Q. Radioactive material 'A' has decay constant '8$\lambda$' and material 'B' has decay constant '$\lambda$'. Initially they have same number of nuclei. After what time, the ratio of number of nuclei of material 'B' to that 'A' will be $\frac{1}{e}$ ?
A) $\frac{1}{\lambda}$
B) $\frac{1}{7\lambda}$
C) $\frac{1}{8\lambda}$
D) $\frac{1}{9\lambda}$
Explanation
[Solution] $N_B/N_A = e^{7\lambda t}$. As written, a ratio of 1/e would need negative time; the intended ratio is $N_A/N_B = 1/e$, giving $7\lambda t = 1$ and $t = 1/(7\lambda)$. Answer (2).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.