If PQRS are four different ligands, then how many geometric isomers will be found for square planar `[Pt. PQRS]^(2+)` ?

Answer

To determine the number of geometric isomers for the complex \([Pt(PQRS)]^{2+}\) where PQRS are four different ligands, we can follow these steps:

### Step 1: Understand the Geometry
The complex is square planar, which means that the ligands will be arranged in a two-dimensional plane around the central platinum ion.

### Step 2: Fix One Ligand
To simplify the counting of isomers, we can fix one ligand in a position. Let's fix ligand P at one position.

### Step 3: Position the Remaining Ligands
With P fixed, we need to arrange the remaining three ligands (Q, R, and S) in the remaining three positions. The arrangement of these ligands will determine the geometric isomers.

### Step 4: Identify Possible Arrangements
1. **First Arrangement**: Place Q opposite P. The remaining two ligands R and S can be arranged in the other two positions. This gives us one geometric isomer:
- P, Q, R, S (with Q opposite P)

2. **Second Arrangement**: Place R opposite P. The remaining two ligands Q and S can be arranged in the other two positions. This gives us a second geometric isomer:
- P, R, Q, S (with R opposite P)

3. **Third Arrangement**: Place S opposite P. The remaining two ligands Q and R can be arranged in the other two positions. This gives us a third geometric isomer:
- P, S, Q, R (with S opposite P)

### Step 5: Count the Isomers
From the arrangements above, we can see that there are three distinct geometric isomers possible when P is fixed and the opposite ligand is varied among Q, R, and S.

### Conclusion
Thus, the total number of geometric isomers for the complex \([Pt(PQRS)]^{2+}\) is **3**.