# Half-life

Number of
half-lives
elapsed
Fraction
remaining
Percentage
remaining
011100
11250
21425
31812.5
41166.25
51323.125
61641.5625
711280.78125
.........
n1/2n100/2n

Half-life (symbol t1⁄2) is the time required for a quantity to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo, or how long stable atoms survive, radioactive decay. The term is also used more generally to characterize any type of exponential or 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 is doubling time.

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.[1] Rutherford applied the principle of a radioactive element's half-life to 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.

## Probabilistic nature

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 law of large numbers: with more atoms, the overall decay is more regular and more predictable.

A half-life usually 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, 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%.[2]

For example, the image on the right 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 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.[3][4][5]

Other Languages
Afrikaans: Halfleeftyd
العربية: عمر النصف
বাংলা: অর্ধায়ু
Bân-lâm-gú: Poàn-kiám-kî
беларуская: Перыяд паўраспаду
भोजपुरी: हाफ-लाइफ
Cymraeg: Hanner oes
Deutsch: Halbwertszeit
Ελληνικά: Χρόνος ημιζωής
Esperanto: Duoniĝa tempo
فارسی: نیمه‌عمر
français: Demi-vie
Gaeilge: Leathré

한국어: 반감기
Bahasa Indonesia: Waktu paruh
íslenska: Helmingunartími
Kreyòl ayisyen: Demi-vi
Limburgs: Halveringstied
Bahasa Melayu: Separuh hayat
Nederlands: Halveringstijd

Nordfriisk: Hualewwäärstidj
norsk nynorsk: Halveringstid
occitan: Semivida
oʻzbekcha/ўзбекча: Yarim yemirilish davri
پنجابی: ادھ جیون
Plattdüütsch: Halfweertstiet
português: Meia-vida
Scots: Hauf-life
Simple English: Half-life (element)
slovenčina: Polčas premeny
slovenščina: Razpolovni čas
کوردی: نیوەتەمەن
српски / srpski: Време полураспада