Everything about The Half-life totally explained
The
half-life of a quantity whose value decreases with time is the interval required for the quantity to decay to half of its initial value. The concept originated in the study of
radioactive decay which is subject to
exponential decay but applies to all phenomena including those which are described by non-exponential decays.
The term
half-life was coined in 1907, but it was always referred to as
half-life period. It wasn't until the early 1950s that the word
period was dropped from the name.
Number of
half-lives
elapsed |
Fraction
remaining |
As
power
of 2 |
As % |
| 0 |
1/1 |
1/20 |
100 |
| 1 |
1/2 |
1/21 |
50 |
| 2 |
1/4 |
1/22 |
25 |
| 3 |
1/8 |
1/23 |
12.5 |
| 4 |
1/16 |
1/24 |
6.25 |
| 5 |
1/32 |
1/25 |
3.125 |
| 6 |
1/64 |
1/26 |
1.5625 |
| 7 |
1/128 |
1/27 |
0.78125 |
| ... |
... |
... |
... |
| |
|
|
|
The table at right shows the reduction of the quantity in terms of the number of half-lives elapsed.
It can be shown that, for exponential decay, the half-life
Experimental determination
The half-life of a process can be determined easily by experiment. In fact, some methods don't require advance knowledge of the law governing the decay rate, be it exponential decay or another pattern.
Most appropriate to validate the concept of half-life for
radioactive decay, in particular when dealing with a small number of atoms, is to perform experiments and correct computer simulations. See in
(External Link
) how to test the behavior of the last atoms. Validation of physics-math models consists in comparing the model's behavior with experimental observations of real physical systems or valid simulations (physical and/or computer). The references given here describe how to test the validity of the exponential formula for small number of atoms with simple simulations, experiments, and computer code.
In radioactive decay, the exponential model
does not apply for a small number of atoms (or a small number of atoms isn't within the domain of validity of the formula or equation or table). The DIY experiments use pennies or
M&M's candies.
(External Link),
(External Link). A similar experiment is performed with isotopes of a very short half-life, for example, see Fig 5 in
(External Link). See how to write a computer program that simulates radioactive decay including the required
randomness in
(External Link) and experience the behavior of the last atoms. Of particular note, atoms undergo radioactive decay in whole units, and so after enough half-lives the remaining original quantity becomes an actual zero rather than
asymptotically approaching zero as with
continuous systems.
Further Information
Get more info on 'Half-life'.
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