Azimuthal Quantum Number (l) and Subshells s, p, d, f

Chemistry · Structure Of Atom · NEET

The azimuthal quantum number (l) tells you the SHAPE of the orbital and names the subshell. Its values go from 0 up to (n-1) for a shell n, and l = 0, 1, 2, 3 map to the subshells s, p, d, f. Memory hook: "Some Poor Dog Fights" for s-p-d-f in the order l = 0, 1, 2, 3.
Azimuthal Quantum Number l and SubshellsFor shell n, l = 0, 1, 2, ... (n-1)l = 0 to sl = 1 to pl = 2 to dl = 3 to fNumber of subshells in a shell = nn = 1 to 1sn = 2 to 2s 2pn = 3 to 3s 3p 3dn = 4 to 4s 4p 4d 4fRule: l must be less than n
The azimuthal quantum number l names each subshell (l = 0, 1, 2, 3 give s, p, d, f) and can only take values from 0 up to (n-1), so the number of subshells in a shell equals n.

Your doubts, answered

What exactly does the azimuthal quantum number (l) tell us?

It tells you the SHAPE of the orbital and which subshell the electron is in. NCERT calls l the 'orbital angular momentum' or 'subsidiary' quantum number. So when NEET asks 'which quantum number gives the shape of the orbital?', the answer is l (azimuthal). Do not confuse it with n, which gives the SIZE.

What is the l value for s, p, d and f subshells?

l = 0 is the s subshell, l = 1 is p, l = 2 is d, and l = 3 is f. This never changes. So an orbital with n = 2, l = 1 is a 2p orbital. Learn it as: 0 to s, 1 to p, 2 to d, 3 to f.

Why does l only go from 0 to (n-1)?

This is a rule that comes out of the Schrodinger equation, so you must accept it. For a shell n, l can take exactly n different whole-number values, starting at 0 and stopping at (n-1). Example: for n = 3, l = 0, 1, 2, which are the 3s, 3p and 3d subshells. l can never equal n or be larger than n.

How many subshells are there in a shell?

The number of subshells in a shell equals n. For n = 1 there is 1 subshell (1s). For n = 2 there are 2 subshells (2s, 2p). For n = 3 there are 3 subshells (3s, 3p, 3d). For n = 4 there are 4 subshells (4s, 4p, 4d, 4f). Just count l = 0 up to (n-1).

What is the difference between n and l?

n (principal) gives the SIZE and main energy of the orbital. l (azimuthal) gives the SHAPE and names the subshell. Match-the-column NEET questions test this every year: n to size, l to shape, m(l) to orientation, m(s) to spin direction.

Does a 2d or 1p subshell exist?

No. For n = 1, l can only be 0, so only 1s exists (no 1p). For n = 2, l can be 0 or 1, so only 2s and 2p exist (no 2d). A subshell exists only when its l value is allowed, meaning l is between 0 and (n-1). This is a very common NEET trap in 'incorrect set of quantum numbers' questions.

⚠️ The NEET trap
Picking n = 3, l = 3 as a valid set because it 'looks fine'.
For n = 3, the largest allowed l is (n-1) = 2. So l = 3 is forbidden; only l = 0, 1, 2 exist in the third shell. Always check that l is less than n.
🧠 l must be strictly less than n. If l is greater than or equal to n, the set is forbidden.

Real NEET questions

2024

Match List-I (Quantum Number) with List-II (Information provided): (A) m_l (B) m_s (C) l (D) n --- (I) shape of orbital (II) size of orbital (III) orientation of orbital (IV) orientation of spin of electrons. Choose the correct option.

A · A-III, B-IV, C-I, D-II
B · A-III, B-IV, C-II, D-I
C · A-II, B-I, C-IV, D-III
D · A-I, B-III, C-II, D-IV
Solution: l (azimuthal) gives the SHAPE of the orbital, so C-I. n (principal) gives the SIZE, so D-II. m_l (magnetic) gives the orientation of the orbital, so A-III. m_s (spin) gives the orientation of spin, so B-IV. Correct match: A-III, B-IV, C-I, D-II.
2023

The incorrect set of quantum numbers from the following is:

A · n=4, l=2, m_l=-2,-1,0,+1,+2, m_s=-1/2
B · n=5, l=3, m_l=-3,-2,-1,0,+1,+2,+3, m_s=+1/2
C · n=4, l=3, m_l=-3,-2,-1,0,+1,+2,+3, m_s=-1/2
D · n=5, l=2, m_l=-2,-1,+1,+2, m_s=+1/2
Solution: For l = 2 the magnetic quantum number must run over -2, -1, 0, +1, +2, which is (2l+1) = 5 values including 0. Option D leaves out m_l = 0, so it is an incomplete and incorrect set. (Options A, B, C all have l less than n and complete m_l ranges, so they are valid.)

Solved Structure Of Atom NEET PYQs

Try the real previous-year questions from this chapter — each with the answer and a full solution.

See all 30 Structure Of Atom NEET PYQs ›
Next concept: Magnetic Quantum Number (m_l) and Number of Orbitals = 2l + 1Keep learning — 2 minFeeling ready? Solve the Structure Of Atom NEET PYQs ›Or practice on your phone — get the free MedicNEET app ›

Frequently asked

Is the azimuthal quantum number the same as the subshell?

They are directly linked. Each value of l names one subshell: l = 0 is s, 1 is p, 2 is d, 3 is f. So knowing l tells you the subshell straight away.

What is the maximum value of l in the 4th shell?

For n = 4, the maximum l is (n-1) = 3. So the fourth shell has l = 0, 1, 2, 3, which are the 4s, 4p, 4d and 4f subshells.

Does l also affect energy?

In a hydrogen atom, energy depends only on n. But in multi-electron atoms, energy depends on both n and l, and within one shell the order is s less than p less than d less than f (NCERT).

How is l written for a 3d orbital?

3d means n = 3 and l = 2 (because d corresponds to l = 2). This is valid because l = 2 is less than n = 3.