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13.Nuclei
medium
The ratio activity of an element becomes $\frac{{1}}{{64}} th$ of its original value in $60\, sec$. Then the half life period is ............$sec$
A
$5$
B
$10$
C
$20$
D
$30$
Solution
(b) $A = {A_0}{\left( {\frac{1}{2}} \right)^{\frac{t}{{{T_{1/2}}}}}} $
$\Rightarrow \frac{1}{{64}} = {\left( {\frac{1}{2}} \right)^{\frac{{60}}{{{T_{1/2}}}}}}$
$ \Rightarrow {\left( {\frac{1}{2}} \right)^6} = {\left( {\frac{1}{2}} \right)^{\frac{{60}}{{{T_{1/2}}}}}} $
$\Rightarrow {T_{1/2}} = 10\sec $
Standard 12
Physics
