Physics - Modern Physics Question with Solution | TestHub

If ${\mathrm{R}}_0$ be the initial activity of the sample, then ${\mathrm{R}}_1={\mathrm{R}}_0{\mathrm{e}}^{\lambda {\mathrm{t}}_1}$ and ${\mathrm{R}}_2={\mathrm{R}}_0{\mathrm{e}}^{-\lambda {\mathrm{t}}_2}$

$$\begin{array}{rlrl}& \text{ Where }\lambda =\frac{1}{\mathrm{T}}\left(\because \text{ Mean life }=\mathrm{T}=\frac{1}{\lambda }\right)& \Rightarrow \frac{{\mathrm{R}}_2}{{\mathrm{R}}_1}=\frac{{\mathrm{e}}^{-\lambda {\mathrm{t}}_2}}{{\mathrm{e}}^{-\lambda {\mathrm{t}}_1}}={\mathrm{e}}^{\lambda \left({\mathrm{t}}_1-{\mathrm{t}}_2\right)}& \Rightarrow {\mathrm{R}}_2={\mathrm{R}}_1\exp \left(\frac{{\mathrm{t}}_1-{\mathrm{t}}_2}{\mathrm{T}}\right)\end{array}$$

][RT-7 XIII 24.02.2013]