Half-life of a substance is 10 years. In what time, it becomes frac{1}{4},th part of initial amount

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13.Nuclei

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Half-life of a substance is $10$ years. In what time, it becomes $\frac{1}{4}\,th$ part of the initial amount ........$years$

A

$5$

B

$10$

C

$20$

D

None of these

Solution

(c) $N = {N_0}{e^{ – t/{T_{1/2}}}}$

$\Rightarrow \frac{1}{4} = {e^{ – t/10}}$

$ \Rightarrow {\left( {\frac{1}{2}} \right)^2} = \frac{1}{{{e^{t/10}}}}$

$\Rightarrow t = 20\;years$

Standard 12

Physics

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