CPB Ljubljana 2018 course book
Radioactive Decay: Activity A
Experimentally , it is found that the activity, A(t), at any instant of time t is directly proportional to the number, N(t), of the radioactive parent nuclei present at that time:
) t (A
N
)t(
where λ is the decay constant. Combining the two equations:
)t(dN
t dN )(
)t (A
N
(
)t
)t(N
tA
)(
and we have
dt
dt
Integrating this differential equation results to:
N
(
)t
N
exp(
) t
0
where N
0 is the (initial) number of radioactive nuclei at t=0, i.e. N 0
=N(0).
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