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. $10.21\,s$
• B. $14.43\,s$
• C. $5.31\,s$
• D. $7.43 \,s$

Answer 1

Answer: (B)

$14.43\,s$

Answer 2

As the number of undecayed nuclei decreases from $25 \%$ to $12.5\%$ in $10\, s$, it shows that the half life of the sample is $10\, s$, i.e. $T_{1/2}=10\,s$ Decay constant, $\lambda=\frac{0.6931}{T_{1 /2}}=\frac{0.6931}{10\,s}$ Mean life, $\tau=\frac{1}{\lambda}=\frac{10\,s}{0.6931}=14.43\,s$