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 of the given transitions involves maximum energy, we will analyze each transition in terms of ionization energy. Ionization energy is the energy required to remove an electron from an atom or ion.

### Step-by-Step Solution:

1. **Identify the transitions:**
- (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 \( M^{+} (g) \)

2. **Analyze each transition:**
- **Transition (1)**: \( M^{-} (g) \) to \( M(g) \)
- This transition involves the removal of an electron from an anion to form a neutral atom. Energy is released when an electron is added to form an anion, but energy is required to remove it. However, this energy is generally lower than the ionization energies of cations.

- **Transition (2)**: \( M^{2+} (g) \) to \( M^{3+} (g) \)
- This transition involves removing an electron from a doubly charged cation. The ionization energy required here is typically high because the effective nuclear charge is greater, pulling the remaining electrons closer to the nucleus.

- **Transition (3)**: \( M^{+} (g) \) to \( M^{2+} (g) \)
- This transition involves removing an electron from a singly charged cation. The ionization energy required is lower than that for the transition from \( M^{2+} \) to \( M^{3+} \) because the effective nuclear charge is less than in the previous case.

- **Transition (4)**: \( M(g) \) to \( M^{+} (g) \)
- This transition involves the removal of an electron from a neutral atom to form a singly charged cation. The ionization energy required here is the first ionization energy, which is generally lower than the subsequent ionization energies.

3. **Compare the energies required for each transition:**
- The energy required for the transition from \( M^{2+} \) to \( M^{3+} \) (Transition 2) is the highest because:
- It involves removing an electron from a cation that already has a high effective nuclear charge, making it more difficult to remove an additional electron.
- The size of the ion decreases with each removal of an electron, increasing the attraction between the nucleus and the remaining electrons, thus requiring more energy.

4. **Conclusion:**
- The transition that involves the maximum energy is **(2) \( M^{2+} (g) \) to \( M^{3+} (g) \)**.

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