Question

The rate of radioactive disintegration at an instant for a radioactive same of half life $2.2 \times 10^9\,s^{-1}$ is $10^{10} \,s^{-1}$. The number of radioactive atoms in that sample at that instant is,

• A. $3.17 \times 10^{20}$
• B. $3.17 \times 10^{17}$
• C. $3.17 \times 10^{18}$
• D. $3.17 \times 10^{19}$

Answer 1

Answer: (D)

$T_{1/2} = 2.2 \times 10^9 \,s, R = 10^{10} s^{-1} , R = N\lambda$
$N = \frac{R}{\lambda} = \frac{R}{0.693}T_{1/2}$
$ = \frac{10^{10} \times 2.2 \times 10^9}{0.693}$
$ = 3.17\times 10^{19}$ atoms