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13.Nuclei
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$N$ atoms of a radioactive element emit $n$ alpha particles per second. The half life of the element is
A
$\frac{n}{N} \,sec$
B
$\frac{N}{n}\,sec$
C
$\frac{{0.693\;N}}{n}\,sec$
D
$\frac{{0.693\;n}}{N}\,sec$
Solution
(c) $\frac{{dN}}{{dt}} = – \lambda N $
$\Rightarrow n = – \lambda N$ (Given $\frac{{dN}}{{dt}} = n$)
$\therefore \lambda = – \frac{n}{N}\;\;$
$\therefore $ Half life $ = \frac{{0.693}}{\lambda } = \frac{{0.693\;N}}{n}\sec $
Standard 12
Physics
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