SATHEE: nuclei Question 34

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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.

$1$

$\begin{matrix} (1) & \begin{aligned} R_{1} & = λ_{1} N_{1} = \frac{0.693}{T_{1}} N_{1} & 1 / 2 R_{2} & = λ_{2} N_{2} = \frac{0.693}{T_{2}} N_{2} & 1 / 2 \frac{R_{1}}{R_{2}} & = \frac{N_{1}}{N_{2}} \times \frac{T_{2}}{T_{1}} & 1 \end{aligned} \end{matrix}$

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