Question

The half-life period and the mean life period of a radioactive element are denoted respectively by \( T_h \) and \( T_m \). Then:

• A. \( T_h = T_m \)
• B. \( T_h>T_m \)
• C. \( T_h<T_m \)
• D. \( T_h \geq T_m \)

Hint:

The mean life is always greater than the half-life for radioactive decay.

Answer 1

The Correct Option is C

Step 1: Relationship between half-life and mean life.
The mean life \( T_m \) is related to the half-life \( T_h \) by the formula: \[ T_m = \frac{T_h}{\ln 2} \] Since \( \ln 2 \) is approximately 0.693, it implies that \( T_m \) is always greater than \( T_h \). Step 2: Conclusion.
Therefore, \( T_h<T_m \).
Final Answer: \[ \boxed{T_h<T_m} \]