Which of the following process represents a `gamma- decay`?

Options

A. `^(A)X_Z +gamma rarr ^(A)X_(Z-1) +a+b`
B. `^(A)X_Z +^(1)n_(0) rarr ^(A-3)X_(Z-2) +ac`
C. `^(A)X_(Z) rarr ^(A)X_(Z) +f`
D. `^(A)X_(Z) +e_(-1) rarr ^(A)X_(Z-1) +g`

Explanation

To determine which process represents gamma decay, we need to understand the characteristics of gamma decay compared to other types of radioactive decay, such as alpha and beta decay.

### Step-by-Step Solution:

1. **Understanding Gamma Decay**:
- Gamma decay is a process where an unstable nucleus releases energy in the form of gamma radiation (high-energy photons) without changing its mass number or atomic number. This typically occurs after other decay processes (like alpha or beta decay) when the nucleus is left in an excited state.

2. **Identifying the Characteristics of Gamma Decay**:
- In gamma decay, the atomic number (Z) and mass number (A) of the nucleus remain unchanged. This means that the element itself does not change; it simply transitions to a lower energy state.

3. **Analyzing the Given Options**:
- We need to look at the options provided in the question to identify which one shows a process where both the atomic number and mass number remain the same.
- For example, if we have a transition like:
- \( \text{X} \rightarrow \text{Y} + \gamma \)
- Here, both X and Y would have the same atomic number and mass number.

4. **Evaluating Each Option**:
- **Option A**: Changes in atomic number but mass number remains the same -> Not gamma decay.
- **Option B**: Changes in mass number but atomic number remains the same -> Not gamma decay.
- **Option C**: Both atomic number and mass number remain the same -> This is gamma decay.
- **Option D**: Similar to option A or B -> Not gamma decay.

5. **Conclusion**:
- The correct option that represents gamma decay is the one where both the atomic number and mass number remain unchanged.

### Final Answer:
The correct option representing gamma decay is **Option C**.