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  • The radioactivity of a sample is at time and <img alt="\mathrm{R_

The radioactivity of a sample is \mathrm{R_1} at time \mathrm{T_1} and \mathrm{R_2} at time \mathrm{T_2}. If the average life of the specimen is \mathrm{T} number of atoms that have disintegrated in time \mathrm{\left(T_2-T_1\right)} is proportional to 

Option: 1

\mathrm{R_1 T_1-R_2 T_2}


Option: 2

\mathrm{\left(R_1-R_2\right) T}


Option: 3

\mathrm{\frac{R_1-R_2}{T}}


Option: 4

\mathrm{\left(R_1-R_2\right)\left(T_1-T_2\right)}


Answers (1)

best_answer

Let number of nuclei at \mathrm{t=T_1} is \mathrm{N_1} and at \mathrm{t=T_2} is \mathrm{N_2}.


\mathrm{\left.\begin{matrix} \Rightarrow R_1=\lambda N_1 & \\ R_2=\lambda N_2 & \end{matrix}\right|\text{Number of nuclei }= N_{2}-N_{1}}
 \mathrm{=\frac{R_2}{\lambda}-\frac{R_1}{\lambda}}
\mathrm{=\frac{R_2-R_1}{\lambda}=\left(R_2-R_1\right) \cdot T}

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vishal kumar

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