Half-life of radioactive Polonium (Po) is 138.6 days. For ten lakh Polonium atoms, number of disinte

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13.Nuclei

hard

The half-life of radioactive Polonium $(Po)$ is $138.6$ days. For ten lakh Polonium atoms, the number of disintegrations in $24$ hours is

A

$2000$

B

$3000$

C

$4000$

D

$5000$

Solution

(d) $n = \frac{{24}}{{24 \times 138.6}} = \frac{1}{{138.6}};$

Now $\frac{N}{{{N_0}}} = {\left( {\frac{1}{2}} \right)^n} = {\left( {\frac{1}{2}} \right)^{1/138.6}}$

$ \Rightarrow N = 10,00000{\left( {\frac{1}{2}} \right)^{1/138.6}} = 995011$

So number of disintegration

$ = 1000000 – 995011 = 4989 \approx 5000$.

Standard 12

Physics

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