Consider a radioactive material of half-life `1.0` minute. If one of the nuclei decays now, the next one will decay

Answer

To solve the question, we need to understand the concept of half-life and the nature of radioactive decay.

### Step-by-Step Solution:

1. **Understanding Half-Life**: The half-life of a radioactive material is the time required for half of the radioactive nuclei in a sample to decay. In this case, the half-life is given as `1.0 minute`.

2. **Radioactive Decay Process**: Radioactive decay is a random process. This means that while we can predict the average behavior of a large number of nuclei, we cannot predict when a specific nucleus will decay.

3. **Decay of One Nucleus**: If one nucleus decays now, it does not imply that the next nucleus will decay after a fixed time. The decay of each nucleus is independent of the others.

4. **Expected Time for Next Decay**: Although we cannot predict the exact time for the next decay, we can calculate the average time between decays for a large number of nuclei. The average time between decays is related to the decay constant (λ) and can be derived from the half-life (T₁/₂) using the formula:
\[ T_{avg} = \frac{1}{\lambda} \]
where \( \lambda = \frac{\ln(2)}{T_{1/2}} \).

5. **Calculating the Decay Constant**: Using the half-life:
\[ \lambda = \frac{\ln(2)}{1 \text{ minute}} \approx 0.693 \text{ min}^{-1} \]

6. **Calculating Average Time Between Decays**:
\[ T_{avg} = \frac{1}{\lambda} = \frac{1}{0.693} \approx 1.44 \text{ minutes} \]
This means that on average, we can expect the next nucleus to decay approximately 1.44 minutes after the first one.

7. **Conclusion**: Therefore, while we cannot determine the exact time for the next decay, we can say that on average, it will occur approximately 1.44 minutes after the first decay.