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

Answer: 1

Activity $(-\frac{dN}{dt})=\lambda N=\left(\frac{1}{t_{mean}}\right)\times N$ $\therefore N=(-\frac{dN}{dt})\times t_{mean}$=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) $=(-\frac{dN}{dt})(t_{mean})(m)$ Substituting the values, we get Total mass of radioactive substance =1 mg $\therefore$ Answer is 1.