Regional Basic Professional Training Course in Korea

❙ 13 ❙
1. Nuclear Reactor Principles
The half-life (T½) of a radioactive element is the time required for one-half of the nuclei
in a sample to decay. It can be obtained by placing N = No/2 in the above equation:
No/2 = No e -λT½
[7]
Dividing by No and taking the logs, we get:
log e(½) = -λ T½ [8]
and
log e(½) = -log e (2) [9]
thus
T½ = loge(2)/ λ = 0.693 /λ [10]
Since the disintegration rate or activityof the sample is proportional to the number of
unstable nuclei, this also varies exponentially with time:
A = Ao e -λt
[11]
This relationship is illustrated in Figure 1.3, which shows the variation in sample activity
with time. In one half-life, the activity decays to one-half its initial value, or ½Ao. In two
half-lives it decays to ¼Ao, and so forth. This method can be applied to isotopes whose
disintegration rates changes appreciably over a reasonable counting period.