A particle isotope has a half life of 10 min.What does that statement imply about a sample of this type of nucleus?

Options

A. All of the nuclei will decay in 10 min
B. All of the nuclei wil decay in 20 min
C. Every time you start with 10 nuclei at the beginning of a 10 -min interval, 5 nuclei will be left at the end of the interval.
D. The expected number of nuclei to decay in 10 min will be one half the number at the beginning of the 10 min.

Answer

To understand what the statement "A particle isotope has a half-life of 10 minutes" implies about a sample of this type of nucleus, we can break it down step by step.

### Step-by-Step Solution:

1. **Definition of Half-Life**:
- The half-life of a radioactive isotope is the time required for half of the radioactive nuclei in a sample to decay. In this case, the half-life is 10 minutes.

2. **Initial Amount of Nuclei**:
- Let's assume we start with an initial amount of nuclei, say \( N_0 = 1000 \) nuclei.

3. **Decay After One Half-Life**:
- After 10 minutes (one half-life), half of the initial nuclei will have decayed. Therefore, the number of remaining nuclei will be:
\[ N = \frac{N_0}{2} = \frac{1000}{2} = 500 \text{ nuclei} \]

4. **Subsequent Decay**:
- After another 10 minutes (the second half-life), the remaining nuclei will again be halved:
\[ N = \frac{500}{2} = 250 \text{ nuclei} \]
- This process continues indefinitely, with the number of nuclei halving every 10 minutes.

5. **Understanding Continuous Decay**:
- It is important to note that the decay does not mean that all nuclei will eventually become zero in a finite time. Instead, as time progresses, the number of remaining nuclei approaches zero but never actually reaches it.

6. **Expected Decay**:
- If you start with any number of nuclei, after each half-life, you can expect approximately half of the remaining nuclei to decay. However, the exact number that decays can vary due to the probabilistic nature of radioactive decay.

### Conclusion:
The statement implies that if you start with a sample of this isotope, after every 10 minutes, you will have half of the remaining nuclei left. This process continues indefinitely, and while the number of nuclei will decrease, it will never reach exactly zero.