The H-O-H bond angles in `H_(3)O^(+)` are approximately `107^(@)`. The orbitals used by oxygen in these bonds are best described as :

Options

A. p-orbitals
B. sp-hybrid orbitals
C. `sp^(2)`-hybrid orbital
D. `sp^(3)`-hybrid orbital

Explanation

To determine the type of orbitals used by oxygen in the hydronium ion \( H_3O^+ \), we can follow these steps:

### Step 1: Understand the Structure of Hydronium Ion
The hydronium ion is formed when a hydrogen ion (\( H^+ \)) combines with a water molecule (\( H_2O \)). The water molecule has two hydrogen atoms bonded to oxygen and one lone pair of electrons on the oxygen atom.

### Step 2: Identify the Bonding and Lone Pairs
In the hydronium ion \( H_3O^+ \):
- There are 3 hydrogen atoms bonded to the oxygen.
- There is 1 lone pair of electrons on the oxygen atom.

### Step 3: Determine the Hybridization
To determine the hybridization, we count the regions of electron density around the oxygen atom:
- 3 bonds (from the 3 hydrogen atoms)
- 1 lone pair

This gives us a total of 4 regions of electron density.

### Step 4: Apply VSEPR Theory
According to VSEPR (Valence Shell Electron Pair Repulsion) theory, 4 regions of electron density will arrange themselves in a tetrahedral geometry. However, the presence of a lone pair will slightly alter the angles, resulting in a bond angle of approximately \( 107^\circ \) instead of \( 109.5^\circ \) (which is the angle in a perfect tetrahedron).

### Step 5: Identify the Type of Hybridization
Since there are 4 regions of electron density, the hybridization of the oxygen atom in the hydronium ion is \( sp^3 \). This means that one s orbital and three p orbitals combine to form four equivalent \( sp^3 \) hybrid orbitals.

### Conclusion
The orbitals used by oxygen in the bonds of the hydronium ion \( H_3O^+ \) are best described as **sp³ hybrid orbitals**.

### Final Answer
The correct option is **sp³ hybrid orbitals** (Option 4).

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