Question

In a radioactive disintegration, the ratio of initial number of atoms to the number of atoms present at an instant of time equal to its mean life is

• A. $1/e^2$
• B. $1/e$
• C. e
• D. $e^2$

Hint:

After one mean life, $N = N_0/e$.

Answer 1

The Correct Option is C

Step 1: Formula
Radioactive decay law: $N = N_0 e^{-\lambda t}$.
Step 2: Substitution
Mean life $\tau = 1/\lambda$. At $t = \tau$, $N = N_0 e^{-\lambda(1/\lambda)} = N_0/e$.
Step 3: Ratio
The ratio of initial atoms to atoms present is $N_0 / (N_0/e) = e$.
Final Answer: (c)