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

Question

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

Answer 1

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