Half life of isotope _{11}N{a^{24}} is 15 ,hrs . How much time does it take for frac{7}{8}th of a sa

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13.Nuclei

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The half life of the isotope $_{11}N{a^{24}}$ is $15 \,hrs$. How much time does it take for $\frac{7}{8}th$ of a sample of this isotope to decay.........$hrs$

A

$75$

B

$65 $

C

$55$

D

$45$

Solution

(d) Undecayed isotope$ = 1 – \frac{{7}}{{8}} = \frac{{1}}{{8}}$

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

$\Rightarrow \left( {\frac{1}{8}} \right) = {\left( {\frac{1}{2}} \right)^{t/15}} $

$\Rightarrow \frac{t}{{15}} = 3$

or $t =45\, hours$

Standard 12

Physics

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