Read the paragraph carefully and answer the questions given below it,
Stereo//space isomerism in coordination compounds
Gcometrical isomerism: Exhibited by square planer and octahedral complexes (not by tetrahedral complexes because relative positions are similar). If opposite positions have similar groups, it is trans, otherwise it is cis,
Optical isomerism: Shown when mirror image is non-superimposable. Cis-isomer shows but trans isomer does not
QHow many geometrical isomers are possible for the square planar complex`[Pt(NO_(2))(Py)(NH_(3))(NH_(2)OH)]NO_(2)`

Options

A. Four
B. Five
C. Eight
D. Three

Answer

To determine the number of geometrical isomers for the square planar complex \([Pt(NO_2)(Py)(NH_3)(NH_2OH)]NO_2\), we can follow these steps:

### Step 1: Identify the Coordination Number and Geometry
The coordination number of the platinum complex is 4, and the geometry is square planar. This is important because geometrical isomerism occurs in square planar and octahedral complexes.

**Hint:** Remember that square planar complexes can exhibit geometrical isomerism due to the arrangement of ligands around the central metal atom.

### Step 2: List the Ligands
The ligands attached to the platinum center are:
1. \(NO_2\) (nitro)
2. \(Py\) (pyridine)
3. \(NH_3\) (ammonia)
4. \(NH_2OH\) (hydroxylamine)

Since all four ligands are different, this will allow for the possibility of geometrical isomers.

**Hint:** Check if all ligands are different, as this is a requirement for geometrical isomerism in square planar complexes.

### Step 3: Determine Possible Geometrical Isomers
For square planar complexes with four different ligands, the formula to calculate the number of geometrical isomers is given by:

- If there are \(n\) different ligands, the number of geometrical isomers is \(2^{(n-2)}\).

In this case, \(n = 4\):
\[ \text{Number of geometrical isomers} = 2^{(4-2)} = 2^2 = 4 \]

However, we need to consider the specific arrangements of the ligands. In a square planar arrangement, we can have cis and trans configurations.

**Hint:** Remember that the arrangement of ligands can lead to different isomers based on their relative positions (cis or trans).

### Step 4: Visualize the Arrangements
1. **Cis Isomers:** Two ligands are adjacent to each other.
2. **Trans Isomers:** Two ligands are opposite each other.

By fixing one ligand (for example, \(NH_2OH\)) and rotating the other three ligands, we can find the distinct arrangements.

- Fix \(NH_2OH\) at one position:
- \(NH_3\) and \(NO_2\) can be adjacent (cis) with \(Py\) opposite.
- \(NH_3\) and \(Py\) can be adjacent (cis) with \(NO_2\) opposite.
- \(NO_2\) and \(Py\) can be adjacent (cis) with \(NH_3\) opposite.

After considering all possible arrangements, we find that there are indeed three distinct geometrical isomers.

### Conclusion
Thus, the total number of geometrical isomers for the square planar complex \([Pt(NO_2)(Py)(NH_3)(NH_2OH)]NO_2\) is **3**.

**Final Answer:** 3

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