The half - life of `I^(131)` is 8 days. Given a sample of `I^(131)` at time `t = 0` , we can assert that

Options

A. No nucleus will decay before t = 4 days
B. No nucleus will decay before t = 8 days
C. No nucleus will decay before t = 16 days
D. A given nucleus may decay at any time after t = 0

Answer

To solve the question regarding the half-life of I-131, we will break down the concepts step by step.

### Step-by-Step Solution:

1. **Understanding Half-Life**:
- The half-life of a radioactive substance is the time it takes for half of the radioactive nuclei in a sample to decay. For I-131, the half-life is given as 8 days.

**Hint**: Remember that the half-life is a statistical measure; it does not mean that no decay occurs until that time.

2. **Initial Condition**:
- At time \( t = 0 \), we have a certain number of I-131 nuclei (let's denote this as \( N_0 \)).

**Hint**: Think of \( N_0 \) as the total number of undecayed nuclei at the start.

3. **Decay Process**:
- After 8 days (one half-life), the number of undecayed nuclei will reduce to half, i.e., \( N_0/2 \). After another 8 days (16 days total), it will reduce to \( N_0/4 \).

**Hint**: Visualize this as a continuous process where the number of nuclei decreases exponentially.

4. **Decay Timing**:
- It is important to note that decay can happen at any moment after \( t = 0 \). This means that while the average behavior can be predicted (like half-life), individual nuclei can decay at any time.

**Hint**: Consider that decay is a random process; some nuclei may decay immediately after \( t = 0 \), while others may take longer.

5. **Conclusion**:
- Therefore, we can assert that no nucleus will decay before \( t = 0 \), but after that, decay can occur at any time. Specifically, it is incorrect to say that no nucleus will decay before 4 days, 8 days, or 16 days; decay can start immediately after \( t = 0 \).

**Hint**: Remember that the decay process is continuous and does not have a strict cutoff at the half-life.

### Final Answer:
The correct assertion is that a given nucleus may decay at any time after \( t = 0 \).