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A radioactive sample \mathrm{S_1} having an activity of  \mathrm{5 \mu C_i}  has twice the number of nuclei as another sample \mathrm{S_2} which has an activity of \mathrm{10 \mu C_i}. The half lives of \mathrm{ S_1} and \mathrm{ S_2} can be -
 

Option: 1

20 year and 5 year
 


Option: 2

104 year each
 


Option: 3

20 year and 104 year
 


Option: 4

 5 year each


Answers (1)

best_answer

\begin{aligned} &\mathrm{ \text { Activity of } \left.S_1=\frac{1}{2} \text { (activity of } S_2\right) }\\ &\mathrm{ \lambda_1 N_1=\frac{1}{2}\left(\lambda_2 N_2\right) }\\ &\mathrm{ \frac{\lambda_1}{\lambda_2}=\frac{N_2}{2 N_1} }\\ &\mathrm{ \frac{T_1}{T_2}=\frac{2 N_1}{N_2} \quad\left[\because T=\text { half - life }=\frac{\ln _2}{\lambda}\right]}\\ &\mathrm{Given, \quad N_1=2 N_2}\\ &\mathrm{\frac{T_1}{T_2}=\frac{1}{4}}\\ \end{aligned}

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Ajit Kumar Dubey

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