Question

why is \([Ni(H_2O)_6]^{2+}\) coloured ? [Atomic number of Ni = 28]

Hint:

Transition metal complexes are generally coloured because: \[ \text{Partially filled } d\text{-orbitals} \] \[ \Longrightarrow \text{Crystal field splitting} \] \[ \Longrightarrow d-d \text{ transitions} \] \[ \Longrightarrow \text{Absorption of visible light} \] \[ \Longrightarrow \text{Colour observed} \] Complexes with \(d^0\) or \(d^{10}\) configurations are generally colourless.

Answer 1

Concept: Most transition metal complexes are coloured because they contain partially filled \(d\)-orbitals. When ligands approach a transition metal ion, the five \(d\)-orbitals split into groups of different energies. This phenomenon is called crystal field splitting. If electrons are present in the lower energy \(d\)-orbitals, they can absorb visible light and get promoted to higher energy \(d\)-orbitals. This transition is called a \(d-d\) transition. The absorbed light corresponds to a particular wavelength, while the complementary colour is observed.

Step 1: Finding the electronic configuration of \(Ni^{2+}\). Atomic number of nickel \[ Z=28 \] Electronic configuration of Ni: \[ Ni=[Ar]\,3d^8\,4s^2 \] For \(Ni^{2+}\), two electrons are removed from the \(4s\) orbital. Therefore, \[ Ni^{2+}=[Ar]\,3d^8 \] Thus, the metal ion contains partially filled \(d\)-orbitals. \[ \boxed{3d^8} \]

Step 2: Formation of the complex ion. The complex ion is \[ [Ni(H_2O)_6]^{2+} \] Water molecules act as ligands and surround the nickel ion in an octahedral arrangement. As a result, the five degenerate \(d\)-orbitals split into two sets: \[ t_{2g} \] (lower energy set) and \[ e_g \] (higher energy set).

Step 3: Occurrence of \(d-d\) transition. Since \(Ni^{2+}\) possesses eight \(d\)-electrons, electrons occupy the lower energy orbitals. When visible light falls on the complex, electrons absorb a certain amount of energy and jump from lower energy \(d\)-orbitals to higher energy \(d\)-orbitals. This process is represented as \[ t_{2g} \longrightarrow e_g \] Such transitions are called \[ \boxed{d-d\text{ transitions}} \]

Step 4: Reason for colour. The energy required for the \(d-d\) transition lies in the visible region of the electromagnetic spectrum. Therefore, the complex absorbs certain wavelengths of visible light and transmits or reflects the complementary colour. As a result, the complex appears coloured.

Final Answer: \[ \boxed{ [Ni(H_2O)_6]^{2+} \text{ is coloured because } Ni^{2+}(3d^8) \text{ has partially filled } d\text{-orbitals and undergoes } d-d \text{ transitions after crystal field splitting.} } \]