When a nucleus with atomic number `Z` and mass number `A` undergoes a radioactive decay process,
(i) Both `Z` and `A` will decrease, if the process is `alpha` decay
(ii) `Z` will decrease but `A` will not change, if the process is `beta^(+)-`decay
(iii) `Z` will increase but `A` will not change, if the process is `beta-`decay
(iv) `Z` and `a` will remain uncharged, if the prices is `gamma` decay

Options

A. both Z and A will decrease, If the process is `alpha` decay
B. Z will decrease but A will not change, if the process is `beta^(+)` decay
C. Z will decrease but A will not change, if the process is `beta^(-)` decay
D. Z and A will remain unchanged, if the process is `beta` decay

Explanation

To solve the question regarding the changes in atomic number (Z) and mass number (A) during different types of radioactive decay, we will analyze each decay process step by step.

### Step-by-Step Solution:

1. **Alpha Decay**:
- In alpha decay, a nucleus emits an alpha particle, which consists of 2 protons and 2 neutrons (essentially a helium nucleus).
- If the parent nucleus has atomic number \( Z \) and mass number \( A \), the daughter nucleus will have:
- New atomic number: \( Z - 2 \)
- New mass number: \( A - 4 \)
- Therefore, both \( Z \) and \( A \) decrease.
- **Conclusion**: Statement (i) is correct.

2. **Beta Plus Decay**:
- In beta plus decay (β+ decay), a proton in the nucleus is converted into a neutron, emitting a positron (which has a positive charge).
- The changes in the nucleus are:
- New atomic number: \( Z - 1 \) (since a proton is lost)
- Mass number remains the same: \( A \)
- Therefore, \( Z \) decreases while \( A \) remains unchanged.
- **Conclusion**: Statement (ii) is correct.

3. **Beta Minus Decay**:
- In beta minus decay (β- decay), a neutron in the nucleus is converted into a proton, emitting an electron (beta particle).
- The changes in the nucleus are:
- New atomic number: \( Z + 1 \) (since a proton is gained)
- Mass number remains the same: \( A \)
- Therefore, \( Z \) increases while \( A \) remains unchanged.
- **Conclusion**: Statement (iii) is correct.

4. **Gamma Decay**:
- In gamma decay, the nucleus releases energy in the form of gamma radiation without changing the number of protons or neutrons.
- Thus, both atomic number and mass number remain unchanged:
- New atomic number: \( Z \)
- New mass number: \( A \)
- **Conclusion**: Statement (iv) is correct.

### Final Summary:
- All four statements regarding the changes in atomic number \( Z \) and mass number \( A \) during different types of radioactive decay are correct.