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 (in $mg$ ) of the radioactive sample is

Answer 1

$\frac{ dN }{ dt }=\lambda N$
$\therefore N =\frac{\left(\frac{ d N }{ dt }\right)}{\lambda}=10^{10} \times 10^{\circ}=10^{19}$ atoms
$m _{\text {sample }=10}^{-25} \times 10^{19} kg =1\, mg$