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  • A radioactive sample decays by -emission. In first two seconds <img alt="' n ' \, \, \beta" src="https://entrancecor

A radioactive sample decays by \beta-emission. In first two seconds ' n ' \, \, \beta - particles are emitted and in next 2 seconds, ' 0.25 n ' \, \, \beta -particles are emitted. The half life of radioactive nuclei is

Option: 1

2sec 


Option: 2

4sec 


Option: 3

1sec


Option: 4

none


Answers (1)

best_answer

\text { Let initially No } \rightarrow \text { atoms were present }

\therefore \mathrm{n}=\mathrm{N}_0-\mathrm{N}_0 \mathrm{e}^{-\lambda(2)} \longrightarrow \text { (i) }

\text { and } 1.25 \mathrm{n}=\mathrm{N}_0-\mathrm{N}_0 \mathrm{e}^{-\lambda(2+2)} \longrightarrow \text { (ii) [Total } \beta \text { particle emitted in } 4 \text { seconds] }

Dividing (ii) by (i)

1.25=\frac{1-\mathrm{e}^{-4 \lambda}}{1-\mathrm{e}^{-2 \lambda}}

\text { On solving } e^{-2 \lambda}=\frac{1}{4}

\therefore \quad-2 \lambda=-\ln 4

\therefore \quad \frac{-2 \ln 2}{T_{\frac{1}{2}}}=-2 \ln 2

\therefore \quad \mathrm{T_{\frac{1}{2}}}=1 \ \mathrm{second}

Posted by

himanshu.meshram

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