Colour of Manganate ion in \(KMnO_4\) is due to:

Charge transfer spectra

The correct answer is option 2. Charge transfer spectra.

The characteristic purple color of the manganate ion (\(MnO_4^-\)) in potassium permanganate (\(KMnO_4\)) is primarily due to charge transfer spectra, making option 2 the correct choice.

1. \(d-d\) transition: This type of transition typically occurs in transition metal complexes where electrons move between d orbitals. However, in the case of permanganate (\(MnO_4^-\)), manganese exists in the +7 oxidation state, and its d orbitals are fully vaccant. Therefore, \(d-d\) transitions are not responsible for the color in this compound.

2. Charge transfer spectra: The purple color of permanganate ion arises from charge transfer transitions between the oxygen ligands \((O^{2-})\) and the manganese ion \((Mn^{7+})\). In this case, the color is due to the absorption of visible light by the compound, which corresponds to the energy required for electrons to move from the oxygen 2p orbitals to the manganese 3d orbitals.

3. \(f-f\) transition: \(f-f\) transitions typically occur in lanthanide and actinide elements due to their partially filled f orbitals. Manganese in permanganate does not have f orbitals involved in its electronic transitions, so \(f-f\) transitions are not relevant.

4. Diamagnetic nature: Diamagnetic substances are generally colorless or exhibit weak colors due to their lack of unpaired electrons. However, the purple color of permanganate is not due to its diamagnetic nature but rather to charge transfer spectra involving the transition metal ion and ligands.

Therefore, the correct answer is 2. Charge transfer spectra.

Additional Information:

The characteristic purple color of the manganate ion (\(MnO_4^-\)) in potassium permanganate (\(KMnO_4\)) is primarily attributed to Ligand-to-Metal (L-M) charge transfer spectra rather than L-M charge transfer spectra.

Explanation:

Ligand-to-Metal (L-M) charge transfer spectra occur when there is a transfer of charge from the ligand (in this case, the oxygen atoms of the permanganate ion) to the central metal ion (manganese). In potassium permanganate, the manganese ion is in the +7 oxidation state, and the oxygen atoms are negatively charged. When light of appropriate energy (wavelength) strikes the permanganate ion, electrons from the oxygen 2p orbitals are excited to higher energy levels. This excitation involves the transfer of electron density from the oxygen ligands to the manganese ion.

As a result, the absorption of light by the permanganate ion corresponds to specific wavelengths in the visible spectrum, typically in the purple range. This absorption of light gives rise to the characteristic purple color observed in potassium permanganate solutions.

Therefore, the color of the manganate ion in \(KMnO_4\) is primarily due to Ligand-to-Metal (L-M) charge transfer spectra rather than L-M charge transfer spectra.