The half-life of a radioactive nuclide is 100 hours. The fraction of original activity that will remain after

Question

The half-life of a radioactive nuclide is 100 hours. The fraction of original activity that will remain after 150 hours would be:

Accepted Answer

1. **Identify the Concept:** Radioactive decay follows first-order kinetics . The activity ($A$) remaining after time $t$ is related to the initial activity ($A_0$) by the formula $A = A_0 (\frac{1}{2})^n$, where $n$ is the number of half-lives elapsed .
2. **Calculate Number of Half-lives ($n$):**
   - Given Half-life ($T_{1/2}$) = 100 hours.
   - Given Time elapsed ($t$) = 150 hours.
   - $n = \frac{t}{T_{1/2}} = \frac{150}{100} = 1.5 = \frac{3}{2}$.
3. **Calculate Fraction of Activity:**
   - Fraction remaining = $\frac{A}{A_0} = (\frac{1}{2})^{n}$.
   - $\frac{A}{A_0} = (\frac{1}{2})^{3/2} = \frac{1}{2^1 	imes 2^{0.5}} = \frac{1}{2\sqrt{2}}$.

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