The number of geometrical isomers possible for the complex `[Pt(NH_(3))(NH_(2)OH)(py)Cl]^(+)` is

Answer

To determine the number of geometrical isomers for the complex \([Pt(NH_3)(NH_2OH)(py)Cl]^+\), we will follow these steps:

### Step 1: Identify the Coordination Number and Geometry
The complex has four ligands: \(NH_3\), \(NH_2OH\), \(py\) (pyridine), and \(Cl\). All these ligands are monodentate, which means they each attach to the platinum ion at one point. Therefore, the coordination number of platinum is 4.

For a coordination number of 4, the common geometrical arrangement is square planar.

### Step 2: Determine the Oxidation State of Platinum
To find the oxidation state of platinum in the complex, we can set up the following equation based on the charges of the ligands:
- \(NH_3\) is neutral.
- \(NH_2OH\) is neutral.
- \(py\) (pyridine) is neutral.
- \(Cl\) has a charge of -1.

Let \(x\) be the oxidation state of platinum:
\[ x + 0 + 0 + 0 - 1 = +1 \]
Solving for \(x\):
\[ x - 1 = 1 \implies x = +2 \]
Thus, platinum is in the +2 oxidation state.

### Step 3: Identify Possible Geometrical Isomers
Since the geometry is square planar, we can arrange the ligands in different configurations. The ligands can be arranged in two distinct types of positions:
1. **Cis Isomers**: where two identical ligands are adjacent to each other.
2. **Trans Isomers**: where two identical ligands are opposite each other.

In our complex, we have:
- One \(NH_3\)
- One \(NH_2OH\)
- One \(py\)
- One \(Cl\)

### Step 4: Count the Geometrical Isomers
Given the arrangement of the ligands:
1. **Cis Isomer 1**: \(NH_3\) and \(NH_2OH\) adjacent, with \(py\) and \(Cl\) adjacent.
2. **Cis Isomer 2**: \(NH_3\) and \(py\) adjacent, with \(NH_2OH\) and \(Cl\) adjacent.
3. **Cis Isomer 3**: \(NH_3\) and \(Cl\) adjacent, with \(NH_2OH\) and \(py\) adjacent.

Since there are no trans isomers possible due to the presence of only one of each type of ligand, we conclude that there are a total of **3 geometrical isomers**.

### Final Answer
The number of geometrical isomers possible for the complex \([Pt(NH_3)(NH_2OH)(py)Cl]^+\) is **3**.

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