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

Activity $\bigg(-\frac{dN}{dt}\bigg)=\lambda N=\bigg(\frac{1}{t_{mean}}\bigg)\times N$ $\therefore N=\bigg(-\frac{dN}{dt}\bigg)\times t_{mean}$=Total number of atoms Mass of one atom is $10^{-25} kg$ = m (say) $\therefore $ Total mass of radioactive substance = (number of atoms) \times (mass of one atom) $=\bigg(-\frac{dN}{dt}\bigg)(t_{mean})(m)$ Substituting the values, we get Total mass of radioactive substance =1 mg $\therefore $ Answer is 1.