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13.Nuclei
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In a radioactive sample there are $1.414 \times 10^6$ active nuclei. If they reduce to $10^6$ within $10\, minute$ then the half life of this sample will be ....... $min$
A
$5$
B
$20$
C
$15$
D
$30$
Solution
$\mathrm{N}=\frac{\mathrm{N}_{0}}{2^{\mathrm{n}}}$
$\Rightarrow 10^{6}=\frac{1.414 \times 10^{6}}{2^{\mathrm{n}}}$
$\Rightarrow 2^{n}=1.414$
$\therefore \quad n=1 / 2$
$\therefore \quad t = \frac{{{T_{1/2}}}}{2} \Rightarrow {T_{1/2}} = 20\,{\rm{mins}}$
Standard 12
Physics
