Question

The fraction of $C{s}^{137}$ atoms decaying in one year is $1/27$. Its mean life will be

• A. $26.5$ years
• B. $18.2$ years
• C. $13.5$ years
• D. $0.037$ years

Answer 1

The correct option is A $26.5$ years

First order decay:
$N\left(t\right)=N_o{e}^{-\lambda t}$
$\frac{26}{27}=e^{-\lambda }$
$ln\left(\frac{27}{26}\right)=\lambda$
$t_{mean}=\frac{1}{\lambda }=\frac{1}{3ln3-ln\left(26\right)}=26.5years$