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.
A=ηmMNAln2T1/2, ⟹ A=\eta \frac m M N_A\frac{\ln 2}{T^{1/2}},\impliesA=ηMmNAT1/2ln2,⟹
T1/2=ηmNAln2AM=1.25⋅109 T^{1/2}=\frac{\eta mN_A \ln2}{AM}=1.25\cdot 10^9~T1/2=AMηmNAln2=1.25⋅109 years.
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