Half life of radioactive Radon is 3.8 days. time at end of which 1/{20^{th}} of Radon sample will re

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13.Nuclei

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The half life of radioactive Radon is $3.8$ days. The time at the end of which $1/{20^{th}}$ of the Radon sample will remain undecayed is ........... $day$ (Given ${\log _{10}}e = 0.4343$)

A

$3.8$

B

$16.5$

C

$33 $

D

$76$

(IIT-1981)

Solution

(b) By the formula $N = {N_0}{e^{ – \lambda t}}$

Given $\frac{N}{{{N_0}}} = \frac{1}{{20}}$

and $\lambda = \frac{{0.6931}}{{3.8}}$

==> $20 = {e^{\frac{{0.6931 \times t}}{{3.8}}}}$

Taking $log$ of both sides

$log\, 20 = \frac{{0.6931 \times t}}{{3.8}}{\log _{10}}e$

$1.3010 = \frac{{0.6931 \times t \times 0.4343}}{{3.8}}$

==> $t = 16.5 \,days$

Standard 12

Physics

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