Explain, in terms of frequencies, why solutions of transition metal ions are often coloured.

Transition metal ions have partially filled d sub-shells. These shells split into two levels and the electrons in the lower levels can be excited to the higher ones by absorbing an amount of energy equivalent to the energy gap. Due to the equation E=hv, this corresponds to light of a specific visible frequency and all other frequencies are transmitted. Thus the solution appears as the complementary colour to the frequency that has been absorbed.