Q.Atomic number of Mn, Fe and Co are 25, 26 and 27 respectively. Which of the following inner orbital octahedral complex ions are diamagnetic?
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🔒 Start your 14-day free trial to unlock the full solution →Concept understanding — Crystal Field Splitting
Crystal Field Splitting: From Intuition to Precision
Imagine you are a negatively charged electron sitting on a metal ion. All around you, the space is perfectly spherical — every direction feels the same. Your energy depends only on how far you are from the nucleus, not on which way you face.
Now imagine that six negative ions (or the negative ends of polar molecules) march in from the x, y, and z axes and stop close to you. Suddenly, the space around you is no longer uniform. If you try to move straight toward one of these approaching ions, you feel a strong repulsion — that path costs extra energy. If you move between the axes (say, along a diagonal), you feel less repulsion because you are farther from the incoming charges.
This is the core intuition: when ligands approach a metal ion, they break the spherical symmetry of the space around the metal. Different directions in space are no longer equivalent. Electrons in orbitals that point directly at the ligands get pushed up in energy; electrons in orbitals that point between the ligands stay lower.
The Precise Statement
Crystal Field Splitting is the splitting of degenerate d orbitals of a transition metal ion into two or more sets of different energies, caused by the electrostatic repulsion between the metal's d electrons and the negative charge (or dipole) of surrounding ligands.
For the most common geometry — octahedral — here is what happens:
- Six ligands sit at the corners of an octahedron, along the +x, −x, +y, −y, +z, −z axes.
- The dx2−y2 and dz2 orbitals point their lobes directly along these axes. These are the eg set. They feel maximum repulsion → higher energy.
- The dxy, dxz, and dyz orbitals point their lobes between the axes (into the octahedral faces). These are the t2g set. They feel less repulsion → lower energy.
The energy gap between these two sets is denoted by Δo (or 10Dq). The t2g set drops by 0.4Δo and the eg set rises by 0.6Δo, keeping the average energy unchanged (the "barycentre" rule).
The labels eg and t2g come from group theory — they describe how the orbitals transform under the symmetry operations of an octahedron. You do not need to memorise the derivation, but the notation is standard in every exam.
Why This Matters
Crystal field splitting explains three things you will see repeatedly:
- Colour — electrons can jump from t2g to eg by absorbing visible light. The gap Δo determines the colour you see.
- Magnetism — if Δo is large, electrons pair up in the lower t2g set (low spin). If Δo is small, electrons spread out (high spin). This changes the number of unpaired electrons. …
Why this formula?
Crystal Field Splitting: Why the Energy Splitting Occurs
Crystal Field Theory (CFT) explains how the d-orbitals of a transition metal ion split in energy when placed in an electrostatic field created by surrounding ligands (anions or polar molecules). The key result is that five degenerate d-orbitals split into two or more sets with different energies. Let's understand why this happens.
1. The Starting Point: Degenerate d-Orbitals
In a free transition metal ion (no ligands), all five d-orbitals have the same energy (degenerate). Their shapes are:
- dxy, dxz, dyz — lobes lie between the x, y, z axes (called t2g set in octahedral symmetry)
- dx2−y2, dz2 — lobes point directly along the x, y, z axes (called eg set)
Key idea: The spatial orientation of each orbital determines how it interacts with approaching ligands.
2. The Octahedral Case: Why eg Orbitals Are Higher in Energy
Imagine six ligands approaching along the +x, –x, +y, –y, +z, –z axes (octahedral geometry).
What happens to dx2−y2 and dz2?
- Their lobes point directly at the ligands.
- The negatively charged ligands repel the electron density in these orbitals.
- This repulsion raises the energy of these orbitals — they become less stable (higher energy).
What happens to dxy, dxz, dyz?
- Their lobes point between the axes (e.g., dxy lobes lie in the xy-plane but at 45° to x and y).
- They avoid the ligands — less repulsion.
- Their energy is lower than the eg set.
The Splitting Pattern
Δoct=E(eg)−E(t2g)
Where:
- E(eg) = energy of dx2−y2 and dz2 (higher)
- E(t2g) = energy of dxy, dxz, dyz (lower)
- Δoct is called the crystal field splitting energy (CFSE)
Why the name? The eg orbitals are "doubly degenerate" (2 orbitals), t2g are "triply degenerate" (3 orbitals). The letters come from group theory symmetry labels.
3. The Energy Conservation Rule
The total energy of all five d-orbitals must remain constant (no energy is created or destroyed). So:
- The center of gravity (average energy) of the split set equals the original degenerate energy.
- For octahedral splitting:
- 2 eg orbitals go up by +0.6Δoct each
- 3 t2g orbitals go down by −0.4Δoct each
Check:
2×(+0.6Δ)+3×(−0.4Δ)=1.2Δ−1.2Δ=0
This conservation of energy is a fundamental constraint — the splitting is not arbitrary.
4. The Tetrahedral Case: Why It's Opposite and Smaller
In a tetrahedral complex, four ligands approach from alternate corners of a cube. The axes are different:
- The dxy, dxz, dyz orbitals now point closer to the ligands (more repulsion).
- The dx2−y2 and dz2 orbitals point away from ligands (less repulsion).
Result:
- e set ( dx2−y2, dz2 ) — lower energy
- t2 set ( dxy, dxz, dyz ) — higher energy
The splitting is inverted compared to octahedral.
Magnitude:
Δtet≈94Δoct
Why smaller?
- Only 4 ligands (vs. 6) → less total repulsion.
- Ligands are not directly along axes → weaker interaction. …
Concept: Crystal Field Splitting — strong-field ligands (like CN⁻, NH₃) cause large Δo, forcing pairing in low-spin (inner orbital) d2sp3 hybrids. Diamagnetic means all electrons paired.
Step 1: Oxidation states and dn configurations
- [Co(NH3)6]3+: Co = 27, Co³⁺ = d6
- [Mn(CN)6]3−: Mn = 25, Mn³⁺ = d4
- [Fe(CN)6]4−: Fe = 26, Fe²⁺ = d6
- [Fe(CN)6]3−: Fe = 26, Fe³⁺ = d5
Step 2: Strong-field pairing
CN⁻ and NH₃ are strong-field ligands → low-spin t2g filling first:
- d6 (Co³⁺, Fe²⁺): t2g6 → all paired → diamagnetic.
- d4 (Mn³⁺): t2g4 → one unpaired → paramagnetic.
- d5 (Fe³⁺): t2g5 → one unpaired → paramagnetic. …
The key is to identify which complex has all electrons paired (diamagnetic) by considering the metal’s oxidation state, d-electron count, and the strong-field (low-spin) nature of CN⁻ and NH₃ ligands in an inner orbital (d²sp³) octahedral geometry. The diamagnetic complexes are (i) [Co(NH3)6]3+ and (iii) [Fe(CN)6]4−.
Why Crystal Field Splitting Decides Magnetism
In an octahedral complex, the five d-orbitals split into two sets: the lower-energy t2g (three orbitals) and the higher-energy eg (two orbitals). The size of this splitting — called Δo — depends on the ligand. Strong-field ligands like CN⁻ and NH₃ cause a large Δo, forcing electrons to pair up in the t2g orbitals before occupying eg. This gives a low-spin configuration.
An inner orbital complex uses the inner (n−1)d orbitals for hybridisation (d²sp³), which is exactly what happens in low-spin cases. A complex is diamagnetic only if all electrons are paired — that is, the d-electron count is such that the low-spin configuration has zero unpaired electrons.
Let’s check each complex one by one.
1. [Co(NH3)6]3+
- Cobalt (atomic number 27) in +3 oxidation state: Co3+ has electron configuration [Ar]3d6.
- NH₃ is a strong-field ligand, so this is a low-spin d⁶ system.
- In low-spin octahedral: all six electrons pair up in the three t2g orbitals → t2g6eg0.
- Zero unpaired electrons → diamagnetic.
For d⁶, low-spin gives all paired electrons. This is the classic example of a diamagnetic Co(III) complex.
2. [Mn(CN)6]3−
- Manganese (atomic number 25) in +3 oxidation state: Mn3+ has [Ar]3d4.
- CN⁻ is a very strong-field ligand → low-spin.
- Low-spin d⁴: four electrons go into t2g, but one must pair up → t2g4eg0.
- That means two unpaired electrons (since t2g4 has one doubly occupied orbital and two singly occupied ones).
- Hence paramagnetic, not diamagnetic.
A common mistake is to think d⁴ always has four unpaired electrons. In strong field, pairing occurs, leaving two unpaired — not zero.
3. [Fe(CN)6]4−
- Iron (atomic number 26) in +2 oxidation state: Fe2+ has [Ar]3d6.
- CN⁻ is strong-field → low-spin d⁶.
- Same as Co³⁺ above: t2g6eg0 — all electrons paired.
- Diamagnetic.
…
Method: Crystal Field Theory (CFT) — Strong Field / Low Spin Analysis
Why this method?
Inner orbital (low spin) complexes form when the ligand is strong (like CN⁻, NH₃).
Diamagnetic means no unpaired electrons — all electrons are paired in the t2g and eg orbitals.
Steps
Step 1: Determine the oxidation state and dn configuration
-
(i) [Co(NH3)6]3+
Co: 27, charge +3 → d6 (Co³⁺)
-
(ii) [Mn(CN)6]3−
Mn: 25, charge +3 → d4 (Mn³⁺)
-
(iii) [Fe(CN)6]4−
Fe: 26, charge +2 → d6 (Fe²⁺)
-
(iv) [Fe(CN)6]3−
Fe: 26, charge +3 → d5 (Fe³⁺)
Step 2: Apply strong field (low spin) filling rule
For octahedral:
- t2g fills first (3 orbitals, each holds 2 electrons)
- Then eg fills
- Strong field → pairing occurs before eg is occupied
| Complex | dn | Low spin t2g | eg | Unpaired electrons | Diamagnetic? |
|---------|-------|-------------------|-------|--------------------|--------------| …
Common Mistakes in Crystal Field Splitting (Inner Orbital / Diamagnetic Complexes)
Mistake 1: Confusing Inner vs. Outer Orbital Complexes
The error: Students think any complex with CN− is automatically inner orbital.
Why it’s wrong: Inner orbital (low-spin) requires the metal ion to use (n−1)d orbitals for hybridisation — this happens only when the ligand is strong enough to cause pairing. But the metal’s oxidation state and dn configuration also matter.
How to avoid:
- For octahedral complexes:
- Inner orbital → d2sp3 hybridisation (uses inner d orbitals) → low-spin
- Outer orbital → sp3d2 hybridisation (uses outer d orbitals) → high-spin
- Strong field ligands (CN−, CO, NH3 for some metals) favour low-spin.
- Always check the dn count first.
Mistake 2: Forgetting to Find the Correct Oxidation State
The error: Students directly use the atomic number without calculating the oxidation state of the metal in the complex ion.
Why it’s wrong: The number of d electrons depends on the charge on the metal ion, not the neutral atom.
How to avoid:
- Let the complex be [M(L)n]x
- Let ligand charge be q (e.g., CN− is −1, NH3 is 0)
- Then: Oxidation state of M = x−(n×q)
- Then: dn = Atomic number of M — oxidation state — (charge of previous noble gas core)
Example:
[Fe(CN)6]4−
- CN− charge = −1, so total ligand charge = 6×(−1)=−6
- Let Fe oxidation state = y
- y+(−6)=−4⇒y=+2
- Fe (atomic no. 26) → Fe2+ = [Ar]3d6
Mistake 3: Assuming All NH3 Complexes Are Low-Spin
The error: Thinking NH3 always causes pairing.
Why it’s wrong: NH3 is a moderate field ligand — it can cause pairing only for certain dn configurations (e.g., d6 in Co3+) but not for all.
How to avoid:
- NH3 is stronger than water but weaker than CN−
- For Co3+ (d6), NH3 is strong enough to cause pairing → low-spin t2g6 → diamagnetic
- For Fe3+ (d5), NH3 is not strong enough → high-spin → paramagnetic
Mistake 4: Confusing Diamagnetic with Paramagnetic
The error: Students think “inner orbital” always means diamagnetic.
Why it’s wrong: Inner orbital means low-spin, but if the t2g set is not completely filled, unpaired electrons remain → paramagnetic.
How to avoid:
- Diamagnetic → all electrons paired → t2g fully filled (e.g., t2g6)
- Paramagnetic → at least one unpaired electron
- For d4, d5, d6, d7 low-spin configurations, check the t2g occupancy:
| dn | Low-spin t2g | Unpaired? |
|---|---|---|
| d4 | t2g4 | 2 unpaired → paramagnetic |
| d5 | t2g5 | 1 unpaired → paramagnetic |
| d6 | t2g6 | 0 unpaired → diamagnetic |
| d7 | t2g6eg1 | 1 unpaired → paramagnetic |
Mistake 5: Ignoring the “Inner Orbital” Condition in the Question
The error: Students check only diamagnetism, forgetting the question asks for inner orbital and diamagnetic.
Why it’s wrong: A complex could be diamagnetic but outer orbital (e.g., [Ni(CN)4]2− is square planar, not relevant here, but the principle holds).
How to avoid: …
Showing the 12 most recent of 17 on this concept.
- KEAM 2026Set eng-2026-04184 marksMCQQ.Which of the following complex ion absorbs yellow colour in the visible region? (A) [Co(NH3)6]+3 (B) [Co(CN)6]3− (C) [Cu(H2O)4]+2 (D) [Co(NH3)5(H2O)]+3 (E) [CoCl(NH3)5]+2
›Reveal solutionSolution
A complex absorbs the colour complementary to the one it appears; the violet/purple [CoCl(NH3)5]2+ absorbs yellow.
Observed colour is complementary to the absorbed colour. A species that absorbs yellow light appears violet/purple. …
- KEAM 2026Set eng-2026-04204 marksMCQQ.The order of field strength of the following ligands in the spectrochemical series is (A) NCS−<CN−<SCN−<S2−<OH− (B) NCS−<OH−<S2−<NCS−<CN− (C) CN−<S2−<OH−<NCS−<SCN− (D) SCN−<S2−<OH−<NCS−<CN− (E) SCN−<S2−<CN−<NCS−<OH−
›Reveal solutionSolution
Field strength increases: SCN−<S2−<OH−<NCS−<CN−. …
- KEAM 2026Set eng-2026-04214 marksMCQQ.The correct increasing order of wavelength of absorption of the following complexes is(i) [CoCl(NH3)5]2+(ii) [Co(NH3)5(H2O)]3+(iii) [Co(NH3)6]3+(iv) [Co(CN)6]3− (A)(i) <(ii) <(iii) <(iv) (B)(i) <(ii) <(iv) <(iii) (C)(ii) <(i) <(iv) <(iii) (D)(iv) <(iii) <(ii) <(i) (E)(iv) <(i) <(ii) < (iii)
›Reveal solutionSolution
Wavelength is inverse to Δo; increasing λ: (iv)<(iii)<(ii)<(i). …
- KEAM 2026Set pha-2026-0420F4 marksMCQQ.Which one of the statements is not the limitation of valence bond theory of complexes? (A) It does not give a quantitative interpretation of the thermodynamic stabilities. (B) It does not give quantitative interpretation of magnetic properties.. (C) It explains the colour exhibited by coordination compounds. (D) It does not distinguish between weak and strong ligands. (E) It does not make exact predictions regarding the tetrahedral structures of 4-coordinated complexes.
›Reveal solutionSolution
A recognised limitation of VBT is that it fails to explain colour; the statement that it explains colour (C) is therefore not a limitation.
Valence bond theory has several well-known limitations: it gives no quantitative account of thermodynamic stabilities (A), no quantitative account of magnetic properties (B), does not distinguish strong from weak ligands (D), and makes no exact prediction of tetrahedral geometries (E) — all genuine shortcomings. …
- KEAM 2025Set eng-2025-04294 marksMCQQ.The complex ions [NiCl4]2− and [Ni(CN)4]2− differ by(i) Magnetic moment(ii) Geometry(iii) Hybridisation of central metal ion(iv) Oxidation state of nickel (A) (i),(ii) and(iv) (B) (i),(ii) and(iii) (C) (ii),(iii) and(iv) (D)(ii) and(iii) (E) (i), (ii),(iii) and (iv)
›Reveal solutionSolution
Both have Ni in the +2 state, so (iv) does not differ. They differ in magnetic moment (i), geometry (ii) and hybridisation (iii) — option (B).
Both complexes have Ni2+ (d8), so the oxidation state (iv) is the same in both — it cannot be a point of difference.
- [NiCl4]2−: Cl− is a weak-field ligand, so no pairing occurs. Configuration d8 with 2 unpaired electrons → sp3 hybridisation → tetrahedral, paramagnetic. …
- KEAM 2025Set eng-2025-04294 marksMCQQ.Four complex ions are given in Column I and the colours of light absorbed are given in Column II. Match the correct answer from the codes given below. Complex:(a) [Ti(H2O)6]3+;(b) [Cu(H2O)4]2+;(c) [CoCl(NH3)5]2+;(d) [Co(NH3)6]3+ Colour of light absorbed:(i) Blue;(ii) Yellow;(iii) Blue green;(iv) Red (A) (a)-(iii), (b)-(iv), (c)-(ii), (d)-(i) (B) (a)-(ii), (b)-(iv), (c)-(iii), (d)-(i) (C) (a)-(iii), (b)-(ii), (c)-(iv), (d)-(i) (D) (a)-(i), (b)-(iv), (c)-(ii), (d)-(iii) (E) (a)-(iii), (b)-(iv), (c)-(i), (d)-(ii)
›Reveal solutionSolution
[!TLDR]
Using crystal-field strength to rank the d-d absorption energies, [Ti(H2O)6]3+ absorbs blue-green, [Cu(H2O)4]2+ red, [CoCl(NH3)5]2+ yellow and [Co(NH3)6]3+ blue — option (A).
Concept
In a transition-metal complex, d-electrons are excited across the crystal-field gap Δ. The complex absorbs the wavelength matching Δ; a stronger ligand field means a larger Δ and absorption of higher-energy (shorter-wavelength, toward blue/violet) light. This CFT reasoning is standard in the NCERT/CBSE coordination-chemistry chapter that the KEAM syllabus draws from.
Solution
- (b) [Cu(H2O)4]2+: aqua ligands give a small Δ; the deep-blue solution absorbs low-energy red light ⇒ (iv).
- (a) [Ti(H2O)6]3+: a single d-d band near 500nm absorbs blue-green light (complex looks purple) ⇒ (iii). …
- KEAM 2025Set pha-2025-0424F4 marksMCQQ.Which of the following is a spin free complex? (A) [Ni(CO)4] (B) [Co(NH3)6]3+ (C) [Ni(CN)4]2− (D) [CoF6]3− (E) [Mn(CN)6]3−
›Reveal solutionSolution
"Spin free" = high spin. Only [CoF6]3−, with the weak-field F− ligand, keeps its d-electrons unpaired (high spin).
A spin-free (high-spin) complex forms with weak-field ligands, where the crystal-field splitting is too small to force pairing.
- [Ni(CO)4]: CO strong field, Ni(0) d10 — diamagnetic, not relevant as "spin-free."
- [Co(NH3)6]3+: NH3 strong-ish field, Co3+ d6 — low spin.
- [Ni(CN)4]2−: CN− strong field — low-spin, square planar, diamagnetic. …
- KEAM 2025Set pha-2025-0424A4 marksMCQQ.Which of the following complex ion is diamagnetic? (A) [MnCl6]3− (B) [Fe(CN)6]3− (C) [Co(C2O4)3]3− (D) [FeF6]3− (E) [CoF6]3−
›Reveal solutionSolution
[Co(C2O4)3]3− is diamagnetic.
Check the unpaired electrons in each ion:
- [MnCl6]3−: Mn3+ d4, weak-field Cl− ⇒ 4 unpaired — paramagnetic.
- [Fe(CN)6]3−: Fe3+ d5 low spin t2g5 ⇒ 1 unpaired — paramagnetic.
- [Co(C2O4)3]3−: Co3+ d6; oxalate is a fairly strong field ligand giving low spin t2g6eg0 ⇒ 0 unpaired — diamagnetic. …
- KEAM 2025Set pha-2025-0429F4 marksMCQQ.Which of the following is an outer orbital complex? (A) [Co(NH3)6]3+ (B) [Mn(CN)6]3− (C) [Co(C2O4)3]3− (D) [MnCl6]3− (E) [Fe(CN)6]3−
›Reveal solutionSolution
Outer-orbital (high-spin) complexes form with weak-field ligands that use the outer d orbitals (sp3d2). Among the options only [MnCl6]3− has a weak-field ligand (Cl−); the rest have strong-field ligands (CN−, NH3, C2O42−) giving inner-orbital (d2sp3) complexes.
Reasoning
Whether a complex is inner- or outer-orbital depends on the ligand field strength:
- [Co(NH3)6]3+ — NH3 strong field, d2sp3, inner orbital.
- [Mn(CN)6]3− — CN− strong field, inner orbital.
- [Co(C2O4)3]3− — Co(III) with oxalate, low-spin inner orbital. …
- KEAM 2024Set eng-2024-06094 marksMCQQ.The type of d-d transition of the electron occurs in [Ti(H2O)6]3+ is (A) t2g2eg1→t2g1eg2 (B) t2g1eg0→t2g1eg0 (C) t2g1eg0→t2g0eg1 (D) t2g0eg1→t2g1eg0 (E) t2g2eg0→t2g1eg1
›Reveal solutionSolution
Ti3+ is a d1 ion; the single electron jumps t2g→eg.
In [Ti(H2O)6]3+, titanium is in the +3 state: Ti is [Ar]3d24s2, so Ti3+ is [Ar]3d1 — a single d electron. In an octahedral field it occupies the lower t2g set: t2g1eg0. Absorption of light (giving the violet col …
- KEAM 2024Set eng-2024-06094 marksMCQQ.The increasing order of field strength of ligands in the spectrochemical series is (A) CO<H2O<Cl−<I− (B) Cl−<H2O<CO<I− (C) H2O<CO<I−<Cl− (D) H2O<I−<Cl−<CO (E) I−<Cl−<H2O<CO
›Reveal solutionSolution
Increasing field strength: I−<Cl−<H2O<CO.
In the spectrochemical series the ligands are arranged by increasing crystal-field splitting power. The relevant fragment is
I−<Br−<Cl−<F−<H2O<NH3<en<CN−≈CO.
Hence for the given ligands the increasing field strength is …
- KEAM 2024Set eng-2024-06094 marksMCQQ.The number of unpaired electrons in [CoF6]3− is (A) one (B) four (C) zero (D) two (E) three
›Reveal solutionSolution
[CoF6]3− is a high-spin d6 complex (weak-field F−) with 4 unpaired electrons.
Cobalt in [CoF6]3− is Co3+: [Ar]3d6. Fluoride is a weak-field ligand, so the splitting Δo is small and the complex is high spin. The six d electrons fill as
t2g4eg2, …
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