Question

The activity of a freshly prepared radioactive sample is ${10}^{10}$ disintegrations per second, whose mean life is ${10}^9$ s. The mass of an atom of this radioisotopes is ${10}^{-25}kg$. The mass (in mg) of the radioactive sample is .....

Answer 1

Given: $\frac{dN}{dt}={10}^{10}$
Mean Life $={10}^{9}s$
$\frac{1}{\lambda }={10}^{9}s$
$\lambda ={10}^{-9}{s}^{-1}$

FIrst order decay:
$\frac{dN}{dt}=\lambda N$
$\lambda N={10}^{10}$
$N={10}^{17}$

Mass of Radioactive sample $={10}^{19}\times {10}^{-25}kg={10}^{-6}kg$
$M={10}^{-6}kg={10}^{-3}gms=1mg$