First slide

Radio activity

Question

Ratio of initial number of active nuclei of two radio active elements x and y is 8 :1. If half life of x is 1 hour and that of y is 2 hour, find the time after which the number of active nuclei of x and y will be the same.

Moderate

A

4 hr
B

12 hr
C

6 hr
D

3 hr

Solution

$N = \frac{{(N_{0})}_{x}}{{(2)}^{\frac{t}{T}}} = \frac{(N_{0}) y}{{(2)}^{\frac{t}{2 T}}}$
$\Rightarrow \frac{{(N_{0})}_{x}}{{(N_{0})}_{y}} = \frac{{(2)}^{\frac{t}{T}}}{{(2)}^{\frac{t}{2 T}}} \Rightarrow 8 = {(2)}^{\frac{t}{2 T}} \Rightarrow \frac{t}{2 T} = 3 \Rightarrow t = 6 T = 6 \times 1 h r$

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