Mean life of a radioactive sample are 30,year and 60,year for α - emission and β - emission respec

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13.Nuclei

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The mean life of a radioactive sample are $30\,year$ and $60\,year$ for $\alpha -$ emission and $\beta -$ emission respectively. If the sample decays both by $\alpha -$ emission and $\beta -$ emission simultaneously, then the time after which, only one-fourth of the sample remain is approximately ............ $years$

A

$28$

B

$20$

C

$40$

D

$45$

Solution

$\mathrm{T}_{1 / 2}=\frac{0.693}{\lambda}=\frac{0.693}{\lambda_{1}+\lambda_{2}}=\frac{0.693}{\frac{1}{30}+\frac{1}{60}}$

${=\frac{0.693 \times 30 \times 60}{90} \approx 14 \text { years }} $

For $\frac{1}{4} $ remains two half lives passed out

${\Rightarrow \mathrm{t}=2 \mathrm{T}_{1 / 2}=28 \mathrm{\,years}}$

Standard 12

Physics

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