Describe d-orbital degeneracy and ligand-field splitting
Represent how a surrounding ligand field splits d orbitals in octahedral and tetrahedral complexes.
Section 28 · Chemistry of transition elements
A Level; Cambridge International Chemistry 9701, 2028–2030 syllabus, Topic 28. Use the first-row transition elements titanium to copper and the species explicitly named in the syllabus. Where redox potentials or stability constants are needed, use the values supplied in the question. Colour descriptions can depend on conditions and concentration. Written practice is self-checked
Before you begin
- Use electron configurations, oxidation numbers, ionic equations, equilibrium expressions and the AS redox and bonding models.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
How many higher-energy d orbitals are shown in the syllabus octahedral split?
What you will learn
- Define degenerate and non-degenerate orbitals
- Show two higher and three lower d orbitals in an octahedral field
- Show three higher and two lower d orbitals in a tetrahedral field
Degenerate orbitals have equal energy
A set of degenerate d orbitals has the same energy. In an isolated gaseous ion, the five d orbitals are treated as degenerate in this syllabus model. Ligands approach the central metal and create an electric field that splits the set into orbitals of different energies.
After splitting, the two sets are non-degenerate: their energies differ by ΔE. Use the stated geometry to decide how many orbitals lie in each set and which set is higher.
Keep the octahedral and tetrahedral splits distinct
In an octahedral complex, the syllabus representation has three lower-energy d orbitals and two higher-energy d orbitals. In a tetrahedral complex, it has two lower-energy orbitals and three higher-energy orbitals.
A labelled energy-level sketch should include a common starting level, the two sets after splitting, their counts and the gap ΔE. This lesson does not require advanced ligand-field calculations or electron-pairing predictions.
Pause and explain
Which set is larger in number for tetrahedral splitting?
Worked example
Describe the d-orbital energy split for an octahedral complex.
Show the worked solution
- Start with five degenerate orbitals.
- Separate them into two energy levels.
- Label three lower, two higher and the gap ΔE.
Answer The five degenerate d orbitals split into three lower-energy and two higher-energy orbitals, separated by ΔE.
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Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Draw an energy-level description in words for five d orbitals before a ligand field acts.
Give me a hint
State the relationship among their energies before splitting.
Compare my reasoning
- Use one common energy level.
- Label five orbitals.
- State that they are degenerate in this model.
Five d orbitals lie at the same energy and are degenerate before splitting.
Look for these in your work
- Five orbitals stated
- Equal energy stated
- Degeneracy defined
A tetrahedral diagram shows two higher and three lower orbitals. Correct it.
Give me a hint
Use the syllabus count for tetrahedral complexes.
Compare my reasoning
- Tetrahedral has two lower orbitals.
- Tetrahedral has three higher orbitals.
- Mark ΔE between the two groups.
Swap the counts: two lower and three higher-energy orbitals, with ΔE between them.
Look for these in your work
- Lower count corrected
- Higher count corrected
- Energy gap shown
A learner uses the octahedral 3-lower/2-higher split for a tetrahedral complex. What exactly must change in the sketch and label?
Give me a hint
Compare the counts specified for each geometry.
Compare my reasoning
- Retain five total d orbitals.
- Use two lower and three higher for tetrahedral.
- Change the geometry label and preserve ΔE as the gap.
Keep five orbitals, but draw two lower and three higher levels and label the arrangement tetrahedral. ΔE still denotes the energy difference between sets.
Look for these in your work
- Total orbitals preserved
- Tetrahedral count correct
- Gap notation retained
Common mistakes
- Reversing the 3:2 counts for octahedral splitting
- Reversing the 2:3 counts for tetrahedral splitting
- Calling the split orbitals degenerate after their energies differ
- Drawing ΔE as a level rather than the gap between levels
What can you explain now?
How many higher-energy d orbitals are shown in the syllabus octahedral split?
Compare with the explanation
Two
The octahedral pattern is three lower and two higher.
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Make it stick
How are degenerate orbitals different from the split sets, and what are the octahedral and tetrahedral counts?
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