Absorption of Light and Wavelength-Frequency Relationship 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 ($\Delta E$) 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.
Example
if a complex absorbs yellow light, it appears violet because violet is yellow's complementary color.
Factors Affecting Color in Transition Metal Complexes
Several factors influence the color of a transition metal complex:
- The Metal Ion: Different transition metals have varying d-electron configurations, which affect d-orbital splitting.
- The Oxidation State: A higher oxidation state increases the positive charge on the metal ion, pulling ligands closer and causing greater splitting energy.
- The Ligands: The nature of the ligands affects the splitting. Strong field ligands like cyanide ($CN^-$) cause greater splitting than weak field ligands like water ($H_2O$).
- Geometry: The spatial arrangement of ligands (e.g., octahedral, tetrahedral) alters the splitting pattern.
Example
- The complex $[Cu(H_2O)_6]^{2+}$ appears blue because it absorbs orange light. g in
- In contrast, $[CuCl_4]^{2-}$ appears yellow-green because it absorbs violet light.
- The difference in color arises because chloride ($Cl^-$) is a weaker ligand than water, resulting in smaller d-orbital splitting.
Example
Other examples of coloured compounds:
1. Hexaaquairon(III) Complex – Yellow-Brown
- Formula: $\text{[Fe(H}_2\text{O)}_6]^{3+}$
- Color: Yellow-brown
- Reason: Absorbs violet and blue light, transmitting yellow and red wavelengths.
2. Tetraamminecopper(II) Complex – Deep Blue (Royal Blue)
- Formula: $\text{[Cu(NH}_3\text{)}_4]^{2+}$
- Color: Deep blue
- Reason: Strong ligand field splitting causes absorption in the red-orange region, transmitting blue.
3. Hexacyanoferrate(III) Complex – Orange-Red
- Formula: $\text{[Fe(CN)}_6]^{3-}$
- Color: Orange-red
- Reason: Cyanide is a strong field ligand, causing higher energy absorption in the blue region, transmitting orange-red light.
4. Hexaamminecobalt(III) Complex – Yellow
- Formula: $\text{[Co(NH}_3\text{)}_6]^{3+}$
- Color: Yellow
- Reason: Absorbs violet and blue light, transmitting yellow.
Tip
- To predict the color of a complex, use the color wheel provided in your data booklet.
- Remember, the absorbed and observed colors are complementary.
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:
- Wavelength ($\lambda$): The distance between two consecutive wave peaks, measured in meters ($\text{m}$).
- Frequency ($f$): The number of wave cycles passing a point per second, measured in hertz ($\text{Hz}$).
- These properties are connected by the speed of light ($c$), which is constant in a vacuum:
$$c = \lambda f$$
where:- $c = 3.00 \times 10^8 \, \text{m s}^{-1}$,
- $\lambda$ 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: $$E = h f$$ 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: $$E = \frac{h c}{\lambda}$$
- 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 $\Delta E$ determines the wavelength of light absorbed.
Example question
The complex $[CuCl_4]^{2-}$ absorbs light with a wavelength of $491 \, \text{nm}$. Calculate the energy gap ($\Delta E$) between the d-orbitals.
Solution
- Convert the wavelength to meters:
$$
\lambda = 491 \, \text{nm} = 491 \times 10^{-9} \, \text{m}
$$ - Calculate the frequency using $c = \lambda f$:
$$
f = \frac{c}{\lambda} = \frac{3.00 \times 10^8 \, \text{m s}^{-1}}{491 \times 10^{-9} \, \text{m}} = 6.11 \times 10^{14} \, \text{Hz}
$$ - Calculate the energy using $E = h f$:
$$
E = (6.63 \times 10^{-34} \, \text{J·s}) (6.11 \times 10^{14} \, \text{Hz}) = 4.05 \times 10^{-19} \, \text{J}
$$
Thus, the energy gap is $4.05 \times 10^{-19} \, \text{J}$.
Common Mistake
- Always convert wavelengths from nanometers (nm) to meters (m) when using the formula $c = \lambda f$.
- Forgetting this step is a common source of error.
Self review
- Why do transition metal complexes often appear colored?
- How are wavelength and frequency related to the energy of light?
- What factors influence the color of a transition metal complex?
