The Half-life of aradioactive material is the time taken for
half the radioactive nuclei in a sample to decay.
It can be shown that T = 0.693/
.
By analysing the formula it can be seen that the value of T depends only
on the decay constant
and is therefore independent of the number of atoms present N, or the
time t, at which the measurements were taken.
The concept of
Half-life can be understood by studying the diagram below.
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Measurement of Half-life
The number of radioactive nuclei in a sample falls exponentially over
time. Likewise, the activity of the sample diminishes exponentially with
time. Therefore, to measure the half-life, we measure the time taken for
the activity to drop by half. After a further half-life the activity
will have dropped by a half (to a quarter of the original value) and
after a further half-life, the activity will have dropped by a half (to
one eight of the original value).
The half-life of different radioactive substances vary greatly, as can
be seen from a few sample values in the table below.
| Radium 226 | 1620 years |
| Radon 222 | 3.8 days |
Polonium 212 |
0.0003 milli-seconds |
Measurement of Half-life
The number of radioactive nuclei in a sample falls exponentially over
time. Likewise, the activity of the sample diminishes exponentially with
time. Therefore, to measure the half-life, we measure the time taken for
the activity to drop by half. After a further half-life the activity
will have dropped by a half (to a quarter of the original value) and
after a further half-life, the activity will have dropped by a half (to
one eight of the original value).