Which of the following transitions involves maximum energy?
(1) `M^(-) (g) to M(g)`
(2) `M^(2+) (g) to M^(3+) (g)`
(3) `M^(+) (g) to M^(2+) (g)`
(4) `M(g) to M^(+) (g)`

Explanation

To determine which transition involves the maximum energy, we need to analyze each option based on the energy required to remove or add electrons to the species involved.

### Step-by-Step Solution:

1. **Understanding the Transitions**:
- (1) `M^(-) (g) to M(g)`: This transition involves removing one electron from a negatively charged ion (an anion) to form a neutral atom.
- (2) `M^(2+) (g) to M^(3+) (g)`: This transition involves removing one electron from a doubly charged cation to form a triply charged cation.
- (3) `M^(+) (g) to M^(2+) (g)`: This transition involves removing one electron from a singly charged cation to form a doubly charged cation.
- (4) `M(g) to M^(+) (g)`: This transition involves removing one electron from a neutral atom to form a singly charged cation.

2. **Energy Considerations**:
- The energy required to remove an electron from an atom or ion is influenced by the effective nuclear charge experienced by the electrons.
- As the positive charge of the ion increases (e.g., from `M^(+)` to `M^(2+)` to `M^(3+)`), the effective nuclear charge experienced by the remaining electrons also increases, making it more difficult to remove an additional electron.

3. **Analyzing Each Option**:
- **Option (1)**: Removing an electron from `M^(-)` to form `M` requires energy but is relatively easier compared to removing electrons from cations.
- **Option (2)**: Removing an electron from `M^(2+)` to form `M^(3+)` is difficult due to the high effective nuclear charge on the remaining electrons, thus requiring a significant amount of energy.
- **Option (3)**: Removing an electron from `M^(+)` to form `M^(2+)` is also difficult, but less so than removing from `M^(2+)`.
- **Option (4)**: Removing an electron from a neutral atom `M` to form `M^(+)` requires energy, but again, it is easier compared to the cation transitions.

4. **Conclusion**:
- Among the given options, the transition `M^(2+) (g) to M^(3+) (g)` (Option 2) involves the maximum energy due to the high effective nuclear charge on the remaining electrons in the doubly charged cation.

### Final Answer:
The transition that involves maximum energy is **Option (2): `M^(2+) (g) to M^(3+) (g)`**.