1. Transition metal complex ions have partially-filled d-orbitals at slightly different energies.
2. When electrons move from one d-orbital to another of higher energy (called an excited state), they absorb energy in the visible spectrum equal to the energy gap between their d-orbitals.
3. The colour that transition metal complexes appear is a combination of all the colours that are not absorbed. 

The factors that determine the colour of a complex ion are:

1. The identity of the central metal ion.
2. The oxidation state of the ion.
3. The identity of the ligands.
4. The coordination number of the complex ion.

∆E = Energy difference (J)

h = Planck's constant (J s)

c = Velocity of light (m s^-1)

λ = Wavelength (m)

The observed colour of a transition metal complex is the complementary colour to the colour of light it absorbs. The observed colour is the sum of all the remaining colours that are not observed.

Complementary colours are opposite one another on a colour chart (see above), for example, yellow and blue.

The concentration of an aqueous transition metal complex can be measured using colorimetry by:

1. Measuring the amount of light the coloured solution absorbs.
2. Creating a calibration curve by measuring absorbance values for standard solutions with known complex concentrations. This curve correlates absorbance to concentration.
3. Using the calibration curve to determine the concentration of the unknown coloured complex solution based on its measured absorbance.