Physics - Modern Physics Question with Solution | TestHub

Activity $\left(-\frac{dN}{dt}\right)=\lambda N=\left(\frac{1}{t_{\text{mean }}}\right)\times N$ $$\begin{array}{rl}& \therefore N=\left(-\frac{dN}{dt}\right)\times t_{\text{mean }}\\ & =\text{ Total number of atoms }\\ & \text{ Mass of one atom is }10^{-25}\mathrm{kg}=m\text{ (say) }\\ & \therefore \text{ Total mass of radioactive substance }\\ & =(\text{ number of atoms) }\\ & \times (\text{ mass of one atom) }\\ & =\left(-\frac{dN}{dt}\right)\left(t_{\text{mean }}\right)(m)\end{array}$$ Substituting the values, we get Total mass of radioactive substance $$=1\mathrm{mg}$$ $\therefore$ Answer is 1 . Analysis of Question Question is very simple. Again in my opinion one can solve it.