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  4. A radioactive substance emits n beta particles in the first 2 seconds and 0.5 n beta particles in the next 2 seconds. The mean life of the sample is

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Q. A radioactive substance emits $n$ beta particles in the first $2$ seconds and $0.5\, n$ beta particles in the next $2$ seconds. The mean life of the sample is

AMUAMU 2012Nuclei

Solution:

We have $\lambda=\frac{0.693}{t_{1 / 2}}$ Mean life
$\tau=\frac{1}{\lambda}=\frac{t_{1 / 2}}{0.693}$
$=\frac{2}{2.303 \log _{2}}=\frac{2}{\ln 2}$