Question

At a given instant, there are 25% undecayed radioactive nuclei in a sample. After 10 seconds the number of undecayed nuclei reduces to $12.5\%$ the mean life of the nuclei is

• A. $10.21s$
• B. $14.43s$
• C. $5.31s$
• D. $7.43s$

Answer 1

Answer: (B)

$14.43s$

Answer 2

: as the number of un decayed nuclei decreases from 25% to $12.5\%$in 10 s, it show that the half life of the sample is 10s

$i.e.T_{12} = 10s$

Decay constant,$\lambda = \frac{0.6931}{T_{12}} = \frac{0.6931}{10s}$

Mean life , $\tau = \frac{1}{\lambda} = \frac{10s}{0.6931} = 14.43s$