In the structure of `[B_(4)O_(5)(OH)_(4)]^(2-)`.

Options

A. All four `B` atoms are trigonal planar.
B. One `B` atom is tetrahedral and the other three `B` atoms are trigonal planar.
C. Three `B` atoms are tetrahedral and one `B` atom is trigonal planar.
D. Two `B` atoms are tetrahedral and other two are trigonal planar.

Answer

To understand the structure of \([B_4O_5(OH)_4]^{2-}\), we will analyze the arrangement of boron (B) and oxygen (O) atoms, as well as the hydroxyl (OH) groups in the compound.

### Step-by-Step Solution:

1. **Identify the Components**:
The compound consists of 4 boron (B) atoms, 5 oxygen (O) atoms, and 4 hydroxyl (OH) groups, along with a 2- charge.

2. **Draw the Basic Structure**:
- Start by placing the 4 boron atoms.
- Arrange them in a way that allows for bonding with oxygen atoms.

3. **Connect the Oxygen Atoms**:
- Connect 5 oxygen atoms to the boron atoms.
- Since there are 4 boron atoms, we can assume that some of the boron atoms will be connected to more than one oxygen atom.

4. **Incorporate Hydroxyl Groups**:
- Attach the 4 hydroxyl (OH) groups to the boron atoms.
- Each OH group will be connected to a boron atom.

5. **Determine Hybridization**:
- Analyze the hybridization of the boron atoms:
- Two of the boron atoms will exhibit tetrahedral geometry (sp³ hybridization).
- The other two boron atoms will exhibit trigonal planar geometry (sp² hybridization).

6. **Charge Distribution**:
- The overall structure has a 2- charge, which should be accounted for in the bonding and arrangement of the atoms.

7. **Final Structure Confirmation**:
- Confirm that the final structure has 2 boron atoms in a tetrahedral arrangement and 2 boron atoms in a trigonal planar arrangement.

### Conclusion:
The correct statement regarding the structure of \([B_4O_5(OH)_4]^{2-}\) is that two boron atoms are tetrahedral and the other two are trigonal planar.