Half-life of a radioactive substance is 20, min . approximate time interval left(t_{2}-t_{1}right) b

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13.Nuclei

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The half-life of a radioactive substance is $20\, min$. The approximate time interval $\left(t_{2}-t_{1}\right)$ between the time $t_{2},$ when $\frac{2}{3}$ of it has decayed and time $t_{1},$ when $\frac{1}{3}$ of it had decayed is (in $min$)

A

$14$

B

$20$

C

$28$

D

$7$

(AIIMS-2018)

Solution

$\therefore N_{1}=N_{0}-\frac{1}{3} N_{0}=\frac{2}{3} N_{0}$

and $N_{2}=N_{0}-\frac{2}{3} N_{0}=\frac{1}{3} N_{0}$

$\therefore \frac{N_{2}}{N_{1}}=\left(\frac{1}{2}\right)^{n} \Rightarrow n=1$

$\therefore t_{2}-t_{1}=$ one half-life $=20 min$

Standard 12

Physics

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