The process requiring absorption of energy is
(1) `F to F^(-)` (2) `Cl to Cl^(-)`
(3) `O to O^(2-)` (4) `H to H^(-)`

Explanation

To determine which process requires the absorption of energy, we need to analyze each option in terms of electron gain enthalpy. The process that absorbs energy is endothermic, meaning energy is required to add an electron to an atom or ion.

### Step-by-step Solution:

1. **Understanding Electron Gain Enthalpy**:
- Electron gain enthalpy is the amount of energy released or absorbed when an electron is added to a neutral atom in the gas phase.
- If energy is released when an electron is added, the process is exothermic (negative enthalpy). If energy is absorbed, the process is endothermic (positive enthalpy).

2. **Analyzing Each Option**:
- **Option 1: F to F⁻**
- Fluorine (F) has an atomic number of 9 and has the electronic configuration of 1s² 2s² 2p⁵.
- When it gains one electron, it becomes F⁻ with the configuration 1s² 2s² 2p⁶, achieving noble gas configuration.
- This process releases energy, hence it is exothermic.

- **Option 2: Cl to Cl⁻**
- Chlorine (Cl) has an atomic number of 17 and an electronic configuration of 1s² 2s² 2p⁶ 3s² 3p⁵.
- Gaining one electron to become Cl⁻ (1s² 2s² 2p⁶ 3s² 3p⁶) also releases energy, making this process exothermic.

- **Option 3: O to O²⁻**
- Oxygen (O) has an atomic number of 8 and an electronic configuration of 1s² 2s² 2p⁴.
- When it gains one electron, it becomes O⁻ (1s² 2s² 2p⁵), which releases energy (exothermic).
- However, to gain a second electron to become O²⁻ (1s² 2s² 2p⁶), there is electron-electron repulsion because O⁻ is already negatively charged.
- This requires energy to overcome the repulsion, making this process endothermic.

- **Option 4: H to H⁻**
- Hydrogen (H) has an atomic number of 1 and an electronic configuration of 1s¹.
- When it gains one electron to become H⁻ (1s²), energy is released, making this process exothermic.

3. **Conclusion**:
- The only process that requires the absorption of energy is **Option 3: O to O²⁻**. Thus, the correct answer is option (3).