Question: Q. 7. (i) Define ‘activity’ of a radioactive substance.
(ii) Two different radioactive elements with half lives $T_{1}$ and $T_{2}$ have $N_{1}$ and $N_{2}$ undecayed atoms respectively present at a given instant. Derive an expression for the ratio of their activities at this instant in terms of $N_{1}$ and $N_{2}$.
U] [Foreign I 2016]
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Solution:
Ans. (i) Number of radioactive nuclei decaying per second at any time.
$$ 1 $$
$$ \begin{array}{rlr} R_{1} & =\lambda_{1} N_{1}=\frac{0.693}{T_{1}} N_{1} & 1 / 2 \ R_{2} & =\lambda_{2} N_{2}=\frac{0.693}{T_{2}} N_{2} & 1 / 2 \ \frac{R_{1}}{R_{2}} & =\frac{N_{1}}{N_{2}} \times \frac{T_{2}}{T_{1}} & 1 \tag{1} \end{array} $$
