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13.Nuclei
medium
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
$3.17 \times 10^{20}$
B
$3.17 \times 10^{19}$
C
$3.17 \times 10^{17}$
D
$3.17 \times 10^{18}$
(NEET-2019)
Solution
$T _{1 / 2}=\frac{\ln 2}{\lambda}=\frac{0.693}{\lambda}$
$2.2 \times 10^9=\frac{0.693}{\lambda}$
$\lambda=\frac{0.693}{2.2 \times 10^9}=3.15 \times 10^{-10}$
$R =\lambda N$
$N =\frac{ R }{\lambda}=\frac{10^{10}}{3.15 \times 10^{-10}}=3.17 \times 10^{19}$
Standard 12
Physics
