Answer to Question #282257 in Atomic and Nuclear Physics for BIGIRMANA Elie

Question

8. A 2.71 g sample of KCl is found to be radioactive. It is decaying at a rate of 4490

Bq. The decay is traced to an isotope of potassium 40K, which constitutes 1.17% of

normal potassium. Calculate the half life of this nuclide.

Answer 1

$A=\eta \frac m M N_A\frac{\ln 2}{T^{1/2}},\implies$

$T^{1/2}=\frac{\eta mN_A \ln2}{AM}=1.25\cdot 10^9~$years.