Question

If a radioactive element disintegrates for its mean life, the fraction of original amount remaining is ________.

• A. $e$
• B. $1-e$
• C. $1-\frac{1}{e}$
• D. $\frac{1}{e}$
• E. $2e$

Hint:

After one mean life, approximately 36.8% of the sample remains.

Answer 1

The Correct Option is D

Step 1: Concept
The decay law is $N = N_0 e^{-\lambda t}$. Mean life $\tau = \frac{1}{\lambda}$.

Step 2: Meaning
Substitute $t = \tau = \frac{1}{\lambda}$ into the decay equation.

Step 3: Analysis
$N = N_0 e^{-\lambda(1/\lambda)} = N_0 e^{-1}$.

Step 4: Conclusion
The fraction remaining is $\frac{N}{N_0} = e^{-1} = \frac{1}{e}$. Final Answer: (D)