Prove that the lowering of the stabilised orbitals is `0.4Delta_(0)` while raising of the destabilised orbitalsw is `0.6Delta_(0)` .

Explanation

To prove that the lowering of the stabilized orbitals is \(0.4 \Delta_0\) while the raising of the destabilized orbitals is \(0.6 \Delta_0\), we will use the concepts from Crystal Field Theory (CFT).

### Step-by-Step Solution:

1. **Understanding the Splitting of d-Orbitals**:
- In a coordination compound, the five d-orbitals split into two sets due to the electrostatic interactions with surrounding ligands: the lower-energy set \(T_{2g}\) (comprising \(d_{xy}\), \(d_{yz}\), and \(d_{zx}\)) and the higher-energy set \(E_g\) (comprising \(d_{x^2-y^2}\) and \(d_{z^2}\)).

2. **Defining Energies**:
...