Uranium-235 ( U or U-235 ) is an isotope of uranium making up about 0.72% of natural uranium . Unlike the predominant isotope uranium-238 , it is fissile , i.e., it can sustain a nuclear chain reaction . It is the only fissile isotope that exists in nature as a primordial nuclide .
31-466: Uranium-235 has a half-life of 703.8 million years. It was discovered in 1935 by Arthur Jeffrey Dempster . Its fission cross section for slow thermal neutrons is about 584.3 ± 1 barns . For fast neutrons it is on the order of 1 barn. Most neutron absorptions induce fission, though a minority (about 15%) result in the formation of uranium-236 . The fission of one atom of uranium-235 releases 202.5 MeV ( 3.24 × 10 J ) inside
62-733: 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
93-407: 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,
124-446: 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 ,
155-946: A statistical computer program . An exponential decay can be described by any of 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
186-417: 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
217-399: 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
248-405: 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 . The original term, half-life period , dating to Ernest Rutherford 's discovery of the principle in 1907,
279-457: 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
310-421: 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
341-500: The SNAP-10A and the RORSATs were powered by nuclear reactors fueled with uranium-235. Half-life 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
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#1732852810547372-417: 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
403-409: The atoms remaining, only approximately , because of 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
434-632: The chain reaction will continue. If the reaction continues to sustain itself, it is said to be critical , and the mass of U required to produce the critical condition is said to be a critical mass. A critical chain reaction can be achieved at low concentrations of U if the neutrons from fission are moderated to lower their speed, since the probability for fission with slow neutrons is greater. A fission chain reaction produces intermediate mass fragments which are highly radioactive and produce further energy by their radioactive decay . Some of them produce neutrons, called delayed neutrons , which contribute to
465-418: 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
496-3783: The fissile component of the primary stage; however, HEU (highly enriched uranium, in this case uranium that is 20% or more U) is frequently used in the secondary stage as an ignitor for the fusion fuel. U 92 235 → 7.038 × 10 8 y α Th 90 231 → 25.52 h β − Pa 91 231 → 3.276 × 10 4 y α Ac 89 227 { → 21.773 y 98.62 % β − Th 90 227 → 18.718 d α → 21.773 y 1.38 % α Fr 87 223 → 21.8 min β − } Ra 88 223 → 11.434 d α Rn 86 219 Rn 86 219 → 3.96 s α Po 84 215 { → 1.778 ms 99.99 % α Pb 82 211 → 36.1 min β − → 1.778 ms 2.3 × 10 − 4 % β − At 85 215 → 0.10 ms α } Bi 83 211 { → 2.13 min 99.73 % α Tl 81 207 → 4.77 min β − → 2.13 min 0.27 % β − Po 84 211 → 0.516 s α } Pb ( stable ) 82 207 {\displaystyle {\begin{array}{r}{\ce {^{235}_{92}U->[\alpha ][7.038\times 10^{8}\ {\ce {y}}]{^{231}_{90}Th}->[\beta ^{-}][25.52\ {\ce {h}}]{^{231}_{91}Pa}->[\alpha ][3.276\times 10^{4}\ {\ce {y}}]{^{227}_{89}Ac}}}{\begin{Bmatrix}{\ce {->[98.62\%\beta ^{-}][21.773\ {\ce {y}}]{^{227}_{90}Th}->[\alpha ][18.718\ {\ce {d}}]}}\\{\ce {->[1.38\%\alpha ][21.773\ {\ce {y}}]{^{223}_{87}Fr}->[\beta ^{-}][21.8\ {\ce {min}}]}}\end{Bmatrix}}{\ce {^{223}_{88}Ra->[\alpha ][11.434\ {\ce {d}}]{^{219}_{86}Rn}}}\\{\ce {^{219}_{86}Rn->[\alpha ][3.96\ {\ce {s}}]{^{215}_{84}Po}}}{\begin{Bmatrix}{\ce {->[99.99\%\alpha ][1.778\ {\ce {ms}}]{^{211}_{82}Pb}->[\beta ^{-}][36.1\ {\ce {min}}]}}\\{\ce {->[2.3\times 10^{-4}\%\beta ^{-}][1.778\ {\ce {ms}}]{^{215}_{85}At}->[\alpha ][0.10\ {\ce {ms}}]}}\end{Bmatrix}}{\ce {^{211}_{83}Bi}}{\begin{Bmatrix}{\ce {->[99.73\%\alpha ][2.13\ {\ce {min}}]{^{207}_{81}Tl}->[\beta ^{-}][4.77\ {\ce {min}}]}}\\{\ce {->[0.27\%\beta ^{-}][2.13\ {\ce {min}}]{^{211}_{84}Po}->[\alpha ][0.516\ {\ce {s}}]}}\end{Bmatrix}}{\ce {^{207}_{82}Pb_{(stable)}}}\end{array}}} Uranium-235 has many uses such as fuel for nuclear power plants and in nuclear weapons such as nuclear bombs . Some artificial satellites , such as
527-428: The fission chain reaction. The power output of nuclear reactors is adjusted by the location of control rods containing elements that strongly absorb neutrons, e.g., boron , cadmium , or hafnium , in the reactor core. In nuclear bombs , the reaction is uncontrolled and the large amount of energy released creates a nuclear explosion . The Little Boy gun-type atomic bomb dropped on Hiroshima on August 6, 1945,
558-462: 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
589-411: The half-life is defined in terms of probability : "Half-life 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
620-403: 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
651-602: 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,
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#1732852810547682-533: 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
713-446: The higher neutron absorption of light water. Uranium enrichment removes some of the uranium-238 and increases the proportion of uranium-235. Highly enriched uranium (HEU), which contains an even greater proportion of uranium-235, is sometimes used in the reactors of nuclear submarines , research reactors and nuclear weapons . If at least one neutron from uranium-235 fission strikes another nucleus and causes it to fission, then
744-459: 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
775-449: The reactor. That corresponds to 19.54 TJ/ mol , or 83.14 TJ/kg. Another 8.8 MeV escapes the reactor as anti-neutrinos. When 92 U nuclei are bombarded with neutrons, one of the many fission reactions that it can undergo is the following (shown in the adjacent image): Heavy water reactors and some graphite moderated reactors can use natural uranium, but light water reactors must use low enriched uranium because of
806-465: The reduction of a quantity as a function of the number of half-lives elapsed. A half-life often describes 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,
837-462: The required critical mass rapidly increasing. Use of a large tamper, implosion geometries, trigger tubes, polonium triggers, tritium enhancement, and neutron reflectors can enable a more compact, economical weapon using one-fourth or less of the nominal critical mass, though this would likely only be possible in a country that already had extensive experience in engineering nuclear weapons. Most modern nuclear weapon designs use plutonium-239 as
868-575: 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
899-412: 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
930-466: Was made of highly enriched uranium with a large tamper . The nominal spherical critical mass for an untampered U nuclear weapon is 56 kilograms (123 lb), which would form a sphere 17.32 centimetres (6.82 in) in diameter. The material must be 85% or more of U and is known as weapons grade uranium, though for a crude and inefficient weapon 20% enrichment is sufficient (called weapon(s)-usable ). Even lower enrichment can be used, but this results in
961-399: Was shortened to half-life in the early 1950s. Rutherford applied 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