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13.Nuclei
medium
$1 \,mg$ gold undergoes decay with $2.7$ days half-life period, amount left after $8.1$ days is ......... $mg$
A
$0.91$
B
$0.25$
C
$0.5$
D
$0.125$
Solution
(d) $N = {N_0}{\left( {\frac{1}{2}} \right)^n} $
$\Rightarrow N = {N_0}{\left( {\frac{1}{2}} \right)^{t/{T_{1/2}}}}$
$ \Rightarrow N = 1 \times {\left( {\frac{1}{2}} \right)^{\frac{{8.1}}{{2.7}}}} = {\left( {\frac{1}{2}} \right)^3} = \frac{1}{8}$
$ \Rightarrow N = \frac{1}{8}mg = 0.125\;mg$
Standard 12
Physics
