Physics - Modern Physics Question with Solution | TestHub

If $N$ is the number of radioactive nuclei present at some instant, then $N=N_0{e}^{-\lambda t}$ The constant $N_0$ represents the number of radioactive nuclei at $t=0$ Now, $\begin{array}{rl}& \frac{N_1}{N_2}=\frac{e^{-{\lambda }_{1}t}}{e^{-{\lambda }_{2}t}}\\ & \frac{N_1}{N_2}=\frac{e^{-5\lambda t}}{e^{-\lambda t}}=e^{-4\lambda t}\\ & \frac{N_1}{N_2}=\frac{1}{e}\end{array}$ but $\frac{N_1}{N_2}=\frac{1}{e}$ (as provided) Therefore, $\frac{1}{e}=\frac{1}{e^{4\lambda t}}$ or $4\lambda t=1$ or $t=\frac{1}{4\lambda }$