Half-life (symbol t ½ ) is the time required for a quantity (of substance) to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable atoms survive. The term is also used more generally to characterize any type of exponential (or, rarely, non-exponential ) decay. For example, the medical sciences refer to the biological half-life of drugs and other chemicals in the human body. The converse of half-life (in exponential growth) is doubling time .
92-537: The Gundremmingen Nuclear Power Plant was a nuclear power station in Germany. It was located in Gundremmingen , district of Günzburg , Bavaria . It was operated by Kernkraftwerk Gundremmingen GmbH, a joint operation of RWE Power AG (75%) and PreussenElektra (25%). Unit B was shut down at the end of 2017. Unit C, the last boiling water reactor in Germany, was shut down on New Year's Eve 2021, as part of
184-490: A generator that produces electricity . As of September 2023 , the International Atomic Energy Agency reported that there were 410 nuclear power reactors in operation in 32 countries around the world, and 57 nuclear power reactors under construction. Building a nuclear power plant often spans five to ten years, which can accrue significant financial costs, depending on how
276-465: A condenser. The condenser is a heat exchanger which is connected to a secondary side such as a river or a cooling tower . The water is then pumped back into the steam generator and the cycle begins again. The water-steam cycle corresponds to the Rankine cycle . The nuclear reactor is the heart of the station. In its central part, the reactor's core produces heat due to nuclear fission. With this heat,
368-442: A coolant is heated as it is pumped through the reactor and thereby removes the energy from the reactor. The heat from nuclear fission is used to raise steam, which runs through turbines , which in turn power the electrical generators. Nuclear reactors usually rely on uranium to fuel the chain reaction. Uranium is a very heavy metal that is abundant on Earth and is found in sea water as well as most rocks. Naturally occurring uranium
460-402: A facility has been completely decommissioned it is released from regulatory control, and the licensee of the station no longer has responsibility for its nuclear safety. Generally speaking, nuclear stations were originally designed for a life of about 30 years. Newer stations are designed for a 40 to 60-year operating life. The Centurion Reactor is a future class of nuclear reactor that
552-733: A first-order reaction is given by the following equation: [ A ] 0 / 2 = [ A ] 0 exp ( − k t 1 / 2 ) {\displaystyle [{\ce {A}}]_{0}/2=[{\ce {A}}]_{0}\exp(-kt_{1/2})} It can be solved for k t 1 / 2 = − ln ( [ A ] 0 / 2 [ A ] 0 ) = − ln 1 2 = ln 2 {\displaystyle kt_{1/2}=-\ln \left({\frac {[{\ce {A}}]_{0}/2}{[{\ce {A}}]_{0}}}\right)=-\ln {\frac {1}{2}}=\ln 2} For
644-407: A first-order reaction, the half-life of a reactant is independent of its initial concentration. Therefore, if the concentration of A at some arbitrary stage of the reaction is [A] , then it will have fallen to 1 / 2 [A] after a further interval of ln 2 k . {\displaystyle {\tfrac {\ln 2}{k}}.} Hence,
736-446: A human being is about 9 to 10 days, though this can be altered by behavior and other conditions. The biological half-life of caesium in human beings is between one and four months. The concept of a half-life has also been utilized for pesticides in plants , and certain authors maintain that pesticide risk and impact assessment models rely on and are sensitive to information describing dissipation from plants. In epidemiology ,
828-404: A nuclear reactor heats the reactor coolant. The coolant may be water or gas, or even liquid metal, depending on the type of reactor. The reactor coolant then goes to a steam generator and heats water to produce steam. The pressurized steam is then usually fed to a multi-stage steam turbine . After the steam turbine has expanded and partially condensed the steam, the remaining vapor is condensed in
920-483: A nuclear station is smaller than the fuel cost for operation of coal or gas plants. Since most of the cost of nuclear power plant is capital cost, there is almost no cost saving by running it at less than full capacity. Nuclear power plants are routinely used in load following mode on a large scale in France, although "it is generally accepted that this is not an ideal economic situation for nuclear stations". Unit A at
1012-516: A number of long-established projects are struggling to find financing, notably Belene in Bulgaria and the additional reactors at Cernavodă in Romania , and some potential backers have pulled out. Where cheap gas is available and its future supply relatively secure, this also poses a major problem for nuclear projects. Analysis of the economics of nuclear power must take into account who bears
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#17327723194651104-452: A plan to convert both units to load management operation , in which the electrical output ("load") is managed. On weekends, at least, these reactors are often throttled back. At the end of 1994, the operators announced agreements with the nuclear reprocessing plants at La Hague , France and Sellafield , England, and with that opted for long-term interim storage. In 1995, plutonium-containing mixed oxide fuel elements ( MOX fuel ) were for
1196-444: A previous goal aimed to reduce nuclear electricity generation share to lower than fifty percent by 2025, this target was postponed to 2035 in 2019 and ultimately discarded in 2023. Russia continues to export the most nuclear power plants in the world, with projects across various countries: as of July 2023, Russia was constructing 19 out of 22 reactors constructed by foreign vendors; however, some exporting projects were canceled due to
1288-404: A reactor building, a machine shed, and a 160 m tall cooling tower. The two units share a 170 m tall exhaust stack. Construction of Units B and C commenced on 19 July 1976. Unit B was completed on 9 March 1984, Unit C on 26 October 1984. Both reactors are designated Series 72 (for 1972, the year in which they were initially conceived). Each reactor is loaded with around 136 tonnes of fuel;
1380-591: A significantly different evaluation of the economics of new nuclear power stations. Following the 2011 Fukushima nuclear accident in Japan , costs are likely to go up for currently operating and new nuclear power stations, due to increased requirements for on-site spent fuel management and elevated design basis threats. However many designs, such as the currently under construction AP1000, use passive nuclear safety cooling systems, unlike those of Fukushima I which required active cooling systems, which largely eliminates
1472-413: A slight decrease from the 2653 TWh produced in 2021. Thirteen countries generated at least one-quarter of their electricity from nuclear sources. Notably, France relies on nuclear energy for about 70% of its electricity needs, while Ukraine , Slovakia , Belgium , and Hungary source around half their power from nuclear. Japan , which previously depended on nuclear for over a quarter of its electricity,
1564-427: A small enough volume to become supercritical. Most reactors require continuous temperature control to prevent a core meltdown , which has occurred on a few occasions through accident or natural disaster, releasing radiation and making the surrounding area uninhabitable. Plants must be defended against theft of nuclear material and attack by enemy military planes or missiles. The most serious accidents to date have been
1656-417: A substance can be complex, due to factors including accumulation in tissues , active metabolites , and receptor interactions. While a radioactive isotope decays almost perfectly according to first order kinetics, where the rate constant is a fixed number, the elimination of a substance from a living organism usually follows more complex chemical kinetics. For example, the biological half-life of water in
1748-482: A three-year research study of offshore floating nuclear power generation. In October 2022, NuScale Power and Canadian company Prodigy announced a joint project to bring a North American small modular reactor based floating plant to market. The economics of nuclear power plants is a controversial subject, and multibillion-dollar investments ride on the choice of an energy source. Nuclear power stations typically have high capital costs, but low direct fuel costs, with
1840-408: A total of three units: Nuclear power station A nuclear power plant ( NPP ), also known as a nuclear power station ( NPS ), nuclear generating station ( NGS ) or atomic power station ( APS ) is a thermal power station in which the heat source is a nuclear reactor . As is typical of thermal power stations, heat is used to generate steam that drives a steam turbine connected to
1932-580: A worldwide perspective, long-term waste storage costs are uncertain. Construction, or capital cost aside, measures to mitigate global warming such as a carbon tax or carbon emissions trading , increasingly favor the economics of nuclear power. Further efficiencies are hoped to be achieved through more advanced reactor designs, Generation III reactors promise to be at least 17% more fuel efficient, and have lower capital costs, while Generation IV reactors promise further gains in fuel efficiency and significant reductions in nuclear waste. In Eastern Europe,
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#17327723194652024-399: Is a half-life describing any exponential-decay process. For example: The term "half-life" is almost exclusively used for decay processes that are exponential (such as radioactive decay or the other examples above), or approximately exponential (such as biological half-life discussed below). In a decay process that is not even close to exponential, the half-life will change dramatically while
2116-434: Is about 1/3 of solar and 1/45 of natural gas and 1/75 of coal . Newer models, like HPR1000 , produce even less carbon dioxide during the whole operating life, as little as 1/8 of power plants using gen II reactors for 1.31g/kWh. Half-life The original term, half-life period , dating to Ernest Rutherford 's discovery of the principle in 1907, was shortened to half-life in the early 1950s. Rutherford applied
2208-527: Is anticipated to resume similar levels of nuclear energy utilization. Over the last 15 years, the United States has seen a significant improvement in the operational performance of its nuclear power plants, enhancing their utilization and efficiency, adding the output equivalent to 19 new 1000 MWe reactors without actual construction. In France, nuclear power plants still produce over sixty percent of this country's total power generation in 2022. While
2300-503: Is being designed to last 100 years. One of the major limiting wear factors is the deterioration of the reactor's pressure vessel under the action of neutron bombardment, however in 2018 Rosatom announced it had developed a thermal annealing technique for reactor pressure vessels which ameliorates radiation damage and extends service life by between 15 and 30 years. Nuclear stations are used primarily for base load because of economic considerations. The fuel cost of operations for
2392-431: Is found in two different isotopes : uranium-238 (U-238), accounting for 99.3% and uranium-235 (U-235) accounting for about 0.7%. U-238 has 146 neutrons and U-235 has 143 neutrons. Different isotopes have different behaviors. For instance, U-235 is fissile which means that it is easily split and gives off a lot of energy making it ideal for nuclear energy. On the other hand, U-238 does not have that property despite it being
2484-457: Is proportional to the square of the concentration. By integrating this rate, it can be shown that the concentration [A] of the reactant decreases following this formula: 1 [ A ] = k t + 1 [ A ] 0 {\displaystyle {\frac {1}{[{\ce {A}}]}}=kt+{\frac {1}{[{\ce {A}}]_{0}}}} We replace [A] for 1 / 2 [A] 0 in order to calculate
2576-429: Is the only nuclear facility that does not use a natural body of water for cooling, instead it uses treated sewage from the greater Phoenix metropolitan area. The water coming from the cooling body of water is either pumped back to the water source at a warmer temperature or returns to a cooling tower where it either cools for more uses or evaporates into water vapor that rises out the top of the tower. The water level in
2668-421: Is the time it takes for a substance (drug, radioactive nuclide, or other) to lose one-half of its pharmacologic, physiologic, or radiological activity. In a medical context, the half-life may also describe the time that it takes for the concentration of a substance in blood plasma to reach one-half of its steady-state value (the "plasma half-life"). The relationship between the biological and plasma half-lives of
2760-402: Is the time required for exactly half of the entities to decay on average ". In other words, the probability of a radioactive atom decaying within its half-life is 50%. For example, the accompanying image is a simulation of many identical atoms undergoing radioactive decay. Note that after one half-life there are not exactly one-half of the atoms remaining, only approximately , because of
2852-489: The BWR , the steam is directed into the suppression chamber and condenses there. The chambers on a heat exchanger are connected to the intermediate cooling circuit. The main condenser is a large cross-flow shell and tube heat exchanger that takes wet vapor, a mixture of liquid water and steam at saturation conditions, from the turbine-generator exhaust and condenses it back into sub-cooled liquid water so it can be pumped back to
Gundremmingen Nuclear Power Plant - Misplaced Pages Continue
2944-513: The German nuclear phase out . However, Gundremmingen unit C as well as the other two German nuclear reactors shut down that day ( Brokdorf and Grohnde ) remained capable of restarting operations in March 2022. In November 1975, Unit A was the site of the first fatal accident in a nuclear power plant in Germany, though the accident was unrelated to radiation. After a later major incident in 1977, Unit A
3036-496: The Russian invasion of Ukraine . Meanwhile, China continues to advance in nuclear energy: having 25 reactors under construction by late 2023, China is the country with the most reactors being built at one time in the world. Nuclear decommissioning is the dismantling of a nuclear power station and decontamination of the site to a state no longer requiring protection from radiation for the general public. The main difference from
3128-801: The Soviet Union . The world's first full scale power station, Calder Hall in the United Kingdom , opened on October 17, 1956 and was also meant to produce plutonium . The world's first full scale power station solely devoted to electricity production was the Shippingport Atomic Power Station in Pennsylvania , United States, which was connected to the grid on December 18, 1957. The conversion to electrical energy takes place indirectly, as in conventional thermal power stations. The fission in
3220-678: The UAE launched the Arab region's first-ever nuclear energy plant. Unit 1 of the Barakah plant in the Al Dhafrah region of Abu Dhabi commenced generating heat on the first day of its launch, while the remaining 3 Units are being built. However, Nuclear Consulting Group head, Paul Dorfman, warned the Gulf nation's investment into the plant as a risk "further destabilizing the volatile Gulf region, damaging
3312-424: The 1970s and 1980s, when it "reached an intensity unprecedented in the history of technology controversies," in some countries. Proponents argue that nuclear power is a sustainable energy source which reduces carbon emissions and can increase energy security if its use supplants a dependence on imported fuels. Proponents advance the notion that nuclear power produces virtually no air pollution, in contrast to
3404-485: The 1979 Three Mile Island accident , the 1986 Chernobyl disaster , and the 2011 Fukushima Daiichi nuclear disaster , corresponding to the beginning of the operation of generation II reactors . Professor of sociology Charles Perrow states that multiple and unexpected failures are built into society's complex and tightly coupled nuclear reactor systems. Such accidents are unavoidable and cannot be designed around. An interdisciplinary team from MIT has estimated that given
3496-572: The Brussels supplementary convention, and the Vienna Convention on Civil Liability for Nuclear Damage . However states with a majority of the world's nuclear power stations, including the U.S., Russia, China and Japan, are not party to international nuclear liability conventions. The nuclear power debate about the deployment and use of nuclear fission reactors to generate electricity from nuclear fuel for civilian purposes peaked during
3588-417: The analogous formula is: 1 T 1 / 2 = 1 t 1 + 1 t 2 + 1 t 3 + ⋯ {\displaystyle {\frac {1}{T_{1/2}}}={\frac {1}{t_{1}}}+{\frac {1}{t_{2}}}+{\frac {1}{t_{3}}}+\cdots } For a proof of these formulas, see Exponential decay § Decay by two or more processes . There
3680-516: The building. The water, and also the gases, were later released from the building into the environment. Political and regulatory bodies required that in addition to repairs, the unit's control and safety systems be modernized. Because modernization would have required an investment of 180 million DM, and since Units B and C were already under construction, the operating authorities later decided not to return Unit A to service. The contaminated steel parts were contained in protective castings and removed to
3772-557: The chief viable alternative of fossil fuel. Proponents also believe that nuclear power is the only viable course to achieve energy independence for most Western countries. They emphasize that the risks of storing waste are small and can be further reduced by using the latest technology in newer reactors, and the operational safety record in the Western world is excellent when compared to the other major kinds of power plants. Opponents say that nuclear power poses many threats to people and
Gundremmingen Nuclear Power Plant - Misplaced Pages Continue
3864-732: The city's drinking water supply in the Lech estuary, the plant was instead located approximately 50 km up-river in Gundremmingen, between Dillingen an der Donau and Günzburg . The plant was proposed on 13 July 1962, quickly approved, on 14 December 1962, and placed in service in December 1966. A protest group, the Notgemeinschaft Atom-Kraftwerk Gundremmingen-Offingen (Gundremmingen-Offingen Atomic Power Plant Emergency Organization)
3956-493: The costs of fuel extraction, processing, use and spent fuel storage internalized costs. Therefore, comparison with other power generation methods is strongly dependent on assumptions about construction timescales and capital financing for nuclear stations. Cost estimates take into account station decommissioning and nuclear waste storage or recycling costs in the United States due to the Price Anderson Act . With
4048-418: The decay is happening. In this situation it is generally uncommon to talk about half-life in the first place, but sometimes people will describe the decay in terms of its "first half-life", "second half-life", etc., where the first half-life is defined as the time required for decay from the initial value to 50%, the second half-life is from 50% to 25%, and so on. A biological half-life or elimination half-life
4140-419: The decay of discrete entities, such as radioactive atoms. In that case, it does not work to use the definition that states "half-life is the time required for exactly half of the entities to decay". For example, if there is just one radioactive atom, and its half-life is one second, there will not be "half of an atom" left after one second. Instead, the half-life is defined in terms of probability : "Half-life
4232-424: The destruction of a turbine in operation from flying towards the reactor. In the case of a pressurized water reactor, the steam turbine is separated from the nuclear system. To detect a leak in the steam generator and thus the passage of radioactive water at an early stage, an activity meter is mounted to track the outlet steam of the steam generator. In contrast, boiling water reactors pass radioactive water through
4324-458: The dismantling of other power stations is the presence of radioactive material that requires special precautions to remove and safely relocate to a waste repository. Decommissioning involves many administrative and technical actions. It includes all clean-up of radioactivity and progressive demolition of the station. Once a facility is decommissioned, there should no longer be any danger of a radioactive accident or to any persons visiting it. After
4416-534: The energy-intensive stages of the nuclear fuel chain are considered, from uranium mining to nuclear decommissioning , nuclear power is not a low-carbon electricity source despite the possibility of refinement and long-term storage being powered by a nuclear facility. Those countries that do not contain uranium mines cannot achieve energy independence through existing nuclear power technologies. Actual construction costs often exceed estimates, and spent fuel management costs are difficult to define. On 1 August 2020,
4508-402: The environment and raising the possibility of nuclear proliferation." Nuclear power plants do not produce greenhouse gases during operation. Older nuclear power plants, like ones using second-generation reactors , produce approximately the same amount of carbon dioxide during the whole life cycle of nuclear power plants for an average of about 11g/kWh, as much power generated by wind , which
4600-775: The environment, and that costs do not justify benefits. Threats include health risks and environmental damage from uranium mining , processing and transport, the risk of nuclear weapons proliferation or sabotage, and the problem of radioactive nuclear waste . Another environmental issue is discharge of hot water into the sea. The hot water modifies the environmental conditions for marine flora and fauna. They also contend that reactors themselves are enormously complex machines where many things can and do go wrong, and there have been many serious nuclear accidents . Critics do not believe that these risks can be reduced through new technology , despite rapid advancements in containment procedures and storage methods. Opponents argue that when all
4692-411: The environment. In addition, many reactors are equipped with a dome of concrete to protect the reactor against both internal casualties and external impacts. The purpose of the steam turbine is to convert the heat contained in steam into mechanical energy. The engine house with the steam turbine is usually structurally separated from the main reactor building. It is aligned so as to prevent debris from
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#17327723194654784-525: The expected growth of nuclear power from 2005 to 2055, at least four serious nuclear accidents would be expected in that period. The MIT study does not take into account improvements in safety since 1970. Nuclear power works under an insurance framework that limits or structures accident liabilities in accordance with the Paris Convention on Third Party Liability in the Field of Nuclear Energy ,
4876-479: The first time used on a large scale in boiling water reactors. Their increased radiation has been repeatedly criticized by environmental protection groups, which have registered around 40,000 protests. Utilization of these fuel elements enables more effective use of available uranium through reprocessing. The operators must guarantee that the reactor can be safely shut down under all operating conditions. And at least once every operating period and upon every alteration to
4968-859: The following four equivalent formulas: N ( t ) = N 0 ( 1 2 ) t t 1 / 2 N ( t ) = N 0 2 − t t 1 / 2 N ( t ) = N 0 e − t τ N ( t ) = N 0 e − λ t {\displaystyle {\begin{aligned}N(t)&=N_{0}\left({\frac {1}{2}}\right)^{\frac {t}{t_{1/2}}}\\N(t)&=N_{0}2^{-{\frac {t}{t_{1/2}}}}\\N(t)&=N_{0}e^{-{\frac {t}{\tau }}}\\N(t)&=N_{0}e^{-\lambda t}\end{aligned}}} where The three parameters t ½ , τ , and λ are directly related in
5060-462: The following way: t 1 / 2 = ln ( 2 ) λ = τ ln ( 2 ) {\displaystyle t_{1/2}={\frac {\ln(2)}{\lambda }}=\tau \ln(2)} where ln(2) is the natural logarithm of 2 (approximately 0.693). In chemical kinetics , the value of the half-life depends on the reaction order : The rate of this kind of reaction does not depend on
5152-532: The fuel elements, boils, and the steam directly drives the turbines. Thus, in boiling water reactors, in contrast to pressurized water reactors , there is only a single, primary coolant loop. Each unit is loaded with 784 fuel elements. One fuel element contains approximately 174 kg uranium and consists of 100 (i.e. 10 x 10) fuel rods. Units B and C together generated a total of approximately 21,000,000,000 kWh of electricity annually. They supplied approximately 30% of Bavaria's electricity. Net electrical output
5244-428: The fuel load in the core, a report on the so-called shut-down reactivity must be submitted, as required by German safety rule KTA 3104. Measured emitted radioactivity in 2004 was 3 TBq airborne and 5 TBq waterborne. The shutdown of the Gundremmingen B reactor took place at the end of 2017; Gundremmingen C was shut down at the end of 2021. Since August 2004, an interim storage facility has been established on
5336-508: The grounds of the nuclear power plant for spent fuel elements with a heavy metal weight of 2,250 tonnes. It contains 192 storage spaces and was placed in operation in 2006. € 30 million have been budgeted for this. Construction of the building (104 m long, 38 m wide, and 18 m tall) was completed at the end of 2005. After interior fitting with electrical, heating, and ventilation equipment, installation of heavyweight hoists, and remaining exterior work, on 25 August 2006
5428-403: The half-life of a first order reaction is given as the following: t 1 / 2 = ln 2 k {\displaystyle t_{1/2}={\frac {\ln 2}{k}}} The half-life of a first order reaction is independent of its initial concentration and depends solely on the reaction rate constant, k . In second order reactions, the rate of reaction
5520-602: The half-life of second order reactions depends on the initial concentration and rate constant . Some quantities decay by two exponential-decay processes simultaneously. In this case, the actual half-life T ½ can be related to the half-lives t 1 and t 2 that the quantity would have if each of the decay processes acted in isolation: 1 T 1 / 2 = 1 t 1 + 1 t 2 {\displaystyle {\frac {1}{T_{1/2}}}={\frac {1}{t_{1}}}+{\frac {1}{t_{2}}}} For three or more processes,
5612-533: The half-life of the reactant A 1 [ A ] 0 / 2 = k t 1 / 2 + 1 [ A ] 0 {\displaystyle {\frac {1}{[{\ce {A}}]_{0}/2}}=kt_{1/2}+{\frac {1}{[{\ce {A}}]_{0}}}} and isolate the time of the half-life ( t ½ ): t 1 / 2 = 1 [ A ] 0 k {\displaystyle t_{1/2}={\frac {1}{[{\ce {A}}]_{0}k}}} This shows that
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#17327723194655704-406: The hot coolant is used as a heat source for a boiler, and the pressurized steam from that drives one or more steam turbine driven electrical generators . In the event of an emergency, safety valves can be used to prevent pipes from bursting or the reactor from exploding. The valves are designed so that they can derive all of the supplied flow rates with little increase in pressure. In the case of
5796-517: The initial investments are financed. Because of this high construction cost and lower operations, maintenance, and fuel costs, nuclear plants are usually used for base load generation, because this maximizes the hours over which the fixed cost of construction can be amortized. Nuclear power plants have a carbon footprint comparable to that of renewable energy such as solar farms and wind farms , and much lower than fossil fuels such as natural gas and coal . Nuclear power plants are among
5888-462: The interim radioactive storage location in Mitterteich . In 1983 the decision was made to dismantle the unit. Dismantling was "far advanced" in 2005 and has led to valuable experience and the development of state of the art processes for the breakdown, handling, and cleansing of radiation-contaminated materials. According to the operators, approximately 10,000 tonnes of scrap have been created in
5980-469: The interim storage facility was opened and the first containers from the power plant moved in. To minimize risk of radiation, the facility has two doors each weighing 50 tonnes and thick concrete walls, although at 85 cm they are thinner than in comparable storage facilities in North Germany (e.g. at Brokdorf 120 cm). At 55 cm, the concrete roof is likewise considerably weaker than
6072-607: The need to spend more on redundant back up safety equipment. According to the World Nuclear Association , as of March 2020: The Russian state nuclear company Rosatom is the largest player in international nuclear power market, building nuclear plants around the world. Whereas Russian oil and gas were subject to international sanctions after the Russian full-scale invasion of Ukraine in February 2022, Rosatom
6164-483: The now decommissioned German Biblis Nuclear Power Plant was designed to modulate its output 15% per minute between 40% and 100% of its nominal power. Russia has led in the practical development of floating nuclear power stations , which can be transported to the desired location and occasionally relocated or moved for easier decommissioning. In 2022, the United States Department of Energy funded
6256-439: The principle of a radioactive element's half-life in studies of age determination of rocks by measuring the decay period of radium to lead-206 . Half-life is constant over the lifetime of an exponentially decaying quantity, and it is a characteristic unit for the exponential decay equation. The accompanying table shows the reduction of a quantity as a function of the number of half-lives elapsed. A half-life often describes
6348-495: The process, of which 86% have been re-usable and 14% are to be disposed of in permanent storage as radioactive waste. In January 2006 the Bayerische Staatsministerium für Umwelt, Gesundheit und Verbraucherschutz (Bavarian State Ministry for Environment, Health, and Consumer Safety) gave permission for the construction of a "technology center" within the confines of the former Unit A - with the exception of
6440-474: The prospect that all spent nuclear fuel could potentially be recycled by using future reactors, generation IV reactors are being designed to completely close the nuclear fuel cycle . However, up to now, there has not been any actual bulk recycling of waste from a NPP, and on-site temporary storage is still being used at almost all plant sites due to construction problems for deep geological repositories . Only Finland has stable repository plans, therefore from
6532-442: The random variation in the process. Nevertheless, when there are many identical atoms decaying (right boxes), the law of large numbers suggests that it is a very good approximation to say that half of the atoms remain after one half-life. Various simple exercises can demonstrate probabilistic decay, for example involving flipping coins or running a statistical computer program . An exponential decay can be described by any of
6624-459: The reactant. Thus the concentration will decrease exponentially. [ A ] = [ A ] 0 exp ( − k t ) {\displaystyle [{\ce {A}}]=[{\ce {A}}]_{0}\exp(-kt)} as time progresses until it reaches zero, and the half-life will be constant, independent of concentration. The time t ½ for [A] to decrease from [A] 0 to 1 / 2 [A] 0 in
6716-416: The reaction elements last approximately five years. Annually, roughly a fifth of them are switched out. Water is drawn from the river via a canal 1.4 km in length; it condenses in the cooling towers at a rate of 0.7 cubic meters per second. It is returned to the river through an underground pipe. Units B and C are, like unit A, boiling water reactors . In this type of reactor, the water flows around
6808-506: The reactor building. Following conversion and modernization, the following work will be possible there: The statement of permission also allows venting of radioactive materials via the exhaust stacks. Maximum permitted annual radioactive emissions are: 50 MBq for aerosol radionuclides with half-lives greater than 8 days (excluding iodine-131 ), 0.5 Mbq for iodine-131, and 100,000 MBq for tritium . Units B and C are neighboring units of identical construction. Each consists of
6900-427: The reactor by the condensate and feedwater pumps. In the main condenser, the wet vapor turbine exhaust come into contact with thousands of tubes that have much colder water flowing through them on the other side. The cooling water typically come from a natural body of water such as a river or lake. Palo Verde Nuclear Generating Station , located in the desert about 97 kilometres (60 mi) west of Phoenix, Arizona,
6992-407: The reactor led to operational errors. Within ten minutes, there was approximately 3 meters of standing water in the reactor building and the temperature had risen to nearly 80 degrees Celsius. Through error, too much water was introduced into the reactor for emergency cooling. Pressure relief valves released between 200 and 400 cubic meters (sources vary) of radioactive coolant water into
7084-540: The risks of future uncertainties. To date all operating nuclear power stations were developed by state-owned or regulated utilities where many of the risks associated with construction costs, operating performance, fuel price, and other factors were borne by consumers rather than suppliers. Many countries have now liberalized the electricity market where these risks and the risk of cheaper competitors emerging before capital costs are recovered, are borne by station suppliers and operators rather than consumers, which leads to
7176-506: The roofs of the interim storage facilities built in North Germany (e.g. Brokdorf 130 cm). The power station operators had submitted a request to store up to 192 containers of spent nuclear fuel. With the assistance of environmental groups, neighboring residents lodged a legal complaint against the project. In a judgment dated 2 January 2006, the Bavarian Administrative Court rejected these complaints. An appeal
7268-660: The safest modes of electricity generation, comparable to solar and wind power plants. The first time that heat from a nuclear reactor was used to generate electricity was on December 21, 1951, at the Experimental Breeder Reactor I , powering four light bulbs. On June 27, 1954, the world's first nuclear power station to generate electricity for a power grid , the Obninsk Nuclear Power Plant , commenced operations in Obninsk , in
7360-407: The same element. Different isotopes also have different half-lives . U-238 has a longer half-life than U-235, so it takes longer to decay over time. This also means that U-238 is less radioactive than U-235. Since nuclear fission creates radioactivity, the reactor core is surrounded by a protective shield. This containment absorbs radiation and prevents radioactive material from being released into
7452-693: The steam generator and the nuclear reactor is controlled using the feedwater system. The feedwater pump has the task of taking the water from the condensate system, increasing the pressure and forcing it into either the steam generators—in the case of a pressurized water reactor — or directly into the reactor, for boiling water reactors . Continuous power supply to the plant is critical to ensure safe operation. Most nuclear stations require at least two distinct sources of offsite power for redundancy. These are usually provided by multiple transformers that are sufficiently separated and can receive power from multiple transmission lines. In addition, in some nuclear stations,
7544-487: The steam turbine, so the turbine is kept as part of the radiologically controlled area of the nuclear power station. The electric generator converts mechanical power supplied by the turbine into electrical power. Low-pole AC synchronous generators of high rated power are used. A cooling system removes heat from the reactor core and transports it to another area of the station, where the thermal energy can be harnessed to produce electricity or to do other useful work. Typically
7636-575: The substrate concentration , [A] . Thus the concentration decreases linearly. [ A ] = [ A ] 0 − k t {\displaystyle [{\ce {A}}]=[{\ce {A}}]_{0}-kt} In order to find the half-life, we have to replace the concentration value for the initial concentration divided by 2: [ A ] 0 / 2 = [ A ] 0 − k t 1 / 2 {\displaystyle [{\ce {A}}]_{0}/2=[{\ce {A}}]_{0}-kt_{1/2}} and isolate
7728-412: The time: t 1 / 2 = [ A ] 0 2 k {\displaystyle t_{1/2}={\frac {[{\ce {A}}]_{0}}{2k}}} This t ½ formula indicates that the half-life for a zero order reaction depends on the initial concentration and the rate constant. In first order reactions, the rate of reaction will be proportional to the concentration of
7820-477: The turbine generator can power the station's loads while the station is online, without requiring external power. This is achieved via station service transformers which tap power from the generator output before they reach the step-up transformer. Nuclear power plants generate approximately 10% of global electricity, sourced from around 440 reactors worldwide. They are recognized as a significant provider of low-carbon electricity , accounting for about one-quarter of
7912-553: The world for spent nuclear fuel, which requires safe containment for thousands of years. Since 1978, approximately one kilometer east of the nuclear power station, at 48°30'47" N, 10°25'13" E, has been the location of a 174 m tall steel and concrete tower with instruments for monitoring climatic conditions, known as the Meteo-Turm or Weather Tower. This tower also houses a ham radio digipeater with callsign DB0DLG for packet radio. The Gundremmingen Nuclear Power Plant has
8004-459: The world's supply in this category. As of 2020, nuclear power stood as the second-largest source of low-carbon energy, making up 26% of the total. Nuclear power facilities are active in 32 countries or regions, and their influence extends beyond these nations through regional transmission grids, especially in Europe. In 2022, nuclear power plants generated 2545 terawatt-hours (TWh) of electricity,
8096-723: Was 1,284 megawatts for Unit B, and 1,288 megawatts for Unit C. An increase in the output of Units B and C from a gross electrical output of 1,344 megawatts each to 1,450 megawatts was requested in September 1999 but has been suspended for years. On 19 December 2007, the Bayerisches Umweltministerium (Bavarian Ministry of the Environment) mandated an increase in performance of 160 thermal megawatts and in electricity generation of 52 megawatts. In addition, in recent years there has been
8188-519: Was never returned to service. Unit A was a boiling water reactor with an output of 237 megawatts, the first large nuclear power plant in Germany. It was in operation from December 1966 until January 1977, and generated a total of 13.79 TWh of energy during those years. Following objections by the city of Nuremberg to the original planned location on the Danube at Bertoldsheim (between Donauwörth und Neuburg an der Donau), because of protected areas for
8280-638: Was not accepted. The plaintiffs protested this decision with a complaint of non-admission to the Federal Administrative Court in Leipzig. On 24 August 2006, this motion was rejected. In addition to concern about catastrophic accidents in particular terrorist attacks, the opposition was motivated by fear that the interim storage facility might develop into an unplanned permanent storage facility, since even in 2005, despite many assurances, there still existed no permanent depository anywhere in
8372-477: Was not targeted by sanctions. However, some countries, especially in Europe, scaled back or cancelled planned nuclear power plants that were to be built by Rosatom. Modern nuclear reactor designs have had numerous safety improvements since the first-generation nuclear reactors. A nuclear power plant cannot explode like a nuclear weapon because the fuel for uranium reactors is not enriched enough, and nuclear weapons require precision explosives to force fuel into
8464-438: Was silenced using monies specifically set aside for the purpose. In 1975 an incident occurred in which two workers were killed by escaping steam: it was the first fatal accident in a nuclear power plant in Germany. On 13 January 1977 a serious incident occurred that resulted in the total loss of Unit A. In cold, damp weather, two high-voltage lines carrying electricity from the plant short-circuited. The ensuing rapid shutdown of
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