# The half life of a radioactive sample undergoing α – decay is 1.4 × 10^17 s. If the number of nuclei in the sample is

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The half life of a radioactive sample undergoing $\alpha$ – decay is 1.4 × 1017 s. If the number of nuclei in the sample is 2.0 × 1021, the activity of the sample is nearly

(1) 103 Bq

(2) 104 Bq

(3) 105 Bq

(4) 106 Bq

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Ans: (2) 104 Bq

Sol. The activity (A) is defined as the rate of decay of radioactive substance.

$A=-{dN\over dt}=N\lambda$

$A=N\times{0.693\over T}\quad$ [T is half life]

$A=2\times10^{21}\times{0.693\over 1.4\times10^{17}}$

A = 104 Bq