, twin primes

twin primes: Hello Elijah What a wonderful name. I have had the pleasure of singing the bass part in Mendellsohn s oratorio by that name. I m pretty sure there isn t any simple algorithm. But in the example you have given, you would look at all values of k for which...

Number Theory: A little help please?, least common multiple, prime number theorem

least common multiple, prime number theorem, colour theorem: Hello Verity The least common multiple of n and n-1 is n(n-1) which is greater than 6n for n 7. The second question is a much stronger statement than Berthold s conjecture, theorem, which took Lagrange ages to prove. And that was, that there was at least...

Number Theory: Num. Theory, induction

induction: Hello Aaron You know that the first step in a proof by induction is to choose n = 1 and check if it is true. n = 1 gives a^2 = 1 (mod 8) This is clearly not true for any even a. e.g. a = 2. That is why I asked you about a restriction on a. Check the...

Number Theory: Number Theory, FLT

FLT: Hello Mallory Is you dad a mountain climber by any chance? It is still not known if George Mallory was the first person to climb Everest. But to business. This is a consequence of FLT. a^q - a = 0 (mod q), so we may write a^q = a + kq for any integer k....

Number Theory: Number Theory, gcd

gcd: Hello Mallory. Here is one way to answer the question. Suppose to the contrary. (a+b,ab) = h, where h 1. Then a+b = xh, ab = yh. With x,y integral. Then a = xh-b and substituting: (xh-b)b = yh Rearrange to give h(xb-y) = b^2 This proves h is a factor...

Number Theory: Number Theory, quadratic conguence, quadratic residue

quadratic conguence, quadratic residue: Hello Aaron The discriminant of this equation must be a qr mod 5. The discriminant (b^2-4ac) = 9 + 8k = 3k - 1 (mod 5) The qr s mod 5 are only 1 and -1. So 3k -1 = 1 or -1 (mod 5) These are easy to solve giving k = 0 or 4 (mod 5) please check. Lagranges...

Number Theory: Number Theory, primitive roots

primitive roots: Hello Suraya n has primitive roots if and only if it is 1,2,4,p^e or 2*p^e, where p is an odd prime. 21 is not of this form, so has no primitive roots. However, to check it out, 8,13 and 20 have order 2. 4 and 16 have order 3, and the others have order...

Number Theory: Number Theory Correction, gcd, integers

gcd, integers, number theory: One way to look at this is that since the gcd(x,y)=g, x=ng and y=mg where n and m are integers. From here, it is known that x+y=2, so ng+mg=s, so (n+m)g=s. If g does not divide s, the equation ng+mg=s would not be true, so n,m would not both exist,...

Number Theory: number theorey for excercise, odd integer, counterexample

odd integer, counterexample, divisor: 1. The lcm(n,n+1) is n*(n+1) for there can be no number besides 1 that divides evenly into n and n+1. Suppose we found some number k that divides evenly into n for a total of m times. The next divisor for that number would be k(m+1) = km + k. Since...

Number Theory: number theorey for excercise, excercise 1, odd power

excercise 1, odd power, odd integer: Hello Anndy 1. Since gcd(n,n+1) = 1, lcm(n,n+1) = n(n+1) 2. This is false since 0 cannot be so expressed. 3. This is true. In the prime decomposition of c, for any prime to an even power, b contains the same prime factors to the same power. Any...

Number Theory: Prime Factorization, unique factorisation in Z(sqrt(2))

unique factorisation in Z(sqrt(2)): Hello Nicole. There are some mistakes in your typing. The first should be (5+3r2)(5-3r2), where r2 stands for sqrt(2). In Z, there are 2 factorisations of 7. 7 = 1*7 = -1*-7. This is because -1 is a unit, i.e. a number whose norm is 1. In Z(i), There...

Number Theory: Congruences/methods of calculation, proper divisor, carmichael numbers

proper divisor, carmichael numbers, euclidean algorithm: Hello Katie Your question has now moved from fresher to graduate school. I did study pseudoprimes about 45 years ago, and Carmichael numbers. There are lots of refs on the web to strong pseudoprimes spsp s. But I m very busy at present, so I don t have...

Number Theory: polynomial congruences, WILSON, Fermat's little theorem

WILSON, Fermat's little theorem, congruence: Hello Ashley An interesting one which I haven t seen before. First of all (p-1)! = -1 (mod p) by Wilson s theorem. Let s have a look at ((p-1)/2)! = (p-1)/2*(p-3)/2*...1. There are k factors. Using the hint, this gives (-1/2)^k*(1*3*5..(p-2)) We need...

Number Theory: (A xor B)+ (B xor C)+ (C xor A)=(A xor B)+ (B xor C), logic, xor

logic, xor: Hello akn This is not quite my field of expertise, but I used to teach computer science, so I can answer the question. If you draw a Venn diagram, it is obvious by shading. The point is that AxorB = AB + A B is split into smaller regions depending whether...

Number Theory: additive/multiplicative inverse, Euler, FLT

Euler, FLT, phi: Hello Annette a always have an additive inverse (mod m). It is -a, or m-a if you need a positive residue. a has a multiplicative inverse only if a is prime to m. The set of natural numbers less than m and prime to m form a multiplicative group. The number...

Number Theory: permutation and combination, erson, resolves

Number Theory: permutation and combination, erson, resolves, coz

Number Theory: permutation and combination, study material, pl

Number Theory: permutation and combination, study material, pl

Number Theory: permutation and combination, inclusion, pl

Number Theory: permutation and combination, inclusion, pl

Number Theory: Mills & Decimals, frac, floor

frac, floor: Hello Kenneth frac() is just the same as decimal part of(). In other words you throw away the integer part of the number. frac(10.5) = 0.5 frac(3 + 3/4) = 3/4. However frac is a function of a number, not a quantity, so frac($1.00) should really be $frac(1.00)...

Number Theory: Number Theory, divisibility, primes

divisibility, primes, number theory: Hello Marissa We are concerned here about divisibility by 4 and 3. So we need to use the fact that P1 =2 and P2 = 3 P(n) = 2*P2P3...+ 1 All the primes after P1 are odd, so their product is of the form 2k+1 2*(2k + 1) + 1 = 4k + 3. P(n) = 6*(2k + 1)...

Number Theory: Number Theory, prime decomposition

prime decomposition: Hello again Marissa Consider 14! + 2, 14! + 3.....14! + 14. The first has factor 2, the second factor 3... the 14th factor 14. So we have 13 consecutive composite numbers. Consider the prime factor decomposition of the integer n. n = p1^n1*p2^n2*p3^n3...p(k)^n(k)....

Number Theory: Number Theory, Euler phi, lagrange

Euler phi, lagrange: Hello Katie With a question like this, a lot depends on which theorems you are allowed to assume. The obvious way is to use group theory. You should be aware that the phi(m) elements 1,...m-1,prime to m form a multiplicative group (mod m). Since d|m, the...

Number Theory: Number Theory, proof by contradiction, irrational number

proof by contradiction, irrational number, logp: Hello Sarah I don t normally answer 4 different questions in one post. Today, you are lucky. I don t have homework to mark. 1. Assume to the contrary. Write a = r/s with gcd(r,s) = 1 and a^(1/k) = t/u: gcd(t,u) = 1. Then r/s = (t/u)^k. and this gives...

Number Theory: number theory, set algebra

set algebra: Hello Gerald First of all consider a Venn diagram. Three intersecting sets. The union of two sets can be illustrated by shading the area of both sets. So the result should be aUbUc. No let s do the algebra. (aUb)U(bUc) = ((aUb)Ub)U((aUb)Uc) = (aUb)U(aUbUc)...

Number Theory: permutation and combination, permutation and combination, intermediate stations

permutation and combination, intermediate stations, ipl: Hello Vepul Perhaps that is the answer to a different question. There is no way the answer can be 10C2 - 10. The only reservation I have is the use of the words during the journey . This may preclude Delhi as one of the stations, so 8C2 = 28 is possible...

Number Theory: permutation and combination, permutation and combination, random choice

permutation and combination, random choice, different games: Hello Vepul Unlike your previous question, this is a very easy one. Give all the children one game. This can be done in n! ways. Now say Who doesn t want their game? The first response child s game is allocated at random to the n-1 other children. ...

Number Theory: permutation and combination, elementary combinatorics, permutation and combination

elementary combinatorics, permutation and combination, separators: Hello vepul kumar I am assuming that by outcome you are only concerned with the count of each digit that ensues, not with the order that they appear in. This is one of the most awkward problems of elementary combinatorics to explain. Suppose a particular...

Number Theory: pythagorean tripples, diophantine, quadratic

diophantine, quadratic, homogeneous: Hello Ashley I ll show you a method for the first one which should enable you to do the second yourself. As with pythag triples, we are really only concerned with primitive solutions, i.e. those in which the variables are coprime. Since the equations...

Number Theory: recursion problem, arithmetic sequence

arithmetic sequence: Hello Gerald I was at the gym on the treadmill this morning, and sometimes that is when I have my best thoughts. It dawned on me that you might have been trying to produce subscripts. When you can t type subscripts, you can use brackets. So, I ll change...

Number Theory: discrete mathematics, rational, irrational

rational, irrational: Hello Evelyn Given t irrational, to prove 3t is irrational. Suppose to the contrary, then 3t = a/b with a,b integers. Then t = a/(3b) showing t is rational, a contradiction. More generally, rational *irrational = irrational. Best wishes vijilan...

Number Theory: Multiple Investment Accounts, algebraic solution, extra 3

algebraic solution, extra 3, simple interest: Hello Kenneth All the amounts must be positive. So 10,000 - 2t 0, 20,000 -t 0 and 3t 0. From the first, 2t 10,000 so t 5000. From the second t 20,000, and from the third t 0. So, putting it all together, t can take any value between 0 and...

Number Theory: number theory, Mersenne prime, factor theorem

Mersenne prime, factor theorem: Hello Marissa For the first, we disprove by giving a counter-example. 1^1 + 1 = 2 is prime, but neither a =1 is even, nor n = 1 is prime. a^n -1, considered as a polynomial function of a has the factor a - 1, by the factor theorem. You may need to...

Number Theory: number theory, least common multiple, lcm

lcm: Hello Bruce You have to find the smallest number which is a multiple of each of the numbers. Start with 5 and 15. Since 15 is a multiple of 5, 15 is the lcm of 5 and 15. 15 and 11 have no factors in common, so the lcm of all 3 is 15*11 = 165. Another...

Number Theory: probability and combinations, permutations, combinations

permutations, combinations: Hello D Not too well actually. For the first part you have calculated the number of ways of permuting BBBBBGGGGG. This is not what is required. The rules say first in must be a boy or girl. 2 alternatives. After that, we have two lists, one for boys,...

Number Theory: sequences, AP, nth term

AP, nth term: Hello Michelle You have the answer in front of you, but you have put an extra comma where there should not have been one. The nth term is -2n-2. Let s check that with n = 1. T(1) = -2*1 -2 = -4. If you want to find the 7th term, you just have to substitute...

Number Theory: congruences mod n, congruence, FLT

congruence, FLT: Greetings Tom There are many methods available. In the case of a composite power the simplest is to calculate 11^14 (mod 3) and (mod 5). 11 = -1 (mod 3), so 11^14 = 1 (mod 3). 11 = 1 (mod 5), so 11^14 = 1 (mod 5). Therefore 11^14 = 1 (mod 15). If the...

Number Theory: fibonacci - prove by induction, mathematical induction, little investigation

mathematical induction, little investigation, fibonacci sequence: Hello Evelyn To do this you need to do a little investigation. Look at the pattern (mod 3) of the fibonacci sequence. 1,1,2,0,2,2,1,0,1,1,2,0,... We notice that every 4th one is 0, and every one before a fourth one is not 0. We can t work out the next...

Number Theory: hi sir pls help in this question, sum of digits, best wishes

sum of digits, best wishes, tens: Hello Vino Take x as the units digit; then the ten s digit is x+4. The value of the number is then 10(x+4) + x = 11x + 40. Then Sum of digits = 2x + 4 = 1/7(11x + 40) 14x + 28 = 11x + 40. I am sure you will be able to complete this easy equation and get...

Number Theory: Multiple Investment Accounts, algebraic solution, extra 3

algebraic solution, extra 3, simple interest: Hello Kenneth You won t let this one go will you. Let s start with one of the solutions for the 3 account problem. 6000 at 2%, 6000 at 3% and 18000 at 5%. If we take any equal amounts from both the 3% and 5% accounts and reinvest at 4%, this will give...

Number Theory: Number puzzle, number puzzles, number puzzle

number puzzles, number puzzle, answer number: Hi Sheila I don t normally answer number puzzles, but since my wife is Sheila, I ll make an exception. 12786 - 9453 = 3333. It isn t the only answer. The order of the last 3 digits can be changed in the same way in both of the left hand side numbers to...

Number Theory: Number Theory: Sums of 2 squares, infinite descent, sum of two squares

infinite descent, sum of two squares, fermat: Hello Terry First we need to prove or assume a theorem of Fermat which states that if p is a prime of the form 4k + 1, it is expressible as the sum of two squares. Take your pick from those at http://en.wikipedia.org/wiki/Proofs_of_Fermat%27s_theorem_on_sums_of_two_squares#Euler.27s_proof_by_infinite_descent...

Number Theory: number theory, diophantine, quadratic

diophantine, quadratic, homogeneous: Hello Theresa I can give a solution of this problem, but there may be a much simpler one. n^2 + m = a^2, n^2 - m = b^2. Then a^2 - n^2 = n^2 - b^2 and factorising (a-n)(a+n) = (n-b)(n+b). This can be written (a-n)/(n-b) = (n+b)/(a+n) = p/q where (p,q)...

Number Theory: proof by induction, summation sign, mathematical induction

summation sign, mathematical induction, saravia: Hello Evelyn I think you must be confusing the notation. = is less than or equals. n! is never greater than n^n. What you may be thinking of is n! and a^n where a is a constant. a^n e.g. 3^n starts out larger than n! but by the time we get to 3^7 it is...

Number Theory: squaring in base 6, best wishes

best wishes: Hello Jared The calculation is the sum of 9 multiplications. 200*200 = 40000 200*30 = 10000 (2*3) = 10 200*5 = 1400 (2*5) = 14 30*200 = 10000 30*30 = 1300 30*5 = 230 5*200 = 1400 5*30 = 230 5*5 = 41 Now we add to...

Number Theory: Possible ways of eliminating for a prime number, fortran code, mersenne

Number Theory: Possible ways of eliminating for a prime number, fortran code, mersenne, prime numbers

Number Theory: logarithms, laws of logs

laws of logs: Hello JKRC Your tutor must be a sadist. These are the trickiest problems I have ever seen on logs. Perhaps they are challenge problems. I assume you are familiar with the laws. I will call them A addition S subtraction M multiplier C change of base....

Number Theory: Possible ways of eliminating for a prime number, Mersenne, FLT

Mersenne, FLT, java: Hello Sastry This is an impossibly difficult question. On September 6th, the 46th known Mersenne prime, 237,156,667-1, a 11,185,272 digit number was found by Hans-Michael Elvenich in Langenfeld near Cologne, Germany! This was the first Mersenne prime to...

Number Theory: prime numbers and divisibility, arithmetic series, perfect square

arithmetic series, perfect square, divisibility: Hello Jackie The sum you require is 3+9+15+...999. That is, the odd multiples of 3. It is an arithmetic series with 167 terms so the sum is 167/2(3+999) = 83667. There are no even numbers in the list as double an even number would be divisible by 4....

Number Theory: clarification, cubic equation, factor theorem

cubic equation, factor theorem: Hello Evelyn After multiplying by 27, you get f(x) = 27x^3 + 27x^2 - 72x + 28 = 0. It is now a matter of using the factor theorem to test for possible factors of the LHS. You should find 3x - 2 is a factor since f(2/3) = 0. Possible factors are of the...

Number Theory: prime-perfect square, squere, sequence x

Number Theory: prime-perfect square, squere, sequence x

Number Theory: finitude of primes, primes 4k-1, primes 4k-3

primes 4k-1, primes 4k-3: Hello Evelyn These are theorems in most textbooks. I ll give you an outline, but you should find the proofs in a textbook. The easy one is primes of form 4k+3. We need a lemma. A composite number of the form 4k+3 has a factor of the same form. An odd...

Number Theory: Interest & Percentages, integral values, integral solutions

integral values, integral solutions, word problem: Hello Kenneth You are still an algebraphobe then. There isn t. If we do use algebra 200 at x% and 800 at y% we arrive at the equation x + 4y = 22. x = 2, y = 5 is the solution you want, but there are others. (6,4), (10,3) and (16,2) are the other integral...

Number Theory: inequalities, AM > GM

AM > GM: Hello Angelo These are very easily proved by using the theorem that for a set of positive numbers, their arithmetic mean is greater than their geometric mean. In the first case, their product is 1, so their GM is 1, while their AM is 1/3(a/b + b/c + c/a)....