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13.Nuclei
medium
The radioactive sources $A$ and $B$ have half lives of $2\ hr$ and $4\ hr$ espectively, initially contain the same number of radioactive atoms. At the end of $2\ hours$, their rates of distintegration are in the ratio
A
$4 : 1$
B
$2 : 1$
C
$\sqrt 2 : 1$
D
$1 : 1$
Solution
$\frac{A_{1}}{A_{2}}=\frac{\lambda_{1} N_{1}}{\lambda_{2} N_{2}}$
$\frac{{\left( {{N_0}{e^{\frac{{ – \ln 2}}{2} \times 2}}} \right)\frac{{\ln 2}}{2}}}{{\left( {{N_0}{e^{\frac{{ – \ln 2}}{4} \times 2}}} \right)\frac{{\ln 2}}{4}}} = \frac{{\frac{1}{2} \times 2}}{{\frac{1}{{\sqrt 2 }}}} = \sqrt 2 $
Standard 12
Physics
