Physics - Modern Physics Question with Solution | TestHub

Let initially No → atoms were present

$$\therefore \mathrm{n}={\mathrm{N}}_0-{\mathrm{N}}_0{\mathrm{e}}^{-\lambda (2)}⟶(\mathrm{i})$$

and $1.25\mathrm{n}={\mathrm{N}}_0-{\mathrm{N}}_0{\mathrm{e}}^{-\lambda (2+2)}⟶$ (ii) [Total $\beta$ particle emitted in 4 seconds] Dividing (ii) by (i)

$$1.25=\frac{1-{\mathrm{e}}^{-4\lambda }}{1-{\mathrm{e}}^{-2\lambda }}$$

On solving ${\mathrm{e}}^{-2\lambda }=\frac{1}{4}$ [RT-11/8 03-03-2007]

$$\begin{array}{rlrl}& \therefore -2\lambda =-\ln 4& \therefore \frac{-2\ln 2}{\mathrm{T}1/2}=-2\ln 2& \therefore \mathrm{T}1/2=1\text{ second] }\end{array}$$