Nuclei - Result Question 59
60. The rate of radioactive disintegration at an instant for a radioactive sample of half life $2.2 \times$ $10^{9} s$ is $10^{10} s^{-1}$. The number of radioactive atoms in that sample at that instant is,
(a) $3.17 \times 10^{19}$
(b) $3.17 \times 10^{20}$
(c) $3.17 \times 10^{17}$
(d) $3.17 \times 10^{18}$
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Answer:
Correct Answer: 60. (a)
Solution:
(a) $t _{1 / 2}=\frac{\ln 2}{\lambda}=\frac{0.693}{\lambda}$
$\lambda=\frac{0.693}{2.2 \times 10^{9}}=3.15 \times 10^{-10}$
$R=\lambda N$ $N=\frac{R}{\lambda}=\frac{10^{10}}{3.15 \times 10^{-10}}=3.17 \times 10^{19}$
