Predict the number of unpaired electrons in a tetrahedral `d^(6)` ion and in a square planar `d^(7)` ion .

Explanation

To determine the number of unpaired electrons in a tetrahedral `d^6` ion and a square planar `d^7` ion, we will analyze the electron configurations and the splitting of d-orbitals in both geometries.

### Step 1: Understand the d-orbital splitting in tetrahedral and square planar complexes.

- In a tetrahedral complex, the d-orbitals split into two sets:
- **e_g** (higher energy) which consists of the orbitals: \(d_{x^2-y^2}\) and \(d_{z^2}\).
- **t_2g** (lower energy) which consists of the orbitals: \(d_{xy}\), \(d_{yz}\), and \(d_{zx}\).

- In a square planar complex, the d-orbitals also split, but the order is different:
- The order of energy levels from highest to lowest is: \(d_{x^2-y^2}\) (highest), \(d_{xy}\), \(d_{yz}\) and \(d_{zx}\) (lower), and \(d_{z^2}\) (lowest).

### Step 2: Fill the d-orbitals for the `d^6` tetrahedral ion.

- For a tetrahedral `d^6` ion, we fill the orbitals according to Hund's rule and the Aufbau principle:
- First, we fill the lower energy orbitals singly before pairing.

1. Fill the three t_2g orbitals with 6 electrons:
- \(d_{xy}\): 1 electron
- \(d_{yz}\): 1 electron
- \(d_{zx}\): 1 electron
- Pairing begins:
- \(d_{xy}\): 2 electrons
- \(d_{yz}\): 2 electrons
- \(d_{zx}\): 2 electrons

- The filling will look like this:
- \(t_{2g}\): ↑↓ ↑↓ ↑↓ (3 pairs)

- **Total unpaired electrons in `d^6` tetrahedral ion = 0.**

### Step 3: Fill the d-orbitals for the `d^7` square planar ion.

- For a square planar `d^7` ion, we fill the orbitals as follows:

1. Fill the orbitals:
- \(d_{x^2-y^2}\): 1 electron
- \(d_{xy}\): 1 electron
- \(d_{yz}\): 1 electron
- \(d_{zx}\): 1 electron
- \(d_{z^2}\): 1 electron
- Pairing begins:
- \(d_{xy}\): 2 electrons
- \(d_{yz}\): 1 electron
- \(d_{zx}\): 1 electron
- \(d_{z^2}\): 1 electron

- The filling will look like this:
- \(d_{x^2-y^2}\): ↑
- \(d_{xy}\): ↑↓
- \(d_{yz}\): ↑
- \(d_{zx}\): ↑
- \(d_{z^2}\): ↑

- **Total unpaired electrons in `d^7` square planar ion = 3.**

### Conclusion:
- The number of unpaired electrons in the tetrahedral `d^6` ion is **0**.
- The number of unpaired electrons in the square planar `d^7` ion is **3**.