45 / 1609
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(N )t(A
λ=
and we have
)t(N )t(A
λ=
where λ is the decay constant. Combining the two equations:
dt
t dN
tA
)(
)(
−=
)t(N
dt
)t(dN
λ=
−
Integrating this differential equation results to:
)t
exp(
N )t(N
0
λ−
=
where N
0
is the (initial) number of radioactive nuclei at t=0, i.e. N
0
=N(0).