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  4. Given a sample of Radium-226 having half-life of 4 days. Find the probability, a nucleus disintegrates after 2 half lives.

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Q. Given a sample of Radium-$226$ having half-life of $4$ days. Find the probability, a nucleus disintegrates after $2$ half lives.

JEE AdvancedJEE Advanced 2006

Solution:

The probability for the decay is
$1-e^{-\lambda t}$
$t =2 t_{\frac{1}{2}}=2\left(\frac{l n_{2}}{\lambda}\right) .$
Therefore,
$P$ (decay) $=1-e^{-\lambda \frac{2(\ln 2)}{\lambda}}$
$=1-e^{-l n \,4}=1-\frac{1}{4}=\frac{3}{4}$