Half Filled Full Filled Stability

8 MCQs9-step worked example

Source: NCERT Structure of AtomPYQ coverage: NEET 2021, 2022, 2023, 2024, 2025Official key: NTA-verifiedLast reviewed: May 2026

Lesson

The trap: When asked for the ground-state electronic configuration of Cr (Z = 24) or Cu (Z = 29), most aspirants mechanically apply the Aufbau principle and write Cr as [Ar] 3d⁴ 4s² and Cu as [Ar] 3d⁹ 4s². Both are wrong. NEET exploits this confusion reliably.

The concept: Half-filled and completely filled d-subshells possess extra stability arising from two factors:

Symmetrical distribution of electrons — electrons in half-filled or fully filled subshells are distributed symmetrically across all orbitals of that subshell, which lowers the overall energy.
Exchange energy — the number of electrons with parallel spin that can exchange positions is maximized in half-filled (d⁵) and fully filled (d¹⁰) configurations. Greater exchange energy = greater stabilization.

Because of this extra stability, chromium adopts [Ar] 3d⁵ 4s¹ (not 3d⁴ 4s²) and copper adopts [Ar] 3d¹⁰ 4s¹ (not 3d⁹ 4s²). One electron is promoted from 4s to 3d to achieve the more stable arrangement.

(Reference: NCERT Class 11 Chemistry Chapter 2, page 40.)

NEET connection: Questions test whether you recall the actual configuration or fall for the Aufbau-predicted one. The wrong option is almost always the "expected" Aufbau configuration — it looks correct to a student who hasn't internalized this exception.

Watch-out: This anomaly applies specifically to Cr and Cu in the 3d series. Do not overgeneralize — Mo and Ag show similar behaviour in the 4d series, but elements like Mn (3d⁵ 4s²) already have a half-filled d-subshell without needing promotion and are NOT anomalous.

Practice MCQs

Select an option to see the explanation. Wrong answers show why your choice was tempting — and name the exact trap it exploits.

MCQ 1Easy RecallPractice

The ground-state electronic configuration of Cr (Z = 24) is:

MCQ 2Easy RecallPractice

The ground-state electronic configuration of Cu (Z = 29) is:

MCQ 3Easy RecallPractice

The extra stability of half-filled and completely filled orbitals is attributed to:

MCQ 4Direct ApplicationPractice

Which of the following elements does NOT show an anomalous electronic configuration due to half-filled/fully filled d-orbital stability?

MCQ 5Direct ApplicationPractice

In the context of exchange energy, which configuration has more exchange pairs among d-electrons: 3d⁴ or 3d⁵ (all spins parallel)?

MCQ 6Direct ApplicationPractice

The electronic configuration of Cu²⁺ (Z = 29) is:

MCQ 7CalculationPractice

Cr³⁺ has the electronic configuration [Ar] 3d³. This is derived by removing electrons from neutral Cr. Which electrons are removed and in what order?

MCQ 8Concept TrapPractice

Among the following, which pair of elements shows anomalous electronic configurations due to the stability of half-filled and fully filled d-orbitals in the 3d series?

Worked Example

Pattern: Electronic configuration with Cr/Cu anomaly (anchored to trap T.CHE.U02.CR_CU_ANOMALY, mistake M.CHE.U02.CR_CU_CONFIG_REGULAR)

1
Given
- Chromium, Z = 24 - Required: ground-state electronic configuration and number of unpaired electrons
2
Required
- Correct configuration accounting for anomaly - Count of unpaired electrons
3
Concept
Half-filled d-subshells (d⁵) have extra stability due to maximized exchange energy and symmetrical electron distribution. Chromium achieves this by promoting one electron from 4s to 3d.
4
Expected (Aufbau) vs. Actual
- Aufbau predicts: [Ar] 3d⁴ 4s² (fill 4s² first, then 3d⁴) - Actual: [Ar] 3d⁵ 4s¹ (one 4s electron promoted to achieve half-filled d⁵)
5
Why the promotion occurs
Exchange pairs for d⁵ = 5(4)/2 = 10. Exchange pairs for d⁴ = 4(3)/2 = 6. Gain = 4 additional exchange pairs. This energy gain exceeds the cost of promoting one electron from 4s to 3d.
6
Counting unpaired electrons
- 3d⁵: five orbitals, each with one electron (all parallel spin by Hund's rule) → 5 unpaired - 4s¹: one orbital with one electron → 1 unpaired - Total unpaired electrons = 6
7
Final answer
Cr: [Ar] 3d⁵ 4s¹, 6 unpaired electrons. Note: The numbers 5, 4, 6, 10 used in exchange-pair counting are exact integers and do not limit significant figures.
8
Common trap
Writing [Ar] 3d⁴ 4s² gives only 4 unpaired electrons (4 in 3d, 0 in paired 4s²). This is the most common wrong answer in NEET for Cr-configuration questions. The distractor "4 unpaired electrons" directly exploits this mistake.
9
Similar NEET-style question
"The number of unpaired electrons in the ground state of Cu (Z = 29) is ___." (Answer: Cu = [Ar] 3d¹⁰ 4s¹ → 3d fully paired (0 unpaired) + 4s¹ (1 unpaired) = 1 unpaired electron. Trap answer: using [Ar] 3d⁹ 4s² gives 1 unpaired in 3d + 0 in 4s = 1 — same numerical answer but wrong reasoning path.) ---

Before solving, remember these

Key Fact

Half-filled and fully-filled stability

Configurations like d⁵ and d¹⁰ have extra stability due to symmetry and exchange energy. Examples: Cr [Ar]3d⁵4s¹ and Cu [Ar]3d¹⁰4s¹ (anomalous configurations).

-- NCERT Class 11 Chemistry, Ch. 2, p. 40

Formulas

Bohr energy (hydrogen-like)

E_{n} = - 13.6 \frac{Z ^{2}}{n ^{2}} eV

Energy of nth orbit. Negative (bound). Ground state H: -13.6 eV.

Symbol	Quantity	SI Unit
E_n	orbit energy	eV
Z	nuclear charge	-
n	principal	-

Valid when

Hydrogen-like atom
Non-relativistic

Bohr radius (hydrogen-like)

r_{n} = (0.529 \overset{˚}{A}) \frac{n ^{2}}{Z}

Radius of nth Bohr orbit for hydrogen-like atom of nuclear charge Z.

Symbol	Quantity	SI Unit
n	principal quantum number	-
Z	nuclear charge	-
r_n	orbit radius	Å

Valid when

Hydrogen-like (one-electron) atom
Non-relativistic

de Broglie wavelength

λ = h / (m v)

Wavelength associated with moving particle of momentum mv.

Symbol	Quantity	SI Unit
h	Planck 6.626e-34	J*s
m	mass	kg
v	velocity	m/s

Valid when

Non-relativistic

Heisenberg uncertainty

Δ x Δ p \geq \frac{h}{4 π}

Position and momentum cannot both be known with arbitrary precision.

Symbol	Quantity	SI Unit
Δx	position uncertainty	m
Δp	momentum uncertainty	kg*m/s

Valid when

Quantum scale; meaningful only when Δx, Δp comparable to atomic dimensions

Rydberg formula (H spectrum)

\frac{1}{λ} = R_{H} Z^{2} (1/ n_{1}^{2} - 1/ n_{2}^{2})

Spectral wavelengths of hydrogen-like atoms. Lyman (n1=1, UV), Balmer (n1=2, visible), Paschen (n1=3, IR).

Symbol	Quantity	SI Unit
lambda	wavelength	m
R_H	Rydberg 1.097e7	1/m
Z	nuclear charge	-
n1, n2	integers, n2>n1	-

Valid when

One-electron atom

Exam Traps & Common Mistakes

These are the exact patterns that cause wrong answers in NEET. Each trap includes when it triggers and how to avoid it.

Trap

Cr / Cu electronic configuration anomaly

Category: Inorganic Exception

Student writes Cr as [Ar]3d⁴4s² (expected) instead of actual [Ar]3d⁵4s¹. Same for Cu: actual [Ar]3d¹⁰4s¹ (one e⁻ promoted from 4s to 3d).

When it triggers

Question asks for ground-state electronic configuration of Cr (Z=24) or Cu (Z=29).

How to avoid

Half-filled (d⁵) and fully filled (d¹⁰) configurations have extra stability from exchange energy and symmetry. Cr and Cu adopt these configurations by promoting one 4s electron.

Trap

Hydrogen-like Z² factor

Category: Similar Terms

Student forgets Z² scaling when applying Bohr formulas to He⁺ (Z=2) or Li²⁺ (Z=3).

When it triggers

Question involves hydrogen-like ion (He+, Li2+, etc.).

How to avoid

E_n = -13.6 × Z²/n² eV. r_n = (0.529/Z) × n² Å. He+: 4× more bound than H. Li²⁺: 9× more bound. Always include Z².

Mistake

Writes Cr as [Ar]3d⁴4s² (expected) instead of actual [Ar]3d⁵4s¹. Same for Cu.

Root cause: concept gap

Correction

Half-filled (d⁵) and full-filled (d¹⁰) configurations have extra exchange-energy stability. Cr and Cu adopt these by promoting one 4s electron.

Mistake

Drops Z² factor when applying Bohr formulas to He⁺ or Li²⁺.

Root cause: formula misuse

Correction

Always include Z². E_n = -13.6 × Z²/n². For He+: 4× more energetic than H. For Li²⁺: 9×.

Past Year Questions

9 questions from NEET 2021, 2022, 2023, 2024, 2025. Answers verified against NTA official keys.

NEET 2025

Higher yield of NO in - 40 - N 2 (g ) + O 2 (g ) 2 N O (g ) can be obtained at [H of the reaction = +180.7 kJ mol–1] A. Higher temperature B. Lower temperature C. Higher concentration of N 2 D. Higher concentration of O 2 Choose the correct answer from the options given below :

1A, C, D only

2A, D only

3B, C only

4B, C, D only

NTA Answer: Option 1(final)

NEET 2024Revised key

Match List I with List II. List I List II (Molecule) (Number and types of bond/s between two carbon atoms) A. ethane I. one -bond and two -bonds B. ethene II. two -bonds C. carbon molecule, C III. one -bonds 2 D. ethyne IV. one -bond and one -bond Choose the correct answer from the options given below:

1A-I, B-IV, C-II, D-III

2A-IV, B-III, C-II, D-I

3A-III, B-IV, C-II, D-I

4A-III, B-IV, C-I, D-II

NTA Answer: Option 3(revised_final)

NEET 2024Revised key

Match List I with List II List I List II (Quantum Number) (Information provided) A. m I. Shape of orbital l B. m II. Size of orbital s C. l III. Orientation of orbital D. n IV. Orientation of spin of electron Choose the correct answer from the options given below :

1A-I, B-III, C-II, D-IV

2A-III, B-IV, C-I, D-II

3A-III, B-IV, C-II, D-I

4A-II, B-I, C-IV, D-III

NTA Answer: Option 2(revised_final)

NEET 2024Revised key

Given below are two statements : Statement I : [Co(NH ) ]3+ is a homoleptic complex whereas [Co(NH ) Cl ]+ is a heteroleptic complex. 3 6 3 4 2 Statement II : Complex [Co(NH ) ]3+ has only one kind of ligands but [Co(NH ) Cl ]+ has more than one kind 3 6 3 4 2 of ligands. In the light of the above statements, choose the correct answer from the options given below.

1Both Statement I and Statement II are true

2Both Statement I and Statement II are false

3Statement I is true but Statement II is false

4Statement I is false but Statement II is true

NTA Answer: Option 1(revised_final)

NEET 2023

Select the correct statements from the following A. Atoms of all elements are composed of two fundamental particles. B. The mass of the electron is 9.10939 × 10–31 kg. C. All the isotopes of a given element show same chemical properties: D. Protons and electrons are collectively known as nucleons. E. Dalton’s atomic theory, regarded the atom as an ultimate particles of matter Choose the correct answer from the options given below

1C, D and E only

2A and E only

3B, C and E only

4A, B and C only

NTA Answer: Option 3(final)

NEET 2023

On balancing the given redox reaction, c aCrO2 bSO2(aq)cH(aq) 2aCr3(aq)bSO2(aq) H O(l) 2 7 3 4 2 2 the coefficients a, b and c are found to be, respectively-

13, 8, 1

21, 8, 3

38, 1, 3

41, 3, 8

NTA Answer: Option 4(final)

NEET 2022

Match List-I with List-II List-I List-II (a) Li (i) absorbent for carbon dioxide (b) Na (ii) electrochemical cells (c) KOH (iii) coolant in fast breeder reactors (d) Cs (iv) photoelectric cell Choose the correct answer from the options given below :

1(a) - (ii), (b) – (iii), (c) – (i), (d) – (iv)

2(a) - (iv), (b) – (i), (c) – (iii), (d) – (ii)

3(a) - (iii), (b) – (iv), (c) – (ii), (d) – (i)

4(a) - (i), (b) – (iii), (c) – (iv), (d) – (ii)

NTA Answer: Option 1(final)

NEET 2021

Statement I : Acid strength increases in the order given as HF << HCl << HBr << HI. Statement II : As the size of the elements F, Cl, Br, I increases down the group, the bond strength of HF, HCl, HBr and HI decreases and so the acid strength increases. In the light of the above statements, choose the correct answer from the options given below.

1Statement I is incorrect but Statement II is true

2Both statement I and Statement II are true

3Both Statement I and Statement II are false

4Statement I : correct but statement II is false

NTA Answer: Option 2(final)

NEET 2021

From the following pairs of ions which one is not an iso-electronic pair? Fe2+, Mn2+

1O2–, F–

2Na+, Mg2+

3Mn2+, Fe3+

4Answer

NTA Answer: Option 1(final)

How NEET usually asks this

Recurring question shapes from past papers. Each pattern shows why wrong options look tempting.

Write electronic configuration, especially handling Cr/Cu anomalies and ions.

InterpretationMedium

Common distractors

misses cr cu anomaly

Writes 3d⁴4s² instead of 3d⁵4s¹

Bohr energy difference between two levels; compute photon energy/wavelength using Rydberg or E_n formulas.

Multi StepMedium

Common distractors

forgets z squared

Drops Z² for hydrogen-like

Apply Δx·Δp ≥ h/(4π) to find minimum uncertainty given the other.

Direct ApplicationEasy

Common distractors

uses h instead of h over 4pi

Drops 4π factor

Given orbital (e.g. 3p_z) or electron, identify n, l, m_l, m_s. Or check forbidden quantum number combinations.

InterpretationEasy

Common distractors

uses wrong l range

Uses l ≤ n instead of l < n

Sources

NCERT refs: Class 11 Chemistry Chapter 2, p.40

Test yourself on this topic with real past-paper questions:

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