Quantum numbers and orbitals: Class 11 practice
n (shell) = 1, 2, 3…; l (subshell) = 0 to n − 1 (s, p, d, f); mₗ = −l to +l; mₛ = ±½. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Atomic structure
The idea behind quantum numbers and orbitals
n (shell) = 1, 2, 3…; l (subshell) = 0 to n − 1 (s, p, d, f); mₗ = −l to +l; mₛ = ±½. A shell has n² orbitals and holds 2n² electrons.
Step-by-step method
- List the allowed l for the given n.
- Count mₗ values (2l + 1) for each l.
- Total orbitals n², electrons 2n².
Worked example 1 (Basic)
How many orbitals and electrons can the n = 4 shell hold?
- Orbitals = n² = 16
- Electrons = 2n² = 32
- Answer: 16 orbitals, 32 electrons
Worked example 2 (Standard)
List the subshells in the n = 2 shell.
- l = 0 to 1
- Answer: 2s, 2p
Worked example 3 (Challenge)
For an electron in a 5f orbital, give n, l and the possible mₗ values.
- n = 5, l = 3
- mₗ = -3, -2, -1, 0, 1, 2, 3
- Answer: n = 5, l = 3, mₗ ∈ {-3, -2, -1, 0, 1, 2, 3}
Common mistakes and misconceptions
- Allowing l = n
- Forgetting the two spin states
Practice questions
- (Basic) How many orbitals and electrons can the n = 3 shell hold?
- (Basic) How many orbitals and electrons can the n = 2 shell hold?
- (Standard) List the subshells in the n = 5 shell.
- (Standard) List the subshells in the n = 3 shell.
- (Challenge) For an electron in a 3d orbital, give n, l and the possible mₗ values.
- (Challenge) For an electron in a 2p orbital, give n, l and the possible mₗ values.
Answer key with full working
- Q1: Orbitals = n² = 9 → Electrons = 2n² = 18 → Answer: 9 orbitals, 18 electrons
- Q2: Orbitals = n² = 4 → Electrons = 2n² = 8 → Answer: 4 orbitals, 8 electrons
- Q3: l = 0 to 4 → Answer: 5s, 5p, 5d, 5f, 5g
- Q4: l = 0 to 2 → Answer: 3s, 3p, 3d
- Q5: n = 3, l = 2 → mₗ = -2, -1, 0, 1, 2 → Answer: n = 3, l = 2, mₗ ∈ {-2, -1, 0, 1, 2}
- Q6: n = 2, l = 1 → mₗ = -1, 0, 1 → Answer: n = 2, l = 1, mₗ ∈ {-1, 0, 1}
Syllabus note
This skill is listed under "Structure of Atom" for Class 11 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is quantum numbers and orbitals in?
"Structure of Atom", Class 11 Chemistry (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.