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: Relation between half-life and decay constant
For a first-order reaction, the half-life is related to the decay constant by:
\( t_{1/2} = \frac{\ln 2}{\lambda} \)

Step 2: Substitute given value
Given:
\( t_{1/2} = 3 \, \text{min} \)

So,
\[ \lambda = \frac{\ln 2}{3} \] \[ \lambda = \frac{0.693}{3} \] \[ \lambda = 0.231 \, \text{min}^{-1} \]

Final Answer:
\( \lambda = 0.231 \, \text{min}^{-1} \)