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  4. In a sample of radioactive -material, what percentage of the initial number of active nuclei will decay during one mean life?

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Q. In a sample of radioactive -material, what percentage of the initial number of active nuclei will decay during one mean life?

Rajasthan PMTRajasthan PMT 2007Nuclei

Solution:

From Rutherford-Soddy law
$N=N_{0} e^{-\lambda \tau}$
$\therefore $ Using $\tau=\frac{1}{\lambda}$, we have
$N=N_{0} e^{-1}=\frac{N_{0}}{e}$
Percentage decayed $=\frac{N_{0}-N}{N_{0}} \times 100$
$=\frac{\left(N_{0}-N_{0} / e\right)}{N_{0}} \times 100 $
$=63 \%$