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. 56Quantum Numbers
8 MCQs9-step worked example
Source: NCERT Structure of AtomPYQ coverage: NEET 2023, 2024Official key: NTA-verifiedLast updated: 21 Sep 2026
Quantum Numbers, explained for NEET
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:
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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.
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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.
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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.
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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 56):
- 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.
Can you answer these Quantum Numbers 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?
Show answer and why every option is right or wrong
Answer: D. The azimuthal quantum number (l) defines the orbital shape: l = 0 is spherical (s), l = 1 is dumbbell (p), l = 2 is cloverleaf (d). NCERT Class 11 Chemistry Chapter 2, page 56.
Why A is wrong: A is wrong because n determines the shell (size and energy), not shape.
Why B is wrong: B is wrong because m_s specifies electron spin direction, unrelated to orbital shape.
Why C is wrong: C is wrong because m_l determines the orientation of the orbital in space, not its shape.
MCQ 2Easy RecallPractice
The total number of orbitals in a shell with principal quantum number n = 3 is:
Show answer and why every option is right or wrong
Answer: A. Total orbitals in a shell = n². For n = 3: 3² = 9 orbitals (one 3s + three 3p + five 3d). NCERT Class 11 Chemistry Chapter 2, page 56.
Why B is wrong: B is wrong — 6 is the number of electrons in a filled p subshell, not the orbital count for n = 3.
Why C is wrong: C is wrong — 3 is the number of subshells (s, p, d) in the third shell, not the total orbitals.
Why D is wrong: D is wrong — 18 is the maximum number of electrons (2n² = 2×9), not orbitals.
MCQ 3Easy RecallPractice
For l = 2, how many values of m_l are possible?
Show answer and why every option is right or wrong
Answer: C. m_l ranges from −l to +l, giving 2l+1 values. For l = 2: 2(2)+1 = 5 values (−2, −1, 0, +1, +2). NCERT Class 11 Chemistry Chapter 2, page 56.
Why A is wrong: A is wrong — confuses with the two possible spin values (m_s = ±½), not the m_l count for d orbitals.
Why B is wrong: B is wrong — 3 is the m_l count for l = 1 (p subshell), not l = 2.
Why D is wrong: D is wrong — 7 is the m_l count for l = 3 (f subshell), not l = 2.
MCQ 4Direct ApplicationPractice
Which of the following sets of quantum numbers is NOT possible?
Show answer and why every option is right or wrong
Answer: A. For n = 2, l can only be 0 or 1 (since l ≤ n−1 = 1). l = 2 violates the constraint. NCERT Class 11 Chemistry Chapter 2, page 56.
Why B is wrong: B is wrong choice — n = 3, l = 2 is valid (l ≤ 2), m_l = −2 is within range (−2 to +2). This set is allowed.
Why C is wrong: C is wrong choice — n = 4, l = 3 is valid (l ≤ 3), m_l = −3 is within range (−3 to +3). This set is allowed.
Why D is wrong: D is wrong choice — n = 3, l = 1 is valid, m_l = +1 is within range (−1 to +1). This set is allowed.
MCQ 5Direct ApplicationPractice
An electron is in a 4d orbital. What are the values of n and l for this electron?
Show answer and why every option is right or wrong
Answer: D. The number before the letter gives n = 4. The letter 'd' corresponds to l = 2 (s=0, p=1, d=2, f=3). NCERT Class 11 Chemistry Chapter 2, page 56.
Why A is wrong: A is wrong because l = 1 corresponds to a p orbital, not d. The designation 4d requires l = 2.
Why B is wrong: B is wrong because while l = 2 is correct for d, the principal quantum number for a 4d orbital is 4, not 3.
Why C is wrong: C is wrong because l = 3 corresponds to an f orbital. The d subshell is l = 2, not 3.
MCQ 6Direct ApplicationPractice
The maximum number of electrons that can have quantum numbers n = 3, l = 2 is:
Show answer and why every option is right or wrong
Answer: C. n = 3, l = 2 identifies the 3d subshell. Electrons in a subshell = 2(2l+1) = 2(5) = 10. NCERT Class 11 Chemistry Chapter 2, page 56.
Why A is wrong: A is wrong — 2 is the maximum per single orbital (one m_l value), not per subshell.
Why B is wrong: B is wrong — 6 is the capacity of a p subshell (l = 1), not a d subshell (l = 2).
Why D is wrong: D is wrong — 14 is the capacity of an f subshell (l = 3). The d subshell (l = 2) holds 10.
MCQ 7CalculationPractice
In a multi-electron atom, two electrons have quantum numbers:• Electron X: n = 3, l = 2, m_l = −1, m_s = +½• Electron Y: n = 3, l = 2, m_l = −1, m_s = +½Which statement is correct?
Show answer and why every option is right or wrong
Answer: B. All four quantum numbers are identical for X and Y. The Pauli exclusion principle states no two electrons in an atom can share all four quantum numbers. Since n, l, m_l, AND m_s are the same, this combination is forbidden. NCERT Class 11 Chemistry Chapter 2, page 56.
Why A is wrong: A is wrong because identical all-four quantum numbers violate the Pauli exclusion principle — two such electrons cannot coexist in the same atom.
Why C is wrong: C is wrong because Hund's rule governs filling order among degenerate orbitals (maximise spin first). The violation here is Pauli's principle (identical quantum number sets), not Hund's rule.
Why D is wrong: D is wrong because same m_l means same orbital. With the same m_s too, they are in the same orbital with the same spin — Pauli forbids this regardless.
MCQ 8CalculationPractice
For n = 4, how many orbitals have l = 1 and m_l = 0?
Show answer and why every option is right or wrong
Answer: B. The set n = 4, l = 1, m_l = 0 specifies exactly one orbital (the 4p_z orbital). Each unique combination of (n, l, m_l) defines a single orbital. NCERT Class 11 Chemistry Chapter 2, page 56.
Why A is wrong: A is wrong — 3 is the total number of p orbitals (m_l = −1, 0, +1) in any shell, but the question specifies m_l = 0, which picks out exactly one.
Why C is wrong: C is wrong — 4 is the number of subshells in n = 4 (s, p, d, f), not the number of orbitals with l = 1, m_l = 0.
Why D is wrong: D is wrong — 16 is n² = total orbitals in the entire n = 4 shell, not the count for one specific (l, m_l) combination.
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How do you solve a Quantum Numbers question? A 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.
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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.
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What to remember before solving Quantum Numbers questions
More in Structure of Atom: 4 exam traps and mistakes · 5 formulas · 2 question patterns from its other lessons.
Quantum Numbers questions from past NEET papers
2 questions from NEET 2023, 2024. Answers verified against NTA official keys.
NEET 2024Revised key
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 2023
1l = 2nₘ + 1
2nₘ = 2l² + 1
3nₘ = l + 2
4l = (nₘ − 1)/2
NTA Answer: Option 4(final)
How does NEET ask about Quantum Numbers?
Recurring question shapes from past papers. Each pattern shows why wrong options look tempting.
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.56
Page numbers are the ones printed in the current NCERT textbook (2023 rationalised edition), unless marked pre-2023. The books are free at ncert.nic.in.
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