Q.Write down the electronic configuration of:
Concept understanding — Stability of Oxidation States
Stability of Oxidation States – From Intuition to Precision
Imagine you're holding a ball on a hill. If you place it exactly at the top, it's balanced — but the slightest push sends it rolling down. That's an unstable position. If you place it in a small dip on the hillside, it stays put even if nudged — that's stable. Oxidation states work the same way: some are like the hilltop (easily changed), others like the dip (hard to change).
The Core Intuition
An oxidation state is just a number we assign to an atom to track how many electrons it has gained or lost compared to its neutral state. But atoms don't "want" to stay in arbitrary oxidation states — they want to reach a configuration that minimises their energy.
Stability here means: how reluctant is that oxidation state to change under normal conditions? A stable oxidation state resists being oxidised further or reduced further. An unstable one readily changes into something else.
The Precise Statement
Stability of an oxidation state refers to the tendency of an element to maintain that particular oxidation state under given conditions (temperature, pH, presence of other reagents). A stable oxidation state is one that does not easily undergo redox reactions — it is neither easily oxidised nor easily reduced.
This depends on three key factors:
- Electronic configuration – Half-filled and fully-filled d or f subshells confer extra stability (e.g., Fe3+ with d5 is more stable than Fe2+ with d6 in some contexts).
- Inert pair effect – Heavier p-block elements (like Tl, Pb, Bi) show lower oxidation states (e.g., +1 for Tl) as more stable than higher ones (+3 for Tl), because the s-electrons become reluctant to participate.
- Disproportionation tendency – Some oxidation states are unstable because they spontaneously convert into two other states (e.g., Cu+ in aqueous solution gives Cu2+ and Cu).
Stability is relative — it depends on the environment. Mn2+ is stable in acidic solution but easily oxidised in alkaline medium. Always specify conditions when discussing stability.
Examples That Make It Concrete
Transition metals – Cr3+ (d3) and Mn2+ (d5) are exceptionally stable because half-filled/half-filled-like configurations have low energy. Cr2+ (d4) is easily oxidised to Cr3+ — it's unstable.
p-block elements – Pb2+ is stable, Pb4+ is a strong oxidising agent (unstable). Sn2+ is a reducing agent (easily oxidised to Sn4+), so Sn4+ is more stable for tin.
Common pattern – For most elements, the most common oxidation state is the most stable one under standard conditions. But "most common" isn't always "most stable" — e.g., Fe3+ is common but Fe2+ is more stable in acidic solution.
Do not confuse "stability" with "occurrence". Mn7+ (as MnO4−) is common in the lab but is a powerful oxidising agent — it is not stable in the sense of resisting change. It readily accepts electrons.
How to Think About It in Exams
When asked "Explain the stability of oxidation states of [element]", follow this mental checklist:
- Write the electronic configuration of the atom.
- Write configurations for each possible oxidation state.
- Look for half-filled, fully-filled, or inert pair effects.
- Check if the state can disproportionate (common for +1 states of Cu, Au, and +3 states of Mn).
- Mention the medium (acidic/alkaline) if relevant.
For d-block elements, remember: d0, d5, and d10 are especially stable. For p-block, the inert pair effect makes lower oxidation states more stable as you go down the group.
The Bottom Line
Stability of an oxidation state is a measure of how strongly an atom holds onto that oxidation number — how hard it is to push it up or down. It's determined by electronic structure, the element's position in the periodic table, and the chemical environment. Master this, and you'll predict redox behaviour without memorising every reaction.
Stability of oxidation states among transition and inner-transition elements is discussed in the NCERT/CBSE Class 12 Chemistry chapter on d- and f-Block Elements, and ‘stability of oxidation states in transition elements’ is a frequently searched important-question topic for board exams, JEE Main and NEET. Predicting which oxidation state is most stable is a reasoning skill regularly tested in competitive-exam inorganic chemistry MCQs.
Why this formula?
Stability of Oxidation States: Why It Works
This concept explains why certain oxidation states of an element are more stable than others — and why some states are never observed at all.
The Core Idea: Energy Minimisation
An oxidation state is stable when the total energy of the system is at a minimum. This depends on three competing factors:
- Ionisation energy (energy needed to remove electrons)
- Lattice energy (for ionic compounds) or bond energy (for covalent compounds)
- Electronic configuration (half-filled / fully-filled subshells)
There is no single formula for stability — instead, we use trends and principles that act as "formulae" for prediction.
Key Principle 1: Inert Pair Effect (for p-block elements)
Why it holds:
For heavier elements (e.g., Tl, Pb, Bi), the 6s² electrons are held very tightly due to poor shielding and relativistic effects. They resist removal.
- Result: Lower oxidation state (e.g., +1 for Tl, +2 for Pb) becomes more stable than the higher state (+3, +4).
- Example: TlX3+ is a strong oxidising agent — it readily gains two electrons to become TlX+.
Derivation logic:
The energy cost to remove the 6s² electrons is greater than the energy gained by forming additional bonds or lattice. So the system stays in the lower state.
Key Principle 2: Half-Filled / Fully-Filled Subshell Stability
Why it holds:
A half-filled (d5, f7) or fully-filled (d10, f14) subshell has extra exchange energy and symmetry — making it unusually stable.
- Example: MnX2+ (d5) is more stable than MnX3+ (d4). FeX3+ (d5) is more stable than FeX2+ (d6).
Derivation logic:
The exchange energy (Hund's rule) is maximum for half-filled configurations. Removing an electron from a half-filled shell costs extra energy — so the half-filled state is favoured.
Key Principle 3: Lattice Energy / Hydration Energy Compensation
For transition metals, stability of a particular oxidation state in aqueous solution depends on:
ΔG∘=ΔHhydration∘−ΔHionisation∘
Why it holds:
- Higher oxidation states have higher ionisation energy (harder to remove electrons).
- But they also have higher hydration energy (smaller, more charged ions attract water more strongly).
- The balance determines which state is stable.
Example:
- CuX+ is unstable in water because its hydration energy is too low to compensate for the loss of the second electron.
- CuX2+ is stable in water.
Key Principle 4: Disproportionation
Some oxidation states are unstable and spontaneously convert to two other states:
2CuX+Cu+CuX2+
Why it holds:
The free energy change ΔG∘ for the reaction is negative. This happens when the intermediate oxidation state is less stable than the extremes.
Formula (for aqueous ions):
If Ereduction∘ for the higher state is more positive than for the lower state, disproportionation is spontaneous.
Summary Table: Why Each "Formula" Holds
| Principle | Why it works | Key exam example |
|---|---|---|
| Inert pair effect | 6s² electrons are too tightly bound | PbX2+ stable, PbX4+ oxidising |
| Half-filled stability | Extra exchange energy | MnX2+ > MnX3+ |
| Hydration vs ionisation | Energy balance in solution | CuX2+ stable, CuX+ not |
| Disproportionation | ΔG<0 for intermediate state | CuX+ in water |
Final Takeaway for Exams
Never memorise stability blindly. Always ask:
- Is the electronic configuration special? (half-filled / inert pair)
- Is the medium aqueous or solid? (hydration vs lattice)
- Does the element belong to a heavier group? (inert pair effect)
The "formula" is really a balance of energies — and the reasoning is what gets you marks.
Concept: Stability of Oxidation States — ions with half-filled, fully-filled, or empty d/f subshells are particularly stable.
Reasoning:
- Write the ground-state configuration of the neutral atom.
- Remove electrons from the outermost orbitals (ns before (n−1)d for transition metals; 6s before 4f for lanthanides/actinides).
- Adjust for stability: Cr3+ loses the 4s1 electron first, then two 3d electrons.
- Cr: [Ar]3d54s1 → remove 4s1 + two 3d → [Ar]3d3
- Pm: [Xe]4f56s2 → remove 6s2 + one 4f → [Xe]4f4
- Cu: [Ar]3d104s1 → remove 4s1 → [Ar]3d10
- Ce: [Xe]4f15d16s2 → remove 6s2 + 5d1 + one 4f → [Xe] (empty 4f)
- Co: [Ar]3d74s2 → remove 4s2 → [Ar]3d7
- Lu: [Xe]4f145d16s2 → remove 6s2 (2 e⁻, matching the +2 charge) → [Xe]4f145d1
- Mn: [Ar]3d54s2 → remove 4s2 → [Ar]3d5
- Th: [Rn]6d27s2 → remove 7s2 + 6d2 → [Rn]
✓Final answer
(i) [Ar]3d3 (ii) [Xe]4f4 (iii) [Ar]3d10 (iv) [Xe] (v) [Ar]3d7 (vi) [Xe]4f145d1 (vii) [Ar]3d5 (viii) [Rn]
The key idea is to first write the ground-state configuration of the neutral atom, then remove electrons from the outermost shells (highest n, then highest l within that n) to form the cation. The final configurations are: (i) [Ar]3d3,
(ii) [Xe]4f4,
(iii) [Ar]3d10,
(iv) [Xe]4f0,
(v) [Ar]3d7,
(vi) [Xe]4f145d1,
(vii) [Ar]3d5,
(viii) [Rn].
When writing electronic configurations for ions, the most common mistake is to remove electrons from the last filled subshell in the neutral atom. That is wrong. The correct rule: electrons are removed from the orbital with the highest principal quantum number n first. If two orbitals share the same n, remove from the one with the higher azimuthal quantum number l (i.e., p before s, d before p, etc.). This is because orbitals with higher n are farther from the nucleus and less tightly bound.
For transition metals and lanthanides/actinides, this means that the ns electrons (where n is the period number) are lost before the (n−1)d or (n−2)f electrons. Let’s apply this step by step.
1. Cr3+
Neutral Cr (Z=24) has configuration: [Ar]3d54s1.
Why 3d54s1 and not 3d44s2? Because a half-filled d subshell (d5) is extra stable — this is an exception you must remember.
To form Cr3+, remove 3 electrons. Start with the highest n: the 4s electron goes first. That gives [Ar]3d5. Then remove two more from the 3d subshell (since n=3 is now the highest). 3d5 minus 2 electrons = 3d3.
Do not remove 4s electrons last. Many students write [Ar]3d24s1 for Cr3+, which is incorrect. The 4s orbital is higher in energy than 3d once the atom is ionized.
Answer: [Ar]3d3
2. Pm3+
Promethium (Pm, Z=61) is a lanthanide. Neutral configuration: [Xe]4f56s2.
Lanthanides fill the 4f subshell after 6s. For Pm3+, remove 3 electrons. Highest n is 6: remove both 6s electrons first. Then remove one more from the 4f subshell (next highest n is 4). 4f5 minus 1 = 4f4.
Answer: [Xe]4f4
3. Cu+
Copper (Cu, Z=29) neutral: [Ar]3d104s1 (another exception — full d subshell is stable).
Remove 1 electron. Highest n is 4: remove the 4s electron. That leaves [Ar]3d10.
Cu+ has a completely filled d subshell (d10), which is very stable. This is why copper(I) compounds are common.
Answer: [Ar]3d10
4. Ce4+
Cerium (Ce, Z=58) neutral: [Xe]4f15d16s2 (NCERT Table 4.9's form; the alternative 4f26s2 is sometimes quoted in the literature).
Remove 4 electrons. First, remove both 6s electrons, then the 5d electron, then the single 4f electron. So the configuration is just the noble gas core [Xe].
Answer: [Xe]
5. Co2+
Cobalt (Co, Z=27) neutral: [Ar]3d74s2.
Remove 2 electrons. Highest n is 4: remove both 4s electrons. That leaves [Ar]3d7.
Answer: [Ar]3d7
6. Lu2+
Lutetium (Lu, Z=71) neutral: [Xe]4f145d16s2.
Remove 2 electrons. Highest n is 6: remove both 6s electrons. That leaves [Xe]4f145d1.
Lu is the last lanthanide; its 4f subshell is full (4f14). The 5d electron is present because after 4f14, the next electron goes into 5d (not 4f).
Answer: [Xe]4f145d1
7. Mn2+
Manganese (Mn, Z=25) neutral: [Ar]3d54s2.
Remove 2 electrons. Highest n is 4: remove both 4s electrons. That leaves [Ar]3d5.
Mn2+ has a half-filled d subshell (d5), which gives it extra stability. This is why manganese(II) is a common oxidation state.
Answer: [Ar]3d5
8. Th4+
Thorium (Th, Z=90) is an actinide. Neutral: [Rn]6d27s2.
Remove 4 electrons. Highest n is 7: remove both 7s electrons. Then remove two from 6d: 6d2 minus 2 = 6d0. So the configuration is just [Rn].
Answer: [Rn]
The configurations are: (i) [Ar]3d3,
(ii) [Xe]4f4,
(iii) [Ar]3d10,
(iv) [Xe],
(v) [Ar]3d7,
(vi) [Xe]4f145d1,
(vii) [Ar]3d5,
(viii) [Rn].
Method: Electronic Configuration Using the Aufbau Principle + Ionization Sequence
This method uses the Aufbau order (filling order: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p) and the rule that for ions, electrons are removed first from the outermost shell (highest n), not from the subshell that was filled last.
Steps
- Write the ground-state configuration of the neutral atom using the Aufbau order.
- Remove electrons equal to the positive charge, starting from the highest principal quantum number (n) shell.
- Write the final configuration in order of increasing n (and within same n, increasing ℓ).
Solutions
(i) Cr3+
- Neutral Cr (Z = 24): [Ar]3d54s1 (Exception: half-filled d-subshell stability)
- Remove 3 electrons: first from 4s (1 e⁻), then from 3d (2 e⁻)
- Cr3+: [Ar]3d3
(ii) Pm3+
- Neutral Pm (Z = 61): [Xe]4f56s2
- Remove 3 electrons: from 6s (2 e⁻), then from 4f (1 e⁻)
- Pm3+: [Xe]4f4
(iii) Cu+
- Neutral Cu (Z = 29): [Ar]3d104s1 (Exception: fully filled d-subshell)
- Remove 1 electron: from 4s
- Cu+: [Ar]3d10
(iv) Ce4+
- Neutral Ce (Z = 58): [Xe]4f15d16s2 (Actual ground state: [Xe]4f15d16s2)
- Remove 4 electrons: from 6s (2 e⁻), then 5d (1 e⁻), then 4f (1 e⁻)
- Ce4+: [Xe] (noble gas core)
(v) Co2+
- Neutral Co (Z = 27): [Ar]3d74s2
- Remove 2 electrons: from 4s
- Co2+: [Ar]3d7
(vi) Lu2+
- Neutral Lu (Z = 71): [Xe]4f145d16s2
- Remove 2 electrons: from 6s (2 e⁻)
- Lu2+: [Xe]4f145d1
(vii) Mn2+
- Neutral Mn (Z = 25): [Ar]3d54s2
- Remove 2 electrons: from 4s
- Mn2+: [Ar]3d5
(viii) Th4+
- Neutral Th (Z = 90): [Rn]6d27s2
- Remove 4 electrons: from 7s (2 e⁻), then 6d (2 e⁻)
- Th4+: [Rn] (noble gas core)
Key Exam Insight
Stability of oxidation states is linked to half-filled (d5, f7) or fully filled (d10, f14) subshells.
For example:
- Mn2+ (d5) is stable → half-filled stability
- Cu+ (d10) is stable → fully filled stability
- Ce4+ ([Xe]) is stable → noble gas configuration
Here are the most common mistakes students make when writing electronic configurations for ions, especially in the context of Stability of Oxidation States (d- and f-block elements), and how to avoid each.
Mistake 1: Forgetting that electrons are removed from the 4s orbital first (for d-block ions)
The Error:
For Cr3+, writing [Ar]3d14s2 — removing all three electrons from 3d and leaving the 4s pair untouched.
The same wrong removal order turns Co2+ into [Ar]3d54s2 instead of the correct [Ar]3d7.
Why it happens:
Students memorise "4s is filled before 3d" but forget that when forming cations, electrons are removed from the 4s orbital first (because 4s is higher in energy once occupied).
How to avoid:
- For any d-block ion, always remove from 4s before 3d.
- Write the neutral atom configuration first, then strip the outermost s-electrons.
- Example:
- Neutral Cr: [Ar]3d54s1
- Cr3+: remove 1 from 4s, then 2 from 3d → [Ar]3d3
- Neutral Co: [Ar]3d74s2
- Co2+: remove 2 from 4s → [Ar]3d7
Mistake 2: Ignoring the stability of half-filled and fully-filled d-subshells
The Error:
For Cu+, students write [Ar]3d94s0 (which is technically possible) but miss that Cu+ is actually [Ar]3d10 (fully filled d — very stable).
Similarly, for Cr3+, they might write [Ar]3d24s1 instead of [Ar]3d3.
Why it happens:
They don't check if a half-filled (d5) or fully-filled (d10) configuration is possible after ionisation.
How to avoid:
- After removing electrons, check if the d-subshell becomes d5 or d10 — these are extra stable.
- For Cu+:
- Neutral Cu: [Ar]3d104s1
- Remove 1 electron (from 4s) → [Ar]3d10 (fully filled) — this is the correct configuration.
- For Cr3+:
- Neutral Cr: [Ar]3d54s1
- Remove 3 electrons (1 from 4s, 2 from 3d) → [Ar]3d3 (not half-filled, but correct).
Mistake 3: Writing f-block configurations with the wrong removal order (6s must go first)
The Error:
For Pm3+, students remove all three electrons from 4f, writing [Xe]4f26s2 instead of the correct [Xe]4f4 (remove the 6s pair first, then one 4f).
For Ce4+, they write [Xe]4f15d1 or [Xe]4f2 instead of [Xe] (empty f — f0).
For Lu2+, they remove the 5d electron first, writing [Xe]4f146s1 instead of the correct [Xe]4f145d1 (the 6s pair goes first).
Why it happens:
f-block elements have complex filling order (4f, 5d, 6s). Students forget that for lanthanides, the 4f is filled before 5d and 6s, and that stable oxidation states often correspond to f⁰, f⁷, f¹⁴.
How to avoid:
- For lanthanides (Ce to Lu), the neutral configuration is [Xe]4fn5d0 or [Xe]4fn−15d1 (exceptions: La, Gd, Lu).
- When forming ions, remove 6s electrons first, then 4f (if needed).
- Examples:
- Ce4+: Neutral Ce = [Xe]4f15d16s2 (or [Xe]4f26s2). Remove 4 electrons → [Xe] (f⁰ — very stable).
- Pm3+: Neutral Pm = [Xe]4f56s2. Remove 3 electrons (2 from 6s, 1 from 4f) → [Xe]4f4.
- Lu2+: Neutral Lu = [Xe]4f145d16s2. Remove 2 electrons (from 6s) → [Xe]4f145d1 (but note: Lu2+ is unstable; the stable ion is Lu3+ = [Xe]4f14).
Mistake 4: Confusing actinide configurations with lanthanides
The Error:
For Th4+, students write [Rn]5f06d07s0 (which is correct) but they might write [Rn]5f2 or [Rn]6d2 because they misremember the neutral configuration.
Why it happens:
Actinides have 5f, 6d, 7s filling that is less regular than lanthanides. Thorium (Th) is an exception: neutral Th = [Rn]6d27s2, not [Rn]5f2.
How to avoid:
- Memorise key exceptions:
- Th (Z=90): [Rn]6d27s2
- Pa (Z=91): [Rn]5f26d17s2
- U (Z=92): [Rn]5f36d17s2
- For Th4+: remove 4 electrons (2 from 7s, 2 from 6d) → [Rn] (noble gas core, f⁰ — very stable).
Mistake 5: Not checking for exceptions in neutral configurations before ionising
The Error:
For Cr3+, students start from [Ar]3d44s2 (wrong neutral Cr) and then remove 3 electrons → [Ar]3d34s0 (correct final, but wrong reasoning).
For Cu+, they start from [Ar]3d94s2 (wrong neutral Cu) → [Ar]3d9 (wrong).
Why it happens:
They don't memorise the anomalous configurations of Cr and Cu in the neutral state.
How to avoid:
- Memorise these neutral exceptions:
- Cr: [Ar]3d54s1 (not 3d44s2)
- Cu: [Ar]3d104s1 (not 3d94s2)
- Also: Nb, Mo, Ru, Rh, Pd, Ag, Pt, Au have similar anomalies.
- Always write the correct neutral configuration first, then remove electrons.
Quick Reference Table for the Given Ions
| Ion | Correct Configuration | Common Mistake |
|---|---|---|
| Cr3+ | [Ar]3d3 | [Ar]3d14s2 or [Ar]3d24s1 |
| Pm3+ | [Xe]4f4 | [Xe]4f5 or [Xe]4f35d1 |
| Cu+ | [Ar]3d10 | [Ar]3d94s0 |
| Ce4+ | [Xe] (f⁰) | [Xe]4f2 or [Xe]4f15d1 |
| Co2+ | [Ar]3d7 | [Ar]3d54s2 (wrong removal order) |
| Lu2+ | [Xe]4f145d1 (unstable) | [Xe]4f135d2 or [Xe]4f146s2 |
| Mn2+ | [Ar]3d5 | [Ar]3d34s2 |
| Th4+ | [Rn] (f⁰) | [Rn]5f2 or [Rn]6d2 |
Final Exam Tip
Always write the neutral configuration first, then remove electrons from the outermost s-orbital (and then d or f if needed). Check for half-filled/full-filled stability. For f-block, remember f⁰, f⁷, f¹⁴ are especially stable.
Showing the 12 most recent of 19 on this concept.
- CBSE 2026Set 56/3/11 markMCQQ.In aqueous solution, Cr2O72− ion converts to which of the following in alkaline medium ? (A) Cr3+ (B) CrO42− (C) CrO (D) CrO3
›Reveal solutionSolution
In alkaline medium, dichromate (Cr2O72−) converts to chromate (CrO42−) without any change in oxidation state — it’s a simple acid-base equilibrium, not a redox reaction. The correct option is (B).
The key to this question lies in understanding that the conversion of dichromate to chromate is not a redox reaction — the oxidation state of chromium remains +6 throughout. Many students instinctively think of reduction to Cr3+ because they associate dichromate with strong oxidizing behaviour, but that only happens in acidic medium. In alkaline conditions, the chemistry is entirely different.
Let’s walk through the reasoning step by step.
-
Recall the oxidation state of chromium in dichromate.
In Cr2O72−, each oxygen is -2, so total from seven oxygens is -14. The ion has a -2 charge, so the sum of oxidation states of the two chromium atoms must be +12. Hence each Cr is in the +6 state.
-
Now consider the alkaline medium.
When you add a base (like NaOH) to a solution of K2Cr2O7, the dichromate ion reacts with hydroxide ions. The reaction is:
Cr2O72−+2OH−→2CrO42−+H2O
Notice that the oxidation state of Cr in CrO42− is also +6 (four oxygens at -2 give -8, charge -2, so Cr = +6). No electrons are transferred — this is an acid-base equilibrium, not a redox change.
- Why does this happen? Dichromate exists in equilibrium with chromate, and the position depends on pH. In acidic solution, the equilibrium shifts toward dichromate; in alkaline solution, it shifts toward chromate. The reaction is:
2CrO42−+2H+⇌Cr2O72−+H2O
Adding OH− removes H+, pulling the equilibrium to the left — producing chromate.
Watch outA common mistake is to think that alkaline medium reduces Cr2O72− to Cr3+. That reduction (Cr6+→Cr3+) requires an acidic environment and a reducing agent. In pure alkaline medium, no reduction occurs — only the structural change from dichromate to chromate.
- Check the options.
- (A) Cr3+ — requires reduction, not happening here.
- (B) CrO42− — correct, as shown.
- (C) CrO — that’s Cr in +2 state, impossible under these conditions.
- (D) CrO3 — chromium trioxide, an acidic oxide that forms in strongly acidic conditions, not alkaline.
TipA quick memory aid: Acid = dichromate (orange), Alkali = chromate (yellow). The colour change from orange to yellow when you add NaOH to K2Cr2O7 is a classic lab demonstration.
✓Final answerThe correct option is (B) CrO42−.
-
- CBSE 2026Set 56/1/11 markMCQQ.Assertion (A) : Actinoids show wide range of oxidation states. Reason (R) : Actinoids are radioactive in nature. (A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A). (B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A). (C) Assertion (A) is true, but Reason (R) is false. (D) Assertion (A) is false, but Reason (R) is true.
›Reveal solutionSolution
The assertion that actinoids show a wide range of oxidation states is true, but the reason given — that they are radioactive — is not the correct explanation. The correct explanation lies in the small energy gap between 5f, 6d, and 7s orbitals, which allows many electrons to participate in bonding. So the answer is option (B).
The question tests your understanding of why actinoids (elements 90–103, from thorium to lawrencium) exhibit so many different oxidation states. Many students memorise that “actinoids show variable oxidation states” and also know they are radioactive, so they assume the second explains the first. That’s a trap.
Let’s break it down properly.
-
Is Assertion (A) true?
Yes. Actinoids display a remarkably wide range of oxidation states. For example, uranium shows +3, +4, +5, and +6; neptunium and plutonium go from +3 to +7. This is far more varied than most d-block elements. The reason is that the 5f, 6d, and 7s orbitals are very close in energy. Electrons from all three can be lost with relatively little energy cost, so many different oxidation numbers become accessible.
-
Is Reason (R) true?
Yes, actinoids are indeed radioactive. All actinoid nuclei are unstable and decay over time. So the reason statement is factually correct.
-
Does the radioactivity explain the wide range of oxidation states?
No. Radioactivity is a nuclear property — it depends on the instability of the nucleus (proton/neutron ratio, nuclear binding energy). Oxidation states are an electronic property — they depend on how easily electrons are lost from the outer orbitals. These two phenomena are completely independent.
Watch outA common mistake is to think that because both statements are true, the reason must be the explanation. But correlation is not causation. Radioactivity does not cause variable oxidation states; the orbital energy structure does.
-
What actually causes the wide range of oxidation states in actinoids?
The key factor is the small energy difference between the 5f, 6d, and 7s subshells. In actinoids, the 5f orbitals are not as deeply buried as the 4f orbitals in lanthanoids. This means that 5f electrons can participate in bonding almost as easily as 6d and 7s electrons. As a result, you can remove anywhere from 3 to 7 (or even more) electrons without a huge energy penalty.
TipCompare with lanthanoids: their 4f orbitals are much more compact and shielded, so they typically show only +3 (and occasionally +2 or +4). The 5f orbitals in actinoids are more diffuse, so they are more “available” for oxidation.
-
Putting it together for the exam format
- Assertion (A): True
- Reason (R): True
- Reason (R) is not the correct explanation of Assertion (A) This matches option (B).
✓Final answerThe correct option is (B): Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
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- CBSE 2026Set ANNUAL1 markMCQQ.Which of the following oxidation states is common for all lanthanoids?(a) +2(b) +3(c) +4(d) +5
›Reveal solutionSolution
All lanthanoids show a characteristic +3 oxidation state because it corresponds to a stable, similar electronic configuration achieved after losing the two 6s and one 4f (or 5d) electron.
Lanthanoids have the general electronic configuration [Xe] 4f^(1-14) 5d^(0-1) 6s2. Removal of the two 6s electrons and one more electron (from 4f or 5d) gives the Ln3+ ion, which is the most stable and commonly observed oxidation state across the entire series, from Ce to Lu.
While some lanthanoids also show +2 or +4 states (e.g., Ce4+, Eu2+) due to the extra stability of empty, half-filled, or fully-filled f-subshells, these are exceptions shown only by a few members - the +3 state alone is common to ALL lanthanoids.
✓Final answer(b) +3.
- CBSE 2025Set 56/4/11 markMCQQ.The product of the oxidation of I− with MnO4− in alkaline medium is : (A) IO4− (B) I2 (C) IO− (D) IO3−
›Reveal solutionSolution
In alkaline medium, permanganate (MnO4−) oxidises iodide (I−) to iodate (IO3−), not to iodine or periodate. The balanced reaction shows I− loses 6 electrons to form IO3−, while MnO4− gains 3 electrons to form MnO2. The correct product is IO3−, option (D).
Why the medium matters
The oxidation state of iodine in its products depends heavily on the pH of the solution. Permanganate is a powerful oxidising agent, but its reduction product changes with medium:
- In acidic medium: MnO4−→Mn2+ (gains 5 electrons)
- In neutral/alkaline medium: MnO4−→MnO2 (gains 3 electrons)
This difference in electron gain per mole of permanganate directly affects how far it can oxidise iodide. In alkaline medium, permanganate is a milder oxidising agent (gains only 3 electrons) compared to acidic medium (gains 5 electrons). Yet it still oxidises I− all the way to IO3−, not stopping at I2.
Step-by-step reasoning
-
Identify the half-reactions
Iodide (I−) has oxidation state −1. The possible products given are:
- IO4−: iodine in +7 state
- I2: iodine in 0 state
- IO−: iodine in +1 state (hypoiodite)
- IO3−: iodine in +5 state (iodate)
In alkaline medium, permanganate reduces to MnO2 (manganese in +4 state, from +7 in MnO4−).
-
Balance the oxidation half-reaction
Iodide going to iodate:
I−→IO3−
Balance oxygen with water (alkaline medium):
I−+3H2O→IO3−+6H+
Balance charge: left side has −1, right side has −1+6=+5. Add 6 electrons to right:
I−+3H2O→IO3−+6H++6e−
In alkaline medium, add OH− to neutralise H+:
I−+6OH−→IO3−+3H2O+6e−
So each I− loses 6 electrons to become IO3−.
-
Balance the reduction half-reaction
Permanganate to manganese dioxide in alkaline medium:
MnO4−→MnO2
Balance oxygen with water:
MnO4−+2H2O→MnO2+4OH−
Balance charge: left −1, right −4. Add 3 electrons to left:
MnO4−+2H2O+3e−→MnO2+4OH−
So each MnO4− gains 3 electrons.
-
Combine the half-reactions
To equalise electrons: multiply reduction half by 2 (gives 6 electrons gained) and oxidation half by 1 (gives 6 electrons lost):
2MnO4−+4H2O+6e−→2MnO2+8OH−
I−+6OH−→IO3−+3H2O+6e−
Adding:
2MnO4−+I−+4H2O+6OH−→2MnO2+IO3−+3H2O+8OH−
Cancel 3H2O from both sides and 6OH− from both sides:
2MnO4−+I−+H2O→2MnO2+IO3−+2OH−
This is the balanced net ionic equation in alkaline medium.
Watch outA common mistake is to assume that in alkaline medium, I− is only oxidised to I2 (as happens in acidic medium with a weaker oxidant). But permanganate is strong enough even in alkaline medium to push iodine to its +5 state. Also, IO4− (periodate, +7) is not formed because that would require even stronger oxidising conditions or a different reagent.
-
Check the options
- IO4−: requires oxidation to +7 — not happening here
- I2: requires oxidation to 0 — possible with weaker oxidants, but MnO4− goes further
- IO−: requires oxidation to +1 — an intermediate that further oxidises to IO3− in alkaline permanganate
- IO3−: oxidation to +5 — this is the stable product
TipYou can remember this as a pattern: permanganate in alkaline medium oxidises iodide to iodate (IO3−), not to periodate. Periodate formation requires a stronger oxidising environment (like acidic permanganate or electrolytic oxidation).
✓Final answerThe product is IO3−, so the correct option is (D).
- CBSE 2025Set 56/6/11 markMCQQ.For the following question, two statements are given — one labelled as Assertion (A) and the other labelled as Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below. (A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A). (B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A). (C) Assertion (A) is true, but Reason (R) is false. (D) Assertion (A) is false, but Reason (R) is true. Assertion (A) : Actinoids show wide range of oxidation states. Reason (R) : Actinoids are radioactive in nature.
›Reveal solutionSolution
The assertion that actinoids show a wide range of oxidation states is true, but the reason given — that they are radioactive — does not explain this property. The correct answer is (B).
The question tests your understanding of why actinoids exhibit variable oxidation states. The key is to separate two distinct facts: actinoids are radioactive, and they do show many oxidation states — but the radioactivity is not the cause of the oxidation state variability.
Let’s break this down.
-
Why do actinoids show a wide range of oxidation states?
The 5f, 6d, and 7s orbitals in actinoids are very close in energy. This means electrons can be removed from any of these orbitals with relatively little energy cost. As you move across the actinoid series, the 5f orbitals gradually become more stable, but early actinoids (like Th, Pa, U, Np, Pu) can lose anywhere from 3 to 7 electrons. For example, uranium shows +3, +4, +5, and +6; plutonium shows +3, +4, +5, +6, and +7. This is the real reason for the wide range — it’s an electronic structure effect, not a nuclear one.
-
What about radioactivity?
Yes, all actinoids are radioactive — their nuclei are unstable and decay over time. But radioactivity is a nuclear property, while oxidation states depend on electron configuration. A nucleus decaying does not directly change how many electrons an atom can lose or gain in a chemical reaction. So while both statements are factually true, the reason does not explain the assertion.
Watch outA common mistake is to assume that because both statements are true, the reason must be the correct explanation. Always check the causal link: does the reason actually cause the assertion? Here, radioactivity and oxidation state variability are independent phenomena.
- Evaluating the options:
- Assertion (A) is true.
- Reason (R) is true.
- But (R) does not explain (A) — the explanation lies in the closeness of 5f, 6d, and 7s orbital energies. This matches option (B).
TipA quick memory aid: Oxidation states come from electrons; radioactivity comes from the nucleus. If a reason talks about nuclear properties (radioactivity, half-life, decay) and the assertion is about chemical properties (oxidation states, colour, complex formation), the reason is almost never the correct explanation.
✓Final answerThe correct option is (B) — both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
-
- CBSE 2025Set ANNUAL1 markQ.What is the common oxidation state of Lanthanoids?
›Reveal solutionSolution
All lanthanoids overwhelmingly favour the +3 oxidation state, since their poorly-bonding 4f electrons are not readily involved, leaving the same outer 5d/6s electrons available across the series.
Across the entire lanthanide series, the +3 oxidation state is by far the most common and stable one, shown by essentially every lanthanoid. This is because the 4f electrons are deeply buried and well-shielded, taking little part in bonding, while the outer 5d0−16s2 electrons are readily lost to give the stable Ln3+ ion. Occasional +2 or +4 states occur only for a few elements where that ion happens to attain a specially stable f0, f7, or f14 configuration (e.g. Ce4+, Eu2+, Tb4+, Yb2+), but these are exceptions to the dominant +3 pattern.
✓Final answerThe common oxidation state of lanthanoids is +3.
- CBSE 2024Set A11 markMCQQ.Which of the following pair of metal oxides are amphoteric?(a) V2O5, Cr2O3(b) Mn2O7, CrO3(c) V2O5, V2O4(d) CrO, V2O5
›Reveal solutionSolution
V2O5 and Cr2O3 are the amphoteric pair — option (a).
For transition-metal oxides, the character changes from basic (low oxidation state) through amphoteric to acidic (high oxidation state). Cr2O3 (Cr in +3) is amphoteric — it dissolves in acids to give Cr3+ salts and in alkali to give chromite. V2O5 (V in +5) is chiefly acidic but is genuinely amphoteric, dissolving in both acids and alkalis. In the other options, Mn2O7 and CrO3 are strongly acidic, while CrO is basic — so only pair (a) is amphoteric.
✓Final answer(a) V2O5, Cr2O3
- CBSE 2024Set ANNUAL1 markMCQQ.Which of the following oxidation state is common for all lanthanoids ?(a) +2(b) +3(c) +4(d) +5
›Reveal solutionSolution
Every lanthanoid shows the +3 oxidation state as its characteristic and most stable state, even though a few also show +2 or +4 in special cases.
Lanthanoids (Ce to Lu) have the general electronic configuration [Xe]4f1−145d0−16s2. Losing the two 6s electrons and one 4f/5d electron gives the stable, half-filled/fully-filled-favouring Ln3+ ion, which is why +3 is the predominant and universally shown oxidation state across the whole series. A handful of lanthanoids additionally show +2 (e.g. Eu2+, Yb2+, favoured by half-filled/fully-filled 4f stability) or +4 (e.g. Ce4+, Tb4+), but +3 is the ONLY state common to every member of the series.
✓Final answer(b) +3.
- CBSE 2023Set 56/1/11 markMCQQ.The most common and stable oxidation state of a Lanthanoid is : (A) + 2 (B) + 3 (C) + 4 (D) + 6
›Reveal solutionSolution
Lanthanoids overwhelmingly prefer the +3 oxidation state due to the stability gained from losing the two 6s and one 5d/4f electron, achieving a configuration analogous to noble gases or half-filled/filled f-subshells. The answer is (B) +3.
Why Lanthanoids Love +3: Electronic Configuration and Stability
The lanthanoid series (elements 57–71: La through Lu) sits in the f-block, where the 4f orbitals are being progressively filled. To understand their oxidation state preference, we need to look at what electrons are available and what configurations become stable upon ionization.
A typical lanthanoid has the general electronic configuration:
[Xe]4f0−145d0−16s2
The 6s electrons are outermost and easiest to remove. The 5d and 4f orbitals are close in energy, so sometimes one electron occupies 5d instead of 4f. When a lanthanoid forms a cation, it loses electrons in a specific order: 6s electrons go first, then 5d, then 4f (because 4f is more tightly held, being an inner orbital).
Step-by-Step Reasoning
-
First ionization removes 6s electrons
All lanthanoids have two 6s electrons. Removing both gives a +2 state, but this is rarely the stopping point because the resulting ion still has relatively accessible 5d or 4f electrons.
-
Third electron removal: the key to +3 stability
After losing the two 6s electrons, removing one more electron (from 5d if occupied, otherwise from 4f) produces the +3 oxidation state. This configuration turns out to be remarkably stable across the entire series.
Why? The resulting Ln3+ ion achieves one of several favorable electronic arrangements:
- For La (4f0): [Xe] — a noble gas configuration.
- For Gd (4f7): half-filled f-subshell with all spins parallel (exchange energy stabilization).
- For Lu (4f14): completely filled f-subshell.
- For others: partially filled 4f with reasonable stability.
-
Why not +2?
The +2 state does exist for a few lanthanoids (Eu, Yb) where it leads to half-filled or filled f-subshells (4f7 for Eu²⁺, 4f14 for Yb²⁺), but these are exceptions, not the rule. Most lanthanoids find +2 too reducing and unstable in aqueous solution.
-
Why not +4 or higher?
Removing a fourth electron means breaking into the tightly held 4f subshell (which is shielded and contracted). The ionization energy jumps dramatically. Only Ce commonly shows +4 (because Ce⁴⁺ achieves 4f0=[Xe]), and even that is a strong oxidizing agent. Higher states like +6 are virtually unknown in lanthanoids—the 4f electrons are too stable to remove.
TipRemember the mnemonic: "Lanthanoids are lazy — they stop at +3." The energy cost to go beyond +3 is prohibitive for nearly all members of the series.
The Dominance of +3 Across the Series
The table below shows how universal the +3 state is:
Element Common Oxidation States Most Stable La–Nd +3 +3 Sm +2, +3 +3 Eu +2, +3 +2, +3 Gd–Tm +3 +3 Yb +2, +3 +3 Lu +3 +3 Even when +2 or +4 appear, they are either rare or highly reactive. The +3 state is stable in water, forms the vast majority of lanthanoid compounds, and is the oxidation state you'll encounter in nearly every chemistry problem involving these elements.
Watch outDon't confuse lanthanoids with actinoids. Actinoids (5f series) show a much wider range of oxidation states (+3, +4, +5, +6) because their 5f orbitals are less tightly bound and more chemically accessible than 4f.
✓Final answerThe correct option is (B) +3.
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- CBSE 2023Set 56/2/11 markMCQQ.The oxidation state of Fe in [Fe(CO)5] is (A) +2 (B) 0 (C) +3 (D) +5
›Reveal solutionSolution
Carbonyl (CO) is a neutral ligand that does not contribute any charge. With five neutral CO ligands, the overall complex is neutral, so Fe must be in the 0 oxidation state. The correct option is (B).
Why this is a trick question — and how to see through it
Most students memorise that transition metals in coordination compounds usually show positive oxidation states like +2 or +3. Iron especially is famous for Fe(II) and Fe(III). So when you see
[Fe(CO)5], the instinct is to guess +2 or +3. That instinct is wrong here — and the reason is beautiful.The key is to ask: What charge does each ligand bring?
CO (carbonyl) is a neutral ligand. It donates a lone pair to the metal but carries no net charge. If every ligand is neutral, and the overall complex is neutral (no square brackets with a superscript charge), then the metal must be in the zero oxidation state.
This is not a rare exception — it is a whole class of compounds called metal carbonyls, where metals often exist in low or zero oxidation states. CO is a strong field ligand that stabilises these low states through back-bonding.
Step-by-step reasoning
1. Identify the charge on each ligand.
CO is carbon monoxide — a neutral molecule. In coordination chemistry, neutral ligands contribute 0 to the oxidation state calculation. Other examples: NH₃, H₂O, PPh₃.
2. Identify the overall charge on the complex.
The formula is written as
[Fe(CO)5]— no superscript charge. That means the complex is neutral: overall charge = 0.3. Set up the oxidation state equation.
Let the oxidation state of Fe be x.
Each CO contributes 0. There are 5 CO ligands.
So:
x+5(0)=0
4. Solve for x.
x=0
That is the entire calculation — it takes one line once you know the rule.
Watch outA common mistake is to treat CO as if it were a charged ligand like CN⁻ or Cl⁻. CO is not cyanide — it is neutral. Do not assign it a −1 charge. Also, do not confuse this with ferrocene or other organometallics where the ligand (like cyclopentadienyl) is anionic.
TipFor any coordination compound, the fastest path to the metal oxidation state is:
Oxidation state of metal = Overall charge of complex − Sum of charges on all ligands
If all ligands are neutral, the metal's oxidation state equals the complex's charge. Here, both are zero.
Why zero is not just "possible" but stable
You might wonder: how can iron be in the 0 state? Isn't that unstable?
In fact, Fe(0) in
[Fe(CO)5]is perfectly stable because CO is a strong π-acceptor. It pulls electron density from the metal through back-bonding, relieving the metal of excess negative charge. This is why low oxidation states are common in carbonyl complexes — the ligand itself stabilises them.For a complex [M(L)n]m where each ligand L has charge qL:
Oxidation state of M=m−n⋅qL
✓Final answerThe oxidation state of Fe in [Fe(CO)5] is 0, so the correct option is (B).
- CBSE 2023Set 56/2/11 markMCQQ.Which of the following characteristics of transition metals is associated with their catalytic activity ? (A) Paramagnetic nature (B) Colour of hydrated ions (C) High enthalpy of atomisation (D) Variable oxidation states
›Reveal solutionSolution
The catalytic activity of transition metals arises primarily from their ability to adopt variable oxidation states, which allows them to form intermediate complexes and lower activation energy. The correct option is (D).
Why this question tests a core idea
Catalysis is about providing an alternative reaction pathway with a lower activation energy. For a substance to be a good catalyst, it must be able to temporarily bind to reactants, change its own electronic state, and then release the products. Transition metals excel at this because they can change their oxidation state easily — often by ±1 — without breaking down. This flexibility lets them shuttle electrons to and from reactants, stabilising transition states that would otherwise be too high in energy.
The other options — paramagnetism, colour, and high enthalpy of atomisation — are important properties of transition metals, but they don't directly explain catalytic activity. Let's see why.
Step-by-step reasoning
-
Paramagnetic nature (A)
Paramagnetism arises from unpaired electrons. While many transition metal ions are paramagnetic, this property has no direct role in catalysis. A catalyst doesn't need unpaired electrons to speed up a reaction — it needs to form bonds with reactants and then break them. Paramagnetism is a consequence of electronic configuration, not a cause of catalytic behaviour.
-
Colour of hydrated ions (B)
The colour of transition metal complexes comes from d–d transitions — electrons jumping between split d orbitals when they absorb visible light. This is fascinating, but it's a spectroscopic property. Colour tells us about the electronic structure of the ion, but it doesn't help the ion catalyse a reaction. A colourless catalyst can be just as effective.
-
High enthalpy of atomisation (C)
This refers to the energy required to convert a solid metal into isolated gaseous atoms. Transition metals have high enthalpies of atomisation because of strong metallic bonding (due to unpaired d electrons contributing to bonding). This property is related to the strength of the metal lattice, not to its ability to change oxidation states during a catalytic cycle. In fact, a very high enthalpy of atomisation might make it harder for the metal to leave the lattice and participate in solution-phase catalysis.
-
Variable oxidation states (D)
This is the key. Transition metals can exist in multiple oxidation states (e.g., Fe²⁺/Fe³⁺, Mn²⁺/Mn⁴⁺/Mn⁷⁺, Cu⁺/Cu²⁺) because the energy difference between successive d orbitals is small. In a catalytic cycle, the metal can:
- Accept electrons from a reactant (reducing itself to a lower oxidation state)
- Donate electrons to another reactant (oxidising itself to a higher state)
This electron-shuttling ability allows the catalyst to stabilise intermediates that would otherwise be too reactive. For example, in the Haber process, iron (Fe) catalyses the formation of ammonia. Iron can cycle between Fe(0) and various oxidation states as it adsorbs N₂ and H₂, weakening the N≡N triple bond.
The catalytic cycle often involves a change in oxidation state of the metal centre:
Mn++Reactant→M(n+1)++Product
followed by re-reduction of the metal by another reactant.
Watch outA common mistake is to think that "high enthalpy of atomisation" means the metal is more reactive. Actually, it means the metal atoms are held together more tightly — this is about lattice stability, not catalytic flexibility. Don't confuse thermodynamic stability with kinetic activity.
Final answer
✓Final answerThe correct option is (D) Variable oxidation states.
-
- CBSE 2023Set ANNUAL1 markMCQQ.Which of the following lanthanoid ions in solution is a good oxidizing agent ?(a) Eu2+(b) Yb2+(c) Sm2+(d) Tb4+
›Reveal solutionSolution
+3 is the overwhelmingly preferred oxidation state across the whole lanthanide series, so an unusual +4 ion like Tb⁴⁺ tends to gain an electron and revert to +3 — making it a good oxidising agent.
Across the lanthanide series, +3 is by far the most stable and common oxidation state (arising from the overall energetics of the whole series, not just an individual ion's own f-subshell configuration). Ions that deviate from +3 — whether to +2 or +4 — tend to revert back to +3, and in doing so they act as either reducing or oxidising agents:
- +2 lanthanide ions (Eu²⁺, Sm²⁺, Yb²⁺) tend to lose an electron to revert to +3 — they act as reducing agents.
- +4 lanthanide ions (Ce⁴⁺, Pr⁴⁺, Tb⁴⁺) tend to gain an electron to revert to +3 — they act as oxidising agents (they are themselves reduced).
Among the given options, Tb⁴⁺ is the +4 ion, so it is the good oxidising agent (readily accepting an electron to become the more stable Tb3+).
✓Final answer(d) Tb⁴⁺ is the good oxidising agent — it is readily reduced back to the more stable Tb³⁺.
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