10 g of radioactive material of half-life 15 year is kept in store for 20 years. The disintegrated material ma

Question

10 g of radioactive material of half-life 15 year is kept in store for 20 years. The disintegrated material mass is

Accepted Answer

1. **Identify Given Values:**
   - Initial mass ($N_0$) = 10 g
   - Half-life ($T_{1/2}$) = 15 years
   - Time elapsed ($t$) = 20 years
2. **Calculate Remaining Mass ($N$):**
   - The formula for the remaining amount of a radioactive substance is $N = N_0 \left(\frac{1}{2}ight)^{t/T_{1/2}}$ .
   - Substitute the values: $N = 10 \left(\frac{1}{2}ight)^{20/15} = 10 \left(\frac{1}{2}ight)^{4/3}$.
   - Calculation: $\left(\frac{1}{2}ight)^{1.333} \approx 0.3968$.
   - $N \approx 10 	imes 0.3968 = 3.97$ g.
3. **Calculate Disintegrated Mass:**
   - The question asks for the mass that has disintegrated (decayed), not the remaining mass.
   - Disintegrated Mass = Initial Mass - Remaining Mass.
   - Disintegrated Mass = $10 	ext{ g} - 3.97 	ext{ g} = 6.03 	ext{ g}$.

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