1s orbital
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Quantum Numbers — The Language of Orbitals

Four quantum numbers uniquely define the state of every electron in an atom

n

Principal Quantum Number

n = 1, 2, 3, 4, ...

Determines the energy level (shell) and the size of the orbital. Larger n → higher energy, larger orbital, electron farther from nucleus.

n=1 n=2 n=3
En = −13.6/n² eV (hydrogen)
📏rn = n² × a₀ (Bohr radius)
🔢Max electrons per shell: 2n²

Azimuthal Quantum Number

ℓ = 0, 1, 2, ..., n−1

Determines the shape of the orbital (subshell) and the angular momentum magnitude of the electron.

s (ℓ=0)
Sphere
p (ℓ=1)
Dumbbell
d (ℓ=2)
Cloverleaf
f (ℓ=3)
Complex
💫Angular momentum: L = ℏ√(ℓ(ℓ+1))
🔢Orientations per subshell: 2ℓ+1
👉Nodes = ℓ (angular nodes in orbital)
m

Magnetic Quantum Number

m = −ℓ, ..., 0, ..., +ℓ

Determines the spatial orientation of the orbital. In a magnetic field, orbitals with different m have different energies — the Zeeman effect.

p orbitals (ℓ=1): 3 orientations
m=−1
px
m=0
pz
m=+1
py
🧲Zeeman splitting in external B field
🔢Total values for ℓ: 2ℓ+1 orientations
ms

Spin Quantum Number

ms = +½ or −½

Describes the intrinsic angular momentum (spin) of the electron. Electrons behave like tiny bar magnets. Two electrons sharing an orbital must have opposite spins.

ms = +½
Spin Up
ms = −½
Spin Down
Pauli Exclusion Principle: No two electrons in an atom can have the same four quantum numbers. Each orbital holds at most 2 electrons with opposite spins.

Allowed Quantum Number Combinations

nSubshellm valuesOrbitalsMax e⁻Shell Max
101s0122
202s0128
12p−1, 0, +136
303s01218
13p−1, 0, +136
23d−2, −1, 0, +1, +2510
404s01232
14p−1, 0, +136
24d−2..+2510
34f−3..+3714

Orbital Shape Reference Chart

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made by Harshveer Singh