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13.Nuclei
medium
The activity of a sample is $64 × 10^{-5}\, Ci.$ Its half-life is $3\, days$. The activity will become $5 × 10^{-6}\, Ci$ after .........$days$
A
$12 $
B
$7$
C
$18 $
D
$21$
Solution
(d) $A = {A_0}{\left( {\frac{1}{2}} \right)^{t/{T_{1/2}}}} \Rightarrow 5 \times {10^{ – 6}} = 64 \times {10^{ – 5}}{\left( {\frac{1}{2}} \right)^{t/3}}$
$ \Rightarrow \frac{1}{{128}} = {\left( {\frac{1}{2}} \right)^{t/3}} \Rightarrow t = 21\,days$
Standard 12
Physics
