The `IUPAC` name for `[AI(OH)(H_(2)O)_(5)]^(2+)` is
(a) Pentahyroaluminium hydroxide
(b) Aquometaaluminate ion
(c ) Pentaaquaaluminate(III)hydroxide
(d) Pentaaquahydroxoaluminium(III) .

Answer

To determine the IUPAC name of the complex ion \([Al(OH)(H_2O)_5]^{2+}\), we will follow these steps:

### Step 1: Identify the central metal ion and its oxidation state
The central metal ion in the complex is Aluminium (Al). To find its oxidation state, we can set up the following equation based on the overall charge of the complex:

Let the oxidation state of Aluminium be \(x\). The hydroxyl ion (OH) has a charge of -1, and each water molecule (H2O) is neutral (0 charge). The overall charge of the complex is +2.

Thus, we can write the equation:
\[ x + (-1) + 0 \times 5 = +2 \]
This simplifies to:
\[ x - 1 = 2 \]
Solving for \(x\):
\[ x = 3 \]
So, the oxidation state of Aluminium is +3.

### Step 2: Identify the ligands and their names
In the complex, we have:
- 5 water molecules (H2O), which are called "aqua" in coordination chemistry.
- 1 hydroxyl group (OH), which is called "hydroxo".

### Step 3: Count the number of each type of ligand
- There are 5 aqua ligands.
- There is 1 hydroxo ligand.

### Step 4: Construct the name of the complex
According to IUPAC nomenclature, ligands are named in alphabetical order, regardless of their quantity. Therefore, we will name the ligands as follows:
- "penta" for 5 aqua ligands becomes "pentaqua".
- "hydroxo" for 1 hydroxyl ligand.

Putting it together, we name the ligands as:
- pentaqua
- hydroxo

### Step 5: Name the central metal ion
Since Aluminium is in the +3 oxidation state, we denote it as "aluminium(III)".

### Step 6: Combine all parts to form the complete name
Combining all parts, we get:
\[ \text{pentaquahydroxoaluminium(III)} \]

### Conclusion
Thus, the IUPAC name for the complex \([Al(OH)(H_2O)_5]^{2+}\) is **pentaquahydroxoaluminium(III)**.

### Final Answer
The correct option is (d) Pentaaquahydroxoaluminium(III).