During mean life of a radioactive element, fraction that disintegrates is

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13.Nuclei

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During mean life of a radioactive element, the fraction that disintegrates is

A

e

B

$\frac{1}{e}$

C

$\frac{{e - 1}}{e}$

D

$\frac{e}{{e - 1}}$

Solution

(c) By using $N = {N_0}{e^{ – \lambda t}}$ and average life time $t = \frac{1}{\lambda }$

So $N = {N_0}{e^{ – \lambda \times 1/\lambda }} = {N_0}{e^{ – 1}}$

$\Rightarrow \frac{N}{{{N_0}}} = {e^{ – 1}} = \frac{1}{e}$

Now disintegrated fraction $ = 1 – \frac{N}{{{N_0}}} = 1 – \frac{1}{e} = \frac{{e – 1}}{e}$

Standard 12

Physics

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