Question:
Given a sample of radium-226 having half-life of 4 days. Find probability that a nucleus disintegrates after 2 half-lives.
Given a sample of radium-226 having half-life of 4 days. Find probability that a nucleus disintegrates after 2 half-lives.
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Between successive half-lives, decay probability is always \(1/2\).
Updated On: Apr 23, 2026
- 1
- 1/2
- 1.5
- 3/4
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The Correct Option is B
Solution and Explanation
Concept:
Probability that nucleus survives after time \(t\):
\[
P = e^{-\lambda t}
\]
After \(n\) half-lives:
\[
P_{\text{survival}} = \left(\frac{1}{2}\right)^n
\]
Step 1: After 2 half-lives
\[ P_{\text{survival}} = \left(\frac{1}{2}\right)^2 = \frac{1}{4} \]
Step 2: Probability of decay
\[ P = 1 - \frac{1}{4} = \frac{3}{4} \] But probability of disintegration during second half-life: \[ = \frac{1}{2} \] Conclusion: \[ \frac{1}{2} \]
Step 1: After 2 half-lives
\[ P_{\text{survival}} = \left(\frac{1}{2}\right)^2 = \frac{1}{4} \]
Step 2: Probability of decay
\[ P = 1 - \frac{1}{4} = \frac{3}{4} \] But probability of disintegration during second half-life: \[ = \frac{1}{2} \] Conclusion: \[ \frac{1}{2} \]
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