Question: Q. 1. (i) Define the terms (i) half-life $\left(T_{1 / 2}\right.$ ) and (ii) average life $(\tau)$. Find out their relationships with the decay constant $(\lambda)$.
(ii) A radioactive nucleus has a decay constant, $\lambda=$ 0.3465 (day) $^{-1}$. How long would it take the nucleus to decay to $75 %$ of its initial amount ?
R U [Foreign 2014]
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Solution:
Ans. (i) (a) Half life : The time taken by a radioactive nuclei to reduce to half of the initial number of radio- nuclei.
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$$ \begin{aligned} & =0.66 \text { hour } \ & =0.66 \times 60 \mathrm{~min} \ & =39.6 \text { minutes } \end{aligned} $$
