A radioactive substance has a half life of 60, minutes . After 3, hours , fraction of atom that have

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13.Nuclei

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A radioactive substance has a half life of $60\, minutes$. After $3\, hours$, the fraction of atom that have decayed would be ......... $\%$

A

$12.5$

B

$87.5$

C

$8.5$

D

$25.1$

Solution

(b) $N = {N_0}{\left( {\frac{1}{2}} \right)^{\frac{t}{{{T_{1/2}}}}}}.$

Hence fraction of atoms decayed

$= 1 – \frac{N}{{{N_0}}} = 1 – {\left( {\frac{1}{2}} \right)^{\frac{t}{{{T_{1/2}}}}}} $

$= 1 – {\left( {\frac{1}{2}} \right)^{\frac{{3 \times 60}}{{60}}}} = \frac{7}{8}$

In percentage it is $\frac{7}{8} \times 100 = 87.5\% $

Standard 12

Physics

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