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1. Principal Quantum Number (n)
Symbol: n
Meaning: Specifies the energy level or shell of the electron.
Values: Positive integers → n = 1, 2, 3, …
Significance:
Indicates the size and energy of the orbital.
Larger n → Higher energy, larger orbital.
Maximum electrons in a shell: 2n²
Examples:
n = 1 → K-shell
n = 2 → L-shell
n = 3 → M-shell
2. Azimuthal Quantum Number (ℓ)
Symbol: ℓ
Meaning: Determines the shape of the orbital and subshell.
Values: ℓ = 0 to (n - 1)
Subshells:
ℓ = 0 → s-subshell (spherical)
ℓ = 1 → p-subshell (dumbbell)
ℓ = 2 → d-subshell (cloverleaf)
ℓ = 3 → f-subshell (complex shape)
Maximum electrons in a subshell: 2(2ℓ + 1)
3. Magnetic Quantum Number (mₗ)
Symbol: mₗ
Meaning: Specifies the orientation of the orbital in space.
Values: mₗ = -ℓ to +ℓ (including zero)
Number of orbitals in a subshell = 2ℓ + 1
Example:
If ℓ = 1 (p-orbital), then mₗ = -1, 0, +1 → 3 orbitals
4. Spin Quantum Number (mₛ)
Symbol: mₛ
Meaning: Specifies the spin of the electron.
Values: +½ (spin up) or -½ (spin down)
Note: Each orbital can hold only 2 electrons with opposite spins.
Summary Table
Quantum Number Symbol Values Describes
Principal n 1, 2, 3, … Shell, energy, size
Azimuthal ℓ 0 to (n-1) Subshell, shape
Magnetic mₗ -ℓ to +ℓ Orientation of orbital
Spin mₛ +½, -½ Spin direction of electron
Examples
1. Find quantum numbers for 3p² electron:
n = 3 (3rd shell)
ℓ = 1 (p-subshell)
mₗ = -1, 0, +1 (any one orbital)
mₛ = +½ or -½

2. Number of orbitals in n = 3:
Possible ℓ: 0 (s), 1 (p), 2 (d)
Orbitals:
s → 1
p → 3
d → 5
→ Total = 9 orbitals