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 radioisotope is ${10}^{-25}kg.$ The mass $\left(inmg\right)$ of the radioactive sample is

Answer 1

$\frac{dN}{dt}=-\lambda N=-{10}^{10}$

$\Rightarrow N={10}^{10}\times \left(\frac{1}{\lambda }\right)$

$m_{total}=N\times m_1$

$={10}^{10}\times {10}^9\times {10}^{-25}\times {10}^{6}mg$


$=1mg$