Half-life
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- Main article: Exponential decay
The half-life of a quantity subject to exponential decay is the time required for the quantity to fall to half of its initial value. The concept originated in the study of radioactive decay, but it now also occurs in many other fields.
| After # of Half-lives | Percent of quantity remaining |
|---|---|
| 0 | 100% |
| 1 | 50% |
| 2 | 25% |
| 3 | 12.5% |
| 4 | 6.25% |
| 5 | 3.125% |
| 6 | 1.5625% |
| 7 | 0.78125% |
| ... | ... |
| N | 
|
| ... | ... |
The table at right shows the reduction of the quantity in terms of the number of half-lives elapsed.
Contents |
[edit] Derivation
Quantities that are subject to exponential decay are commonly denoted by the symbol N. (This convention suggests a decaying number of discrete items. This interpretation is valid in many, but not all, cases of exponential decay.) If the quantity is denoted by the symbol N, the value of N at a time t is given by the formula:
where
is the initial value of N (at t=0)
- λ is a positive constant (the decay constant).
When t=0, the exponential is equal to 1, and N(t) is equal to . As t approaches infinity, the exponential approaches zero.
In particular, there is a time 
such that:
Substituting into the formula above, we have:
Thus the half-life is 69.3% of the mean lifetime.
[edit] Examples
- Main article: Exponential decay#Applications and examples
The generalized constant λ can represent many different specific physical quantities, depending on what process is being described.
- In an RC circuit or RL circuit, λ is the reciprocal of the circuit's time constant τ. For simple RC and RL circuits, λ equals
or 
, respectively.
- In first-order chemical reactions, λ is the reaction rate constant.
[edit] Decay by two or more processes
Some quantities decay by two processes at once (see Exponential decay#Decay by two or more processes). In a fashion similar to the previous section, we can calculate the new total half-life 
and we'll find it to be:
or, in terms of the two half-lives
where 
is the half-life of the first process, and 
is the half life of the second process.
[edit] See also
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Wiktionary:
half-life
ar:عمر النصف ca:Període de semidesintegració cs:Poločas rozpadu da:Halveringstid de:Halbwertszeit et:Poolestusaeg es:Vida media y Vida mitad eo:Duoniĝtempo eu:Semidesintegrazio-periodo fr:Demi-vie ko:반감기 id:Waktu paruh is:Helmingunartímihe:מחצית חיים hu:Felezési idő nl:Halfwaardetijdno:Halveringstid nn:Halveringstidpt:Meia-vida ru:Период полураспада sr:Време полураспада fi:Puoliintumisaika sv:Halveringstid ta:அரைவாழ்வுக் காலம் th:ครึ่งชีวิตzh:半衰期
| This page uses content from the English-language version of Wikipedia. The original article was at Half-life. The list of authors can be seen in the page history. As with Psychology Wiki, the text of Wikipedia is available under the GNU Free Documentation License. |
