First slide

Radio activity

Question

In 10 hours 75% mass of a radio active sample is converted into a stable element. Then mean life of the radio active element is

Moderate

A

3.225 hr
B

7.215 hr
C

5.325 hr
D

9.125 hr

Solution

If $m_{0}$ be the original mass of radio active element and T be its half life, then after 10 hours mass of remaining radio active element will be $m_{0} / 4$
$∴ \frac{m_{0}}{4} = \frac{m_{0}}{{(2)}^{\frac{10}{T}}} \Rightarrow \frac{1}{{(2)}^{2}} = \frac{1}{{(2)}^{10 / T}} \Rightarrow \frac{10}{T} = 2 \Rightarrow T = 5 hrs$
If half life is $T$ , then $T^{1} = \frac{T}{\ln 2_{}} = \frac{5}{0 .693} hr = 7 .215 hr$

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