Dipole moment will be zero in the complexes
I. `[Ni(CN)_(4)]^(2-)`
II. Cis-`Pt[(NH_(3))_(2)Cl_(2)]`
trans-`[Pt(NH_(3))_(2)Cl_(2)]`

Options

A. I and II
B. I and III
C. II and III
D. I, II and III

Explanation

To determine whether the dipole moment is zero in the given complexes, we need to analyze their molecular geometry and the distribution of charge within the complexes.

### Step-by-Step Solution:

1. **Analyze the first complex: `[Ni(CN)₄]²⁻`**
- Nickel (Ni) in this complex is in a +2 oxidation state and is surrounded by four cyanide (CN) ligands.
- The geometry of this complex is square planar.
- In a square planar geometry, the ligands are arranged symmetrically around the central metal ion.
- The CN ligands are linear and have a dipole moment, but because they are symmetrically arranged, their dipole moments cancel each other out.
- Therefore, the overall dipole moment of `[Ni(CN)₄]²⁻` is **zero**.

2. **Analyze the second complex: Cis-`[Pt(NH₃)₂Cl₂]`**
- In this complex, platinum (Pt) is surrounded by two ammonia (NH₃) and two chloride (Cl) ligands.
- The geometry of this complex is square planar.
- In the cis configuration, the two NH₃ ligands are adjacent to each other, and the two Cl ligands are also adjacent.
- The dipole moments of NH₃ (which is polar) and Cl (which is also polar) do not cancel out due to their arrangement.
- Therefore, the overall dipole moment of Cis-`[Pt(NH₃)₂Cl₂]` is **not zero**.

3. **Analyze the third complex: Trans-`[Pt(NH₃)₂Cl₂]`**
- In the trans configuration, the NH₃ ligands are opposite each other, and the Cl ligands are also opposite each other.
- This symmetrical arrangement allows the dipole moments of the NH₃ and Cl ligands to cancel out.
- Therefore, the overall dipole moment of Trans-`[Pt(NH₃)₂Cl₂]` is **zero**.

### Conclusion:
- The dipole moment is zero in:
- I. `[Ni(CN)₄]²⁻`
- III. Trans-`[Pt(NH₃)₂Cl₂]`
- The dipole moment is **not zero** in:
- II. Cis-`[Pt(NH₃)₂Cl₂]`

### Summary:
- **Dipole moment is zero**: `[Ni(CN)₄]²⁻`, Trans-`[Pt(NH₃)₂Cl₂]`
- **Dipole moment is not zero**: Cis-`[Pt(NH₃)₂Cl₂]`