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The half life of a radioactive sample undergoing $\alpha$-decay is $1.4\times10^{17}$ s. If the number of nuclei in the sample is $2.0\times10^{21}$, the activity of the sample is nearly
A
$10^3$ Bq
B
$10^4$ Bq
C
$10^5$ Bq
D
$10^6$ Bq
Detailed Solution
Decay constant $\lambda=\dfrac{0.693}{T_{1/2}}=\dfrac{0.693}{1.4\times10^{17}}\approx4.95\times10^{-18}\ s^{-1}$. Activity $A=\lambda N=4.95\times10^{-18}\times2.0\times10^{21}\approx0.99\times10^4\approx10^4$ Bq.