If ' f ' denotes the ratio of the number of nuclei decayed ( N_d ) to the number of nuclei at t =0 ( N_0) then for a collection of radioactive…

If ' $\displaystyle f$ ' denotes the ratio of the number of nuclei decayed $\displaystyle \left(\mathrm{N}_{\mathrm{d}}\right)$ to the number of nuclei at $\displaystyle \mathrm{t}=0$ $\displaystyle \left(\mathrm{N}_0\right)$ then for a collection of radioactive nuclei, the rate of change of ' $\displaystyle f$ ' with respect to time is given as : [ $\displaystyle \lambda$ is the radioactive decay constant]