In a sample of radioactive material, what percentage of initial number of active nuclei will decay d

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13.Nuclei

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In a sample of radioactive material, what percentage of the initial number of active nuclei will decay during one mean life .......... $\%$

A

$69.3$

B

$63$

C

$50$

D

$37$

Solution

(b) Number of atoms remains undecayed $N = {N_0}{e^{ – \lambda t}}$

Number of atoms decayed = ${N_0}(1 – {e^{ – \lambda t}})$

$ = \,{N_0}\,\left( {1 – {e^{ – \lambda \times \frac{1}{\lambda }}}} \right) = {N_0}\left( {1 – \frac{1}{e}} \right)$

$ = 0.63\,{N_0} = 63\% $ of $N_0$ .

Standard 12

Physics

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