S3.1.10 Color of transition metal complexes (Higher Level Only)

Absorption of Light and Wavelength-Frequency Relationship in Transition Metal Complexes

1. You're holding a gemstone, marveling at its vibrant color—perhaps the deep red of a ruby or the dazzling green of an emerald.
2. Have you ever wondered what gives these stones their stunning hues?

The answer lies in the fascinating interaction between light and electrons in transition metal complexes.

Color and the Promotion of d-Electrons in Transition Metal Complexes

What Causes Color in Transition Metal Complexes?

• Transition metal complexes are often brightly colored due to the behavior of their d-electrons.
• Transition metals have partially filled d-orbitals, and when they form complexes with ligands (molecules or ions that donate electron pairs), the normally degenerate (equal energy) d-orbitals split into two sets with different energies.
• This process, known as d-orbital splitting, happens because ligands interact more strongly with some d-orbitals than others.

• When white light shines on a transition metal complex, specific wavelengths of light are absorbed.
• This occurs because electrons in lower-energy d-orbitals absorb energy and are promoted to higher-energy d-orbitals.
• The energy difference ($\mathrm{\Delta }E$) between these split d-orbitals matches the energy of the absorbed light.

• The wavelengths not absorbed are transmitted or reflected, determining the observed color.
• The color you observe is the complementary color of the light absorbed.

Factors Affecting Color in Transition Metal Complexes

Several factors influence the color of a transition metal complex:

1. The Metal Ion: Different transition metals have varying d-electron configurations, which affect d-orbital splitting.
2. The Oxidation State: A higher oxidation state increases the positive charge on the metal ion, pulling ligands closer and causing greater splitting energy.
3. The Ligands: The nature of the ligands affects the splitting. Strong field ligands like cyanide ($C{N}^{-}$) cause greater splitting than weak field ligands like water ($H_{2}O$).
4. Geometry: The spatial arrangement of ligands (e.g., octahedral, tetrahedral) alters the splitting pattern.

The Relationship Between Wavelength and Frequency

The Physics of Light

Light is a type of electromagnetic radiation that behaves as a wave. Two key properties define these waves:

1. Wavelength ($\lambda$): The distance between two consecutive wave peaks, measured in meters (m).
2. Frequency ($f$): The number of wave cycles passing a point per second, measured in hertz (Hz).

These properties are connected by the speed of light ($c$), which is constant in a vacuum:
$$c=\lambda f$$
Where:

• $c=3.00\times {10}^8\text{m/s}$,
• $\lambda$ is the wavelength in meters,
• $f$ is the frequency in hertz.

Energy of Light and d-Orbital Splitting

• The energy of light absorbed during the promotion of d-electrons is directly proportional to its frequency: $$E=hf$$

Where:

• $E$ is the energy in joules (J),
• $h=6.63\times {10}^{-34}\text{J·s}$ (Planck's constant),
• $f$ is the frequency in hertz.

• By combining this with the wavelength-frequency relationship, we can express energy in terms of wavelength: $$E=\frac{hc}{\lambda }$$

This equation reveals that shorter wavelengths (e.g., violet light) correspond to higher energy, while longer wavelengths (e.g., red light) correspond to lower energy.

In transition metal complexes, the magnitude of $\mathrm{\Delta }E$ determines the wavelength of light absorbed.

Reflection and Review