For radioactive material, the half-life is 10 minutes. If initially, there are 600 number of nuclei, the time

Question

For radioactive material, the half-life is 10 minutes. If initially, there are 600 number of nuclei, the time taken (in minutes) for the disintegration of 450 nuclei is:

Accepted Answer

1. **Identify Given Values:**
   - Half-life ($T_{1/2}$) = 10 minutes.
   - Initial number of nuclei ($N_0$) = 600.
   - Number of disintegrated nuclei = 450.
2. **Calculate Remaining Nuclei ($N$):**
   - $N = N_0 - 	ext{disintegrated nuclei}$.
   - $N = 600 - 450 = 150$.
3. **Determine Decay Factor:**
   - Ratio of remaining to initial nuclei: $\frac{N}{N_0} = \frac{150}{600} = \frac{1}{4}$.
4. **Relate to Half-Lives:**
   - We know that $\frac{1}{4} = (\frac{1}{2})^2$. This means 2 half-lives have passed ($n=2$) .
5. **Calculate Time ($t$):**
   - $t = n 	imes T_{1/2}$.
   - $t = 2 	imes 10 	ext{ minutes} = 20 	ext{ minutes}$.

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