Half-life of B{i^{210}} is 5, days . What time is taken by (7/8)^{th} part of sample to decay.......

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13.Nuclei

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The half-life of $B{i^{210}}$ is $5\, days$. What time is taken by $(7/8)^{th}$ part of the sample to decay.........$days$

A

$3.4$

B

$10 $

C

$15 $

D

$20 $

Solution

(c) By using$N = {N_0}{\left( {\frac{1}{2}} \right)^{t/T}};$

where $N = \left( {1 – \frac{7}{8}} \right)\,{N_0} = \frac{1}{8}{N_0}$

So $\frac{1}{8}{N_0} = {N_0}{\left( {\frac{1}{2}} \right)^{t/T}}$

==>${\left( {\frac{1}{2}} \right)^3} = {\left( {\frac{1}{2}} \right)^{t/5}}$

==> $t =15\, days.$

Standard 12

Physics

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