${\mathrm{CrO}}_4^{-2},{\mathrm{MnO}}_4^{-} \mathrm{ions}$are coloured due to

The color exhibited by the CrO₄ ²⁻ and MnO₄⁻ ions can be explained using the concept of charge transfer and not by the typical d-d transitions seen in many other colored ions. Let's break it down further:

CrO₄ 2− Ion

In the CrO₄ ²⁻ ion, chromium (Cr) is in the +6 oxidation state. Chromium in this state has a d0 electron configuration, meaning there are no electrons in the d-orbital. This configuration prevents d-d transitions from occurring, which are responsible for the color in many transition metal complexes.

The color of the CrO₄ ²⁻ ion is primarily due to the charge transfer between the chromium center and the oxygen atoms in the ion. In charge transfer absorption, an electron from the oxygen atom is transferred to the chromium ion. This electron movement results in the absorption of specific wavelengths of light, giving rise to the characteristic color of the ion.

MnO₄⁻ Ion

The MnO₄⁻ ion, in which manganese (Mn) is in the +7 oxidation state, also exhibits color due to charge transfer. In this case, the color is not due to d-d transitions, but rather due to an electron being transferred from the oxide ion (O2−) to the manganese ion. This charge transfer process results in the absorption of certain wavelengths, leading to the purple color observed in MnO₄⁻

Thus, both  CrO₄ ²⁻  and MnO₄⁻ ions are colored due to the charge transfer phenomenon, rather than the typical d-d transition found in many other metal complexes.