Step 1: Understanding the Complex.
The complex \( [Ni(H_2O)_6]^{2+} \) is an octahedral coordination compound where the nickel ion (Ni\(^{2+}\)) is surrounded by six water molecules as ligands. Nickel has an atomic number of 28, and in this complex, the oxidation state of nickel is +2.
Step 2: Electronic Configuration of Ni\(^{2+}\).
The electronic configuration of neutral nickel (Ni) is:
\[
\text{Ni: } [Ar] 3d^8 4s^2
\]
When nickel loses two electrons to form Ni\(^{2+}\), the electron configuration becomes:
\[
\text{Ni}^{2+}: [Ar] 3d^8
\]
In this configuration, the 3d orbitals are partially filled.
Step 3: Explanation of Colour.
The colour of a coordination complex like \( [Ni(H_2O)_6]^{2+} \) arises due to d-d transitions, which occur when electrons in the d-orbitals of the metal ion absorb specific wavelengths of light and move to higher energy levels. In this case, the Ni\(^{2+}\) ion has partially filled 3d orbitals, which can absorb light in the visible region, leading to the appearance of colour.
The energy difference between the d-orbitals in the octahedral field of Ni\(^{2+}\) allows these d-d transitions, which gives the complex its characteristic colour (usually green).
Conclusion.
The complex \( [Ni(H_2O)_6]^{2+} \) is coloured because the Ni\(^{2+}\) ion undergoes d-d transitions, absorbing visible light and producing colour due to the electronic configuration of the nickel ion and its interaction with the ligands.