First slide

Radio activity

Question

At any instant, the ratio of the amount of two radioactive substances is 2 : 1. If their half lives be respectively 12 h and 16 h, then after one days what will be the ratio of the substances?

Moderate

A

$\sqrt{2} : 1$
B

2 : 1
C

1 : 2
D

1 : 4

Solution

$\begin{array}{l} \frac{N_{1}}{{(N_{0})}_{1}} = \frac{1}{{(2)}^{t / T_{1}}} and \frac{N_{2}}{{(N_{0})}_{2}} = \frac{1}{{(2)}^{t / T_{2}}} \\ ∴ \frac{N_{1}}{N_{2}} . \frac{{(N_{0})}_{2}}{{(N_{0})}_{1}} = {(2)}^{t (\frac{1}{T_{2}} - \frac{1}{T_{1}})} \end{array}$
$\begin{array}{l} \Rightarrow \frac{N_{1}}{N_{2}} . (\frac{1}{2}) = {(2)}^{24 (\frac{1}{16} - \frac{1}{12})} = {(2)}^{- \frac{1}{2}} \\ \Rightarrow \frac{N_{1}}{N_{2}} = \sqrt{2} \end{array}$

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