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 transition in terms of the energy required to remove electrons from the species involved. The transitions are as follows:

1. **Transition 1: \( M^{-} (g) \) to \( M(g) \)**
- This transition involves the removal of one electron from a negatively charged ion (\( M^{-} \)) to form a neutral atom (\( M \)). This process requires energy to overcome the attraction between the negatively charged electron and the positively charged nucleus.

2. **Transition 2: \( M^{2+} (g) \) to \( M^{3+} (g) \)**
- Here, we are removing one electron from a doubly charged cation (\( M^{2+} \)) to form a triply charged cation (\( M^{3+} \)). This transition involves a higher effective nuclear charge, as there are more protons in the nucleus than electrons. Thus, it requires more energy to remove an electron from \( M^{2+} \) compared to removing an electron from \( M^{-} \).

3. **Transition 3: \( M^{+} (g) \) to \( M^{2+} (g) \)**
- This transition involves the removal of one electron from a singly charged cation (\( M^{+} \)) to form a doubly charged cation (\( M^{2+} \)). Similar to the previous transition, this also requires energy, but it is less than the energy required for the transition from \( M^{2+} \) to \( M^{3+} \).

4. **Transition 4: \( M(g) \) to \( M^{+} (g) \)**
- This transition involves the removal of one electron from a neutral atom (\( M \)) to form a singly charged cation (\( M^{+} \)). This requires energy but is generally less than the energy required for the other transitions involving cations.

Now, comparing the energy requirements for each transition:
- Transition 1 requires energy to remove one electron from \( M^{-} \).
- Transition 2 requires the most energy because it involves removing an electron from a cation with a higher positive charge (\( M^{2+} \) to \( M^{3+} \)).
- Transition 3 requires less energy than Transition 2.
- Transition 4 requires the least energy among all.

Thus, the transition that involves the maximum energy is:

**Answer: (2) \( M^{2+} (g) \) to \( M^{3+} (g) \)**