First slide

Radio activity

Question

Half life of a radioactive element is T. Then what fraction of initial number of active nuclei will decay in the time interval t = T to t = 2T?

Easy

A

1/2
B

1/4
C

1/8
D

1/6

Solution

If $N_{0}$ be the initial number of active nuclei of the radio active sample, then
$N_{1} = \frac{N_{0}}{{(2)}^{\frac{T}{T}}} = \frac{N_{0}}{2}$
and $N_{2} = \frac{N_{0}}{{(2)}^{\frac{2 T}{T}}} = \frac{N_{0}}{4}$
$∴$ Required fraction $= \frac{N_{1} - N_{2}}{N_{0}} = \frac{\frac{N_{0}}{2} - \frac{N_{0}}{4}}{N_{0}} = \frac{1}{4}$

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