Question

The half-life period of Radium is 3 minutes. Its decay constant is:

• A. \( 1.5 \, \text{minute}^{-1} \)
• B. \( 0.693 \, \text{minute}^{-1} \)
• C. \( 0.231 \, \text{minute}^{-1} \)
• D. \( 0.5 \, \text{minute}^{-1} \)

Hint:

The decay constant \( \lambda \) is inversely related to the half-life period of a radioactive substance.

Answer 1

The Correct Option is B

Step 1: Use the relation between half-life and decay constant. The half-life \( t_{1/2} \) is related to the decay constant \( \lambda \) by: \[ t_{1/2} = \frac{\ln 2}{\lambda} \] Substituting \( t_{1/2} = 3 \, \text{min} \), we find: \[ \lambda = \frac{\ln 2}{3} = 0.693 \, \text{minute}^{-1} \]