Chemistry - Radioactivity Question with Solution | TestHub

$$\begin{array}{rl}& \text{Initial nuclei}=N_0\\ & \text{Nuclei left after }36sec=N_0-10^5\\ & \text{Nuclei left after }108sec=N_0-1.75\times 10^5\\ & \lambda (36)=\ln \left(\frac{N_0}{N_0-10^5}\right)\\ & \lambda (108)=\ln \left(\frac{N_0}{N_0-1.75\times 10^5}\right)\\ & \left(\frac{N_0}{N_0-1.75\times 10^5}\right)={\left(\frac{N_0}{N_0-10^5}\right)}^3\\ & {\left(N_0-10^5\right)}^3=N_0^2\left(N_0-1.75\times 10^5\right)\\ & N_0^3-3\times 10^5{N}_0^2+3\times 10^{10}{N}_0-10^{15}=N_0^3-1.75\times 10^5{N}_0^2\\ & 1.25\times 10^5{N}_0^2-3\times 10^{10}{N}_0+10^{15}=0\\ & N_0=\frac{3\times 10^{10}\pm \sqrt{9\times 10^{20}-5\times 10^{20}}}{2\times 1.25\times 10^5}\\ & N_0=\frac{3\times 10^{10}\pm 2\times 10^{10}}{2\times 1.25\times 10^5}\\ & N_0=2\times 10^5\\ & t_{1/2}=36sec\end{array}$$