Quantum Numbers

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 that costs marks: confusing the allowed ranges of quantum numbers — particularly writing l = n (forbidden) instead of l ≤ n−1, or assigning m_l values outside −l to +l.

Four quantum numbers specify each electron's state in an atom:

Principal quantum number (n): Positive integers (1, 2, 3…). Determines the shell and governs energy in hydrogen-like atoms. Higher n → larger orbital, higher energy.
Azimuthal quantum number (l): Integer values from 0 to (n−1). Determines orbital shape and subshell designation: l = 0 (s), 1 (p), 2 (d), 3 (f). The maximum value is n−1, never n itself.
Magnetic quantum number (m_l): Integer values from −l to +l, giving (2l+1) orientations. For a p subshell (l = 1): m_l = −1, 0, +1 → three orbitals.
Spin quantum number (m_s): Only +½ or −½. Two electrons per orbital, with opposite spins (Pauli exclusion).

Key constraints (NCERT Class 11 Chemistry Chapter 2, page 28):

n ≥ 1 (integer)
0 ≤ l ≤ n−1
−l ≤ m_l ≤ +l
m_s = +½ or −½

Maximum electrons: Each shell holds 2n² electrons; each subshell holds 2(2l+1).

Watch-out for NEET: Questions frequently present a set of four quantum numbers and ask which combination is "not possible." The forbidden combination almost always violates l < n or |m_l| ≤ l. Train yourself to check these two inequalities first — that single reflex saves 30 seconds and prevents sign-off on a tempting distractor.

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

Which quantum number determines the shape of an orbital?

MCQ 2Easy RecallPractice

The total number of orbitals in a shell with principal quantum number n = 3 is:

MCQ 3Easy RecallPractice

For l = 2, how many values of m_l are possible?

MCQ 4Direct ApplicationPractice

Which of the following sets of quantum numbers is NOT possible?

MCQ 5Direct ApplicationPractice

An electron is in a 4d orbital. What are the values of n and l for this electron?

MCQ 6Direct ApplicationPractice

The maximum number of electrons that can have quantum numbers n = 3, l = 2 is:

MCQ 7CalculationPractice

In a multi-electron atom, two electrons have quantum numbers:

MCQ 8CalculationPractice

For n = 4, how many orbitals have l = 1 and m_l = 0?

Worked Example

Pattern: Identify valid/forbidden quantum number sets (NEET pattern: quantum numbers assignment)

1
Given
A student claims an electron exists with quantum numbers: n = 2, l = 1, m_l = +2, m_s = −½.
2
Required
Determine whether this quantum number set is allowed or forbidden, and identify the violated constraint.
3
Concept
Each quantum number has strict range rules: - l ranges from 0 to n−1 - m_l ranges from −l to +l - m_s is +½ or −½
4
Formula
Constraint: |m_l| ≤ l
5
Substitution
Given l = 1, the allowed m_l values are: −1, 0, +1. The claimed m_l = +2. Check: |+2| = 2 > l = 1.
6
Calculation
2 > 1 → constraint violated.
7
Final answer
The set is **forbidden**. The magnetic quantum number m_l = +2 exceeds the maximum allowed value of +1 for l = 1. **Note on exact values:** n, l, m_l, m_s are all exact integers or half-integers by definition — they do not contribute to significant-figure considerations.
8
Common trap
Students check only l < n and forget to verify |m_l| ≤ l. In this problem, l = 1 is valid for n = 2, so students who stop at the first check would accept the set as valid — missing the m_l violation entirely.
9
Similar NEET-style question
"Which of the following quantum number sets is not possible: (a) n=3, l=2, m_l=+3, m_s=+½ (b) n=4, l=0, m_l=0, m_s=−½ (c) n=2, l=1, m_l=−1, m_s=+½ (d) n=5, l=4, m_l=−4, m_s=−½?" Answer: (a) — for l=2, m_l can be at most +2; m_l=+3 violates |m_l| ≤ l. ---

Before solving, remember these

Key Fact

Quantum numbers

n (principal): 1,2,3,... (energy); l (azimuthal): 0..n-1 (subshell s,p,d,f); m_l (magnetic): -l..+l (orbital orientation); m_s (spin): ±½. Each electron unique (n,l,m_l,m_s).

-- NCERT Class 11 Chemistry, Ch. 2, p. 28

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.28

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

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