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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
2526:
A biological half-life or elimination half-life 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
2511:
discussed below). In a decay process that is not even close to exponential, the half-life will change dramatically while 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
2399:
2549:
While a radioactive isotope decays almost perfectly according to so-called "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.
1744:
883:{\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}}}
2289:
1884:
In second order reactions, the rate of reaction is proportional to the square of the concentration. By integrating this rate, it can be shown that the concentration of the reactant decreases following this formula:
549:
Simulation of many identical atoms undergoing radioactive decay, starting with either 4 atoms per box (left) or 400 (right). The number at the top is how many half-lives have elapsed. Note the consequence of the
2091:
1061:
629:
1961:
2579:, the concept of half-life can refer to the length of time for the number of incident cases in a disease outbreak to drop by half, particularly if the dynamics of the outbreak can be modeled
2512:
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.
2479:, the half-life of a species is the time it takes for the concentration of that substance to fall to half of its initial value. In a first-order reaction the half-life of the reactant is
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2168:
1870:
1600:
1374:
2507:
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
1808:
1304:
546:
2553:
For example, the biological half-life of water in a human being is about 9 to 10 days, though this can be altered by behavior and other conditions. The biological half-life of
1605:
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1216:
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2985:
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In first order reactions, the rate of reaction will be proportional to the concentration of the reactant. Thus the concentration will decrease exponentially.
448:
583:
For example, the accompanying image is a simulation of many identical atoms undergoing radioactive decay. Note that after one half-life there are not
983:
1990:
2979:
537:
for the exponential decay equation. The accompanying table shows the reduction of a quantity as a function of the number of half-lives elapsed.
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3396:
1746:
For a first-order reaction, the half-life of a reactant is independent of its initial concentration. Therefore, if the concentration of
1890:
2534:
The relationship between the biological and plasma half-lives of a substance can be complex, due to factors including accumulation in
1872:
The half-life of a first order reaction is independent of its initial concentration and depends solely on the reaction rate constant,
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2991:
441:
1819:
591:, because of the random variation in the process. Nevertheless, when there are many identical atoms decaying (right boxes), the
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1505:
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602:
Various simple exercises can demonstrate probabilistic decay, for example involving flipping coins or running a statistical
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3305:
1385:
formula indicates that the half-life for a zero order reaction depends on the initial concentration and the rate constant.
2717:
475:) is the time required for a quantity (of substance) to reduce to half of its initial value. The term is commonly used in
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1221:
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1218:
In order to find the half-life, we have to replace the concentration value for the initial concentration divided by 2:
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Some quantities decay by two exponential-decay processes simultaneously. In this case, the actual half-life
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as time progresses until it reaches zero, and the half-life will be constant, independent of concentration.
1105:
2957:
The
Medical Department of the United States Army in the World War, vol. IX: Communicable and Other Diseases
376:
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3228:
2992:
Researchers Nikhef and UvA measure slowest radioactive decay ever: Xe-124 with 18 billion trillion years
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3460:
3315:
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2652:
2427:
the half-life is the length of time after which there is a 50% chance that an atom will have undergone
367:
31:
17:
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3198:
2576:
2394:{\displaystyle {\frac {1}{T_{1/2}}}={\frac {1}{t_{1}}}+{\frac {1}{t_{2}}}+{\frac {1}{t_{3}}}+\cdots }
499:
of drugs and other chemicals in the human body. The converse of half-life (in exponential growth) is
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3193:
3057:
2999:
Interactive radioactive decay simulator demonstrating how half-life is related to the rate of decay
487:
or how long stable atoms survive. The term is also used more generally to characterize any type of
422:
903:
is the initial quantity of the substance that will decay (this quantity may be measured in grams,
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3017:
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2170:
This shows that the half-life of second order reactions depends on the initial concentration and
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2508:
1739:{\displaystyle kt_{1/2}=-\ln \left({\frac {_{0}/2}{_{0}}}\right)=-\ln {\frac {1}{2}}=\ln 2}
592:
551:
533:
Half-life is constant over the lifetime of an exponentially decaying quantity, and it is a
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Fantke, Peter; Gillespie, Brenda W.; Juraske, Ronnie; Jolliet, Olivier (11 July 2014).
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620:
An exponential decay can be described by any of the following four equivalent formulas:
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615:
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321:
300:
2682:"Re: What happens during half-lifes [sic] when there is only one atom left?"
522:
half-life in studies of age determination of rocks by measuring the decay period of
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2900:
2535:
2436:
603:
519:
30:
This article is about the scientific and mathematical concept. For other uses, see
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3432:
3248:
3160:
3150:
3002:
942:
476:
2858:"Tebufenozide in the product Mimic 700 WP Insecticide, Mimic 240 SC Insecticide"
2209:
that the quantity would have if each of the decay processes acted in isolation:
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3253:
3243:
3165:
3155:
3125:
2428:
956:
572:
405:
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3130:
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2572:
rely on and are sensitive to information describing dissipation from plants.
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1084:
946:
500:
2419:
There is a half-life describing any exponential-decay process. For example:
570:: "Half-life is the time required for exactly half of the entities to decay
3350:
3310:
3175:
2924:
2528:
2856:
Australian
Pesticides and Veterinary Medicines Authority (31 March 2015).
2284:{\displaystyle {\frac {1}{T_{1/2}}}={\frac {1}{t_{1}}}+{\frac {1}{t_{2}}}}
554:: with more atoms, the overall decay is more regular and more predictable.
3092:
1812:
Hence, the half-life of a first order reaction is given as the following:
1750:
at some arbitrary stage of the reaction is , then it will have fallen to
904:
567:
400:
920:
is the quantity that still remains and has not yet decayed after a time
3140:
3087:
2539:
2472:
tends to be used rather than "half-life", but they mean the same thing.
2447:
2443:
2905:
2880:
2531:
to reach one-half of its steady-state value (the "plasma half-life").
518:
in the early 1950s. Rutherford applied the principle of a radioactive
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3135:
3082:
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3033:
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2959:. Washington: U.S.: U.S. Government Printing Office. pp. 116–7.
285:
3077:
3062:
1154:
1095:
The rate of this kind of reaction does not depend on the substrate
527:
492:
2857:
3355:
2718:"Assignment #2: Data, Simulations, and Analytic Science in Decay"
2554:
2432:
2939:
545:
523:
2086:{\displaystyle {\frac {1}{_{0}/2}}=kt_{1/2}+{\frac {1}{_{0}}}}
1056:{\displaystyle t_{1/2}={\frac {\ln(2)}{\lambda }}=\tau \ln(2)}
609:
3180:
3067:
2881:"Estimating Half-Lives for Pesticide Dissipation from Plants"
2878:
2565:
1502:
in a first-order reaction is given by the following equation:
580:
of a radioactive atom decaying within its half-life is 50%.
2776:
480:
2720:. Astro.GLU.edu. Archived from the original on 2011-09-29.
599:
to say that half of the atoms remain after one half-life.
514:'s discovery of the principle in 1907, was shortened to
495:) decay. For example, the medical sciences refer to the
2941:
The SIR Model When S(t) is a Multi-Exponential
Function
2293:
For three or more processes, the analogous formula is:
27:
Time for exponential decay to remove half of a quantity
2997:
https://academo.org/demos/radioactive-decay-simulator/
2560:
The concept of a half-life has also been utilized for
1778:
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1993:
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627:
2974:
https://www.calculator.net/half-life-calculator.html
1984:
in order to calculate the half-life of the reactant
3032:
2639:
2415:Exponential decay § Applications and examples
2403:Exponential decay § Decay by two or more processes
2393:
2283:
2162:
2085:
1956:{\displaystyle {\frac {1}{}}=kt+{\frac {1}{_{0}}}}
1955:
1864:
1802:
1738:
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1368:
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1210:
1145:
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3484:
2557:in human beings is between one and four months.
2435:, and is usually determined experimentally. See
2431:decay. It varies depending on the atom type and
1074:
2679:
1099:, . Thus the concentration decreases linearly.
2810:. Demos Medical Publishing, LLC. p. 251.
2515:
566:Instead, the half-life is defined in terms of
3018:
2835:. New Jersey: World Scientific. p. 451.
442:
2715:
2647:Physics and Technology for Future Presidents
1083:, the value of the half-life depends on the
563:be "half of an atom" left after one second.
2570:pesticide risk and impact assessment models
2502:
610:Formulas for half-life in exponential decay
3025:
3011:
2944:(Thesis). East Tennessee State University.
2938:Balkew, Teshome Mogessie (December 2010).
2468:, respectively. For this example the term
2163:{\displaystyle t_{1/2}={\frac {1}{_{0}k}}}
1865:{\displaystyle t_{1/2}={\frac {\ln 2}{k}}}
1595:{\displaystyle _{0}/2=_{0}\exp(-kt_{1/2})}
1369:{\displaystyle t_{1/2}={\frac {_{0}}{2k}}}
980:are directly related in the following way:
935:is the half-life of the decaying quantity,
449:
435:
2914:
2904:
2833:Water: Molecular Structure and Properties
2750:Nuclear- and Radiochemistry: Introduction
2598:List of radioactive nuclides by half-life
1879:
544:
2954:
2948:
2743:
2741:
2093:and isolate the time of the half-life (
1388:
540:
14:
3485:
3366:Wireless electronic devices and health
2937:
2931:
2885:Environmental Science & Technology
2849:
2777:Jonathan Crowe; Tony Bradshaw (2014).
1090:
587:one-half of the atoms remaining, only
3006:
2747:
3392:List of civilian radiation accidents
3361:Wireless device radiation and health
3356:Biological dose units and quantities
3306:Electromagnetic radiation and health
2830:
2738:
2568:, and certain authors maintain that
1803:{\displaystyle {\tfrac {\ln 2}{k}}.}
1299:{\displaystyle _{0}/2=_{0}-kt_{1/2}}
2872:
2748:Rösch, Frank (September 12, 2014).
2633:
2630:(1989), Cambridge University Press.
2401:For a proof of these formulas, see
24:
3341:Radioactivity in the life sciences
2976:Comprehensive half-life calculator
2797:
2680:Chivers, Sidney (March 16, 2003).
25:
3519:
2967:
2191:can be related to the half-lives
479:to describe how quickly unstable
2986:System Dynamics – Time Constants
2982:, Nucleonica.net (archived 2016)
955:is a positive number called the
284:
2716:Wallin, John (September 1996).
2442:The current flowing through an
2824:
2770:
2709:
2688:
2673:
2620:
2178:Decay by two or more processes
2145:
2136:
2071:
2062:
2009:
2000:
1941:
1932:
1908:
1900:
1686:
1677:
1658:
1649:
1589:
1562:
1547:
1538:
1518:
1509:
1456:{\displaystyle =_{0}\exp(-kt)}
1450:
1438:
1423:
1414:
1408:
1400:
1346:
1337:
1263:
1254:
1234:
1225:
1190:
1181:
1175:
1167:
1120:
1112:
1050:
1044:
1023:
1017:
840:
834:
787:
781:
719:
713:
641:
635:
36:
13:
1:
2613:
1075:Half-life and reaction orders
385:Lindemann–Weierstrass theorem
2804:Lin VW; Cardenas DD (2003).
1768:after a further interval of
7:
3229:Cosmic background radiation
2783:. OUP Oxford. p. 568.
2586:
2516:In biology and pharmacology
2450:decays with a half-life of
2408:
223:
201:
179:
157:
135:
114:
93:
72:
10:
3524:
3458:
3316:Lasers and aviation safety
2653:Princeton University Press
2519:
2412:
1157:of zero order kinetics is:
613:
32:Half-life (disambiguation)
29:
3456:
3420:
3384:
3346:Radioactive contamination
3271:
3199:Electromagnetic radiation
3189:
3101:
3048:
3041:
2955:Ireland, MW, ed. (1928).
2730:: CS1 maint: unfit URL (
2696:"Radioactive-Decay Model"
959:of the decaying quantity.
949:of the decaying quantity,
907:, number of atoms, etc.),
247:
51:
3459:See also the categories
3397:1996 Costa Rica accident
3058:Acoustic radiation force
2831:Pang, Xiao-Feng (2014).
2503:In non-exponential decay
1211:{\displaystyle =_{0}-kt}
3371:Radiation heat-transfer
3224:Gravitational radiation
2860:. Australian Government
1146:{\displaystyle d/dt=-k}
1071:(approximately 0.693).
597:very good approximation
576:". In other words, the
559:one second, there will
3412:1990 Zaragoza accident
3407:1984 Moroccan accident
3376:Linear energy transfer
3050:Non-ionizing radiation
2496:reaction rate constant
2395:
2285:
2164:
2087:
1957:
1866:
1804:
1740:
1596:
1475:for to decrease from
1457:
1370:
1300:
1212:
1147:
1069:natural logarithm of 2
1057:
884:
595:suggests that it is a
555:
274:mathematical constant
3508:Temporal exponentials
3402:1987 Goiânia accident
3204:Synchrotron radiation
3194:Earth's energy budget
3176:Radioactive materials
3171:Particle accelerators
2413:Further information:
2396:
2286:
2165:
2088:
1958:
1880:Second order kinetics
1867:
1805:
1741:
1597:
1458:
1371:
1306:and isolate the time:
1301:
1213:
1148:
1058:
963:The three parameters
885:
548:
423:Schanuel's conjecture
3473:Radiation protection
3326:Radiation protection
3214:Black-body radiation
3121:Background radiation
3036:(physics and health)
2807:Spinal cord medicine
2522:Biological half-life
2509:biological half-life
2297:
2213:
2106:
1991:
1891:
1820:
1774:
1606:
1602:It can be solved for
1506:
1397:
1389:First order kinetics
1310:
1222:
1164:
1106:
984:
625:
593:law of large numbers
552:law of large numbers
541:Probabilistic nature
497:biological half-life
306:Exponential function
267:a series of articles
3443:Radiation hardening
3385:Radiation incidents
3321:Medical radiography
3280:Radiation syndrome
3234:Cherenkov radiation
2897:2014EnST...48.8588F
2698:. Exploratorium.edu
2593:Half time (physics)
2423:As noted above, in
1091:Zero order kinetics
535:characteristic unit
506:The original term,
377:representations of
3438:Radioactive source
3259:Radiation exposure
3239:Askaryan radiation
3219:Particle radiation
3103:Ionizing radiation
2980:wiki: Decay Engine
2916:20.500.11850/91972
2643:(April 12, 2010).
2641:Muller, Richard A.
2628:20th Century Words
2608:Median lethal dose
2527:of a substance in
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1953:
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556:
3493:Chemical kinetics
3480:
3479:
3461:Radiation effects
3331:Radiation therapy
3267:
3266:
3209:Thermal radiation
3146:Neutron radiation
3111:Radioactive decay
2906:10.1021/es500434p
2891:(15): 8588–8602.
2817:978-1-888799-61-3
2763:978-3-11-022191-6
2754:Walter de Gruyter
2490:(also denoted as
2477:chemical reaction
2425:radioactive decay
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1081:chemical kinetics
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616:Exponential decay
512:Ernest Rutherford
485:radioactive decay
459:
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322:compound interest
301:Natural logarithm
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16:(Redirected from
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3421:Related articles
3336:Radiation damage
3161:Nuclear reactors
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2437:List of nuclides
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1963:We replace for
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934:
923:
919:
902:
889:
887:
886:
881:
879:
875:
874:
859:
858:
826:
825:
824:
816:
806:
805:
773:
772:
771:
769:
768:
764:
748:
738:
737:
705:
704:
702:
701:
697:
681:
679:
675:
667:
660:
659:
604:computer program
508:half-life period
474:
451:
444:
437:
380:
371:
360:
327:Euler's identity
288:
279:
262:
261:
256:
255:
251:
245:
244:
240:
234:
221:
220:
216:
199:
198:
194:
177:
176:
172:
155:
154:
150:
133:
132:
128:
112:
111:
107:
91:
90:
86:
70:
69:
65:
37:
21:
3523:
3522:
3518:
3517:
3516:
3514:
3513:
3512:
3503:Nuclear fission
3483:
3482:
3481:
3476:
3475:
3452:
3448:Havana syndrome
3433:Nuclear physics
3416:
3380:
3273:
3263:
3249:Unruh radiation
3185:
3166:Nuclear weapons
3151:Nuclear fission
3097:
3037:
3031:
2970:
2965:
2964:
2953:
2949:
2936:
2932:
2877:
2873:
2863:
2861:
2854:
2850:
2843:
2829:
2825:
2818:
2802:
2798:
2791:
2775:
2771:
2764:
2752:. Vol. 1.
2746:
2739:
2723:
2722:
2714:
2710:
2701:
2699:
2694:
2693:
2689:
2678:
2674:
2667:
2638:
2634:
2625:
2621:
2616:
2589:
2524:
2518:
2505:
2491:
2487:
2480:
2458:
2451:
2417:
2411:
2377:
2373:
2368:
2357:
2353:
2348:
2337:
2333:
2328:
2313:
2309:
2305:
2300:
2298:
2295:
2294:
2273:
2269:
2264:
2253:
2249:
2244:
2229:
2225:
2221:
2216:
2214:
2211:
2210:
2207:
2201:
2198:
2192:
2189:
2183:
2180:
2148:
2144:
2139:
2135:
2130:
2117:
2113:
2109:
2107:
2104:
2103:
2100:
2094:
2074:
2070:
2065:
2061:
2056:
2043:
2039:
2035:
2018:
2012:
2008:
2003:
1999:
1994:
1992:
1989:
1988:
1985:
1982:
1974:
1971:
1968:
1967:
1965:
1964:
1944:
1940:
1935:
1931:
1926:
1903:
1899:
1894:
1892:
1889:
1888:
1882:
1873:
1846:
1844:
1831:
1827:
1823:
1821:
1818:
1817:
1780:
1777:
1775:
1772:
1771:
1769:
1761:
1758:
1755:
1754:
1752:
1751:
1747:
1714:
1689:
1685:
1680:
1676:
1667:
1661:
1657:
1652:
1648:
1646:
1642:
1620:
1616:
1612:
1607:
1604:
1603:
1579:
1575:
1571:
1550:
1546:
1541:
1527:
1521:
1517:
1512:
1507:
1504:
1503:
1500:
1492:
1489:
1486:
1485:
1483:
1482:
1479:
1476:
1473:
1467:
1426:
1422:
1417:
1403:
1398:
1395:
1394:
1391:
1383:
1377:
1356:
1349:
1345:
1340:
1336:
1334:
1321:
1317:
1313:
1311:
1308:
1307:
1286:
1282:
1278:
1266:
1262:
1257:
1243:
1237:
1233:
1228:
1223:
1220:
1219:
1193:
1189:
1184:
1170:
1165:
1162:
1161:
1153:The integrated
1123:
1115:
1107:
1104:
1103:
1093:
1077:
1064:
1010:
1008:
995:
991:
987:
985:
982:
981:
977:
973:
970:
964:
952:
943:positive number
938:
933:
927:
921:
910:
901:
895:
890:
877:
876:
864:
860:
854:
850:
843:
828:
827:
815:
811:
807:
801:
797:
790:
775:
774:
760:
756:
752:
747:
743:
739:
733:
729:
722:
707:
706:
693:
689:
685:
680:
666:
662:
661:
655:
651:
644:
628:
626:
623:
622:
618:
612:
543:
493:non-exponential
477:nuclear physics
472:
465:
455:
408:
378:
369:
358:
332:Euler's formula
275:
253:
249:
248:
242:
238:
237:
232:
218:
214:
213:
196:
192:
191:
174:
170:
169:
152:
148:
147:
130:
126:
125:
109:
105:
104:
88:
84:
83:
67:
63:
62:
53:
48:
43:
41:
35:
28:
23:
22:
15:
12:
11:
5:
3521:
3511:
3510:
3505:
3500:
3495:
3478:
3477:
3457:
3454:
3453:
3451:
3450:
3445:
3440:
3435:
3430:
3424:
3422:
3418:
3417:
3415:
3414:
3409:
3404:
3399:
3394:
3388:
3386:
3382:
3381:
3379:
3378:
3373:
3368:
3363:
3358:
3353:
3348:
3343:
3338:
3333:
3328:
3323:
3318:
3313:
3308:
3303:
3298:
3296:Health physics
3293:
3292:
3291:
3286:
3277:
3275:
3269:
3268:
3265:
3264:
3262:
3261:
3256:
3254:Dark radiation
3251:
3246:
3244:Bremsstrahlung
3241:
3236:
3231:
3226:
3221:
3216:
3211:
3206:
3201:
3196:
3190:
3187:
3186:
3184:
3183:
3178:
3173:
3168:
3163:
3158:
3156:Nuclear fusion
3153:
3148:
3143:
3138:
3133:
3128:
3126:Alpha particle
3123:
3118:
3113:
3107:
3105:
3099:
3098:
3096:
3095:
3090:
3085:
3080:
3075:
3070:
3065:
3060:
3054:
3052:
3043:
3039:
3038:
3030:
3029:
3022:
3015:
3007:
3001:
3000:
2994:
2989:
2988:, Bucknell.edu
2983:
2977:
2969:
2968:External links
2966:
2963:
2962:
2947:
2930:
2871:
2848:
2841:
2823:
2816:
2796:
2789:
2769:
2762:
2737:
2708:
2687:
2672:
2665:
2632:
2618:
2617:
2615:
2612:
2611:
2610:
2605:
2600:
2595:
2588:
2585:
2546:interactions.
2517:
2514:
2504:
2501:
2500:
2499:
2473:
2440:
2410:
2407:
2390:
2387:
2380:
2376:
2372:
2367:
2360:
2356:
2352:
2347:
2340:
2336:
2332:
2327:
2320:
2316:
2312:
2308:
2304:
2276:
2272:
2268:
2263:
2256:
2252:
2248:
2243:
2236:
2232:
2228:
2224:
2220:
2205:
2196:
2187:
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2147:
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2134:
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2124:
2120:
2116:
2112:
2098:
2077:
2073:
2064:
2060:
2055:
2050:
2046:
2042:
2038:
2034:
2031:
2025:
2021:
2015:
2011:
2002:
1998:
1980:
1947:
1943:
1934:
1930:
1925:
1922:
1919:
1916:
1910:
1902:
1898:
1881:
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1707:
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1674:
1670:
1664:
1660:
1651:
1645:
1641:
1638:
1635:
1632:
1627:
1623:
1619:
1615:
1611:
1591:
1586:
1582:
1578:
1574:
1570:
1567:
1564:
1561:
1558:
1553:
1549:
1540:
1537:
1534:
1530:
1524:
1520:
1511:
1498:
1477:
1471:
1452:
1449:
1446:
1443:
1440:
1437:
1434:
1429:
1425:
1416:
1413:
1410:
1402:
1390:
1387:
1381:
1362:
1359:
1352:
1348:
1339:
1333:
1328:
1324:
1320:
1316:
1293:
1289:
1285:
1281:
1277:
1274:
1269:
1265:
1256:
1253:
1250:
1246:
1240:
1236:
1227:
1207:
1204:
1201:
1196:
1192:
1183:
1180:
1177:
1169:
1159:
1158:
1142:
1139:
1136:
1133:
1130:
1126:
1122:
1114:
1111:
1092:
1089:
1085:reaction order
1076:
1073:
1052:
1049:
1046:
1043:
1040:
1037:
1034:
1029:
1025:
1022:
1019:
1016:
1013:
1007:
1002:
998:
994:
990:
968:
961:
960:
957:decay constant
950:
936:
931:
925:
908:
899:
873:
870:
867:
863:
857:
853:
849:
846:
844:
842:
839:
836:
833:
830:
829:
822:
819:
814:
810:
804:
800:
796:
793:
791:
789:
786:
783:
780:
777:
776:
767:
763:
759:
755:
751:
746:
742:
736:
732:
728:
725:
723:
721:
718:
715:
712:
709:
708:
700:
696:
692:
688:
684:
678:
673:
670:
665:
658:
654:
650:
647:
645:
643:
640:
637:
634:
631:
630:
621:
614:Main article:
611:
608:
542:
539:
470:
457:
456:
454:
453:
446:
439:
431:
428:
427:
426:
425:
417:
416:
415:Related topics
412:
411:
410:
409:
406:Leonhard Euler
403:
395:
394:
390:
389:
388:
387:
382:
374:
362:
361:
354:
353:
352:
351:
350:
349:
334:
329:
324:
316:
315:
311:
310:
309:
308:
303:
295:
294:
290:
289:
281:
280:
271:
270:
258:
257:
246:
235:
229:
228:
225:
222:
211:
207:
206:
203:
200:
189:
185:
184:
181:
178:
167:
163:
162:
159:
156:
145:
141:
140:
137:
134:
123:
119:
118:
116:
113:
102:
98:
97:
95:
92:
81:
77:
76:
74:
71:
60:
56:
55:
50:
45:
26:
9:
6:
4:
3:
2:
3520:
3509:
3506:
3504:
3501:
3499:
3498:Radioactivity
3496:
3494:
3491:
3490:
3488:
3474:
3470:
3466:
3465:Radioactivity
3462:
3455:
3449:
3446:
3444:
3441:
3439:
3436:
3434:
3431:
3429:
3426:
3425:
3423:
3419:
3413:
3410:
3408:
3405:
3403:
3400:
3398:
3395:
3393:
3390:
3389:
3387:
3383:
3377:
3374:
3372:
3369:
3367:
3364:
3362:
3359:
3357:
3354:
3352:
3349:
3347:
3344:
3342:
3339:
3337:
3334:
3332:
3329:
3327:
3324:
3322:
3319:
3317:
3314:
3312:
3309:
3307:
3304:
3302:
3299:
3297:
3294:
3290:
3287:
3285:
3282:
3281:
3279:
3278:
3276:
3270:
3260:
3257:
3255:
3252:
3250:
3247:
3245:
3242:
3240:
3237:
3235:
3232:
3230:
3227:
3225:
3222:
3220:
3217:
3215:
3212:
3210:
3207:
3205:
3202:
3200:
3197:
3195:
3192:
3191:
3188:
3182:
3179:
3177:
3174:
3172:
3169:
3167:
3164:
3162:
3159:
3157:
3154:
3152:
3149:
3147:
3144:
3142:
3139:
3137:
3134:
3132:
3131:Beta particle
3129:
3127:
3124:
3122:
3119:
3117:
3116:Cluster decay
3114:
3112:
3109:
3108:
3106:
3104:
3100:
3094:
3091:
3089:
3086:
3084:
3081:
3079:
3076:
3074:
3071:
3069:
3066:
3064:
3061:
3059:
3056:
3055:
3053:
3051:
3047:
3044:
3042:Main articles
3040:
3035:
3028:
3023:
3021:
3016:
3014:
3009:
3008:
3005:
2998:
2995:
2993:
2990:
2987:
2984:
2981:
2978:
2975:
2972:
2971:
2958:
2951:
2943:
2942:
2934:
2926:
2922:
2917:
2912:
2907:
2902:
2898:
2894:
2890:
2886:
2882:
2875:
2859:
2852:
2844:
2842:9789814440424
2838:
2834:
2827:
2819:
2813:
2809:
2808:
2800:
2792:
2790:9780199662883
2786:
2782:
2781:
2773:
2765:
2759:
2755:
2751:
2744:
2742:
2733:
2727:
2719:
2712:
2697:
2691:
2684:. MADSCI.org.
2683:
2676:
2668:
2666:9780691135045
2662:
2658:
2654:
2649:
2648:
2642:
2636:
2629:
2623:
2619:
2609:
2606:
2604:
2603:Mean lifetime
2601:
2599:
2596:
2594:
2591:
2590:
2584:
2582:
2581:exponentially
2578:
2573:
2571:
2567:
2563:
2558:
2556:
2551:
2547:
2545:
2541:
2537:
2532:
2530:
2523:
2513:
2510:
2497:
2484:
2478:
2474:
2471:
2466:
2462:
2455:
2449:
2445:
2441:
2438:
2434:
2430:
2426:
2422:
2421:
2420:
2416:
2406:
2404:
2388:
2385:
2378:
2374:
2370:
2365:
2358:
2354:
2350:
2345:
2338:
2334:
2330:
2325:
2318:
2314:
2310:
2306:
2302:
2291:
2274:
2270:
2266:
2261:
2254:
2250:
2246:
2241:
2234:
2230:
2226:
2222:
2218:
2204:
2195:
2186:
2175:
2173:
2172:rate constant
2154:
2149:
2132:
2127:
2122:
2118:
2114:
2110:
2097:
2075:
2058:
2053:
2048:
2044:
2040:
2036:
2032:
2029:
2023:
2019:
2013:
1996:
1945:
1928:
1923:
1920:
1917:
1914:
1896:
1886:
1877:
1857:
1853:
1850:
1847:
1841:
1836:
1832:
1828:
1824:
1815:
1813:
1797:
1791:
1787:
1784:
1781:
1733:
1730:
1727:
1724:
1719:
1716:
1711:
1708:
1705:
1702:
1698:
1690:
1672:
1668:
1662:
1643:
1639:
1636:
1633:
1630:
1625:
1621:
1617:
1613:
1609:
1584:
1580:
1576:
1572:
1568:
1565:
1559:
1556:
1551:
1535:
1532:
1528:
1522:
1470:
1464:
1447:
1444:
1441:
1435:
1432:
1427:
1411:
1386:
1380:
1360:
1357:
1350:
1331:
1326:
1322:
1318:
1314:
1291:
1287:
1283:
1279:
1275:
1272:
1267:
1251:
1248:
1244:
1238:
1205:
1202:
1199:
1194:
1178:
1156:
1140:
1137:
1134:
1131:
1128:
1124:
1109:
1102:
1101:
1100:
1098:
1097:concentration
1088:
1086:
1082:
1072:
1070:
1047:
1041:
1038:
1035:
1032:
1027:
1020:
1014:
1011:
1005:
1000:
996:
992:
988:
967:
958:
951:
948:
947:mean lifetime
944:
937:
930:
926:
917:
913:
909:
906:
898:
894:
893:
892:
871:
868:
865:
861:
855:
851:
847:
845:
837:
831:
820:
817:
812:
808:
802:
798:
794:
792:
784:
778:
765:
761:
757:
753:
749:
744:
740:
734:
730:
726:
724:
716:
710:
698:
694:
690:
686:
682:
676:
671:
668:
663:
656:
652:
648:
646:
638:
632:
617:
607:
605:
600:
598:
594:
590:
589:approximately
586:
581:
579:
575:
574:
569:
564:
562:
553:
547:
538:
536:
531:
529:
525:
521:
517:
513:
509:
504:
502:
501:doubling time
498:
494:
491:(or, rarely,
490:
486:
482:
478:
473:
469:
463:
452:
447:
445:
440:
438:
433:
432:
430:
429:
424:
421:
420:
419:
418:
414:
413:
407:
404:
402:
399:
398:
397:
396:
392:
391:
386:
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3311:Laser safety
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3093:Ultraviolet
3088:Radio waves
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578:probability
568:probability
489:exponential
401:John Napier
368:proof that
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3274:and health
3272:Radiation
3141:Cosmic ray
2702:2012-04-25
2614:References
2562:pesticides
2520:See also:
2448:RL circuit
2444:RC circuit
573:on average
337:half-lives
293:Properties
54:remaining
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3428:Half-life
3301:Dosimetry
3136:Gamma ray
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3073:Starlight
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