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13.Nuclei
medium
The half-life of a radioactive substance is $48$ hours. How much time will it take to disintegrate to its $\frac{1}{{16}} \,th$ part ............$hour$
A
$12$
B
$16$
C
$48$
D
$192$
Solution
(d)$\frac{N}{{{N_0}}} = {\left( {\frac{1}{2}} \right)^{t/T}} \Rightarrow \frac{1}{{16}} = {\left( {\frac{1}{2}} \right)^{t/48}}$
$ \Rightarrow {\left( {\frac{1}{2}} \right)^4} = {\left( {\frac{1}{2}} \right)^{t/48}} \Rightarrow t = 192\;hour.$
Standard 12
Physics