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  • The radioactive sources and half lives of <img alt="\mathrm{2\, \mathrm{h

The radioactive sources \mathrm{A} and \mathrm{B} half lives of \mathrm{2\, \mathrm{hrs}} and \mathrm{4\, \mathrm{hrs}} respectively, initially contain the same no. of radio active atoms. At the end of \mathrm{2\, \mathrm{hrs}} , their rates of disintegration are in the ratio: 

Option: 1

\mathrm{4: 1}


Option: 2

\mathrm{2:1}


Option: 3

\sqrt{2}: 1


Option: 4

1: 1


Answers (1)

best_answer

\mathrm{\text{Rate of disintegration of}\, A_1=A_0 / 2^n}.

\mathrm{\text{Rate of disintegration of}\, B_{2}= \frac{A_{0}}{2^{n}}}.

\mathrm{A_1=\frac{\lambda_1 \cdot N_0}{2} ; \, A_2=\frac{\lambda_2 N_0}{2^{1 / 2}}}

\mathrm{\frac{A_1}{A_2}=\left(\frac{\lambda_1}{\lambda_2}\right) \cdot \frac{1}{\sqrt{2}} }


\mathrm{\frac{\lambda_1}{\lambda_2}=2 \quad \Rightarrow \frac{A_1}{A_2}=\sqrt{2}: 1 }

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vishal kumar

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