Quantum Number Calculator
Calculate all possible quantum numbers for electrons in atomic orbitals and shells
Calculate Quantum Numbers
Main energy shell (1-7). Determines electron energy level and distance from nucleus.
Quantum Number Results
Subshells in Shell n = 1:
All Quantum Number Combinations
| n | l | mₗ | mₛ | Orbital |
|---|---|---|---|---|
| 1 | 0 | 0 | +1/2 | 1s |
| 1 | 0 | 0 | -1/2 | 1s |
Four Quantum Numbers
Principal (n)
Energy level, shell
1, 2, 3, 4, ...
Angular (l)
Orbital shape, subshell
0 to n-1 (s,p,d,f,...)
Magnetic (mₗ)
Orbital orientation
-l to +l
Spin (mₛ)
Electron spin direction
+½ or -½
Orbital Types
Quantum Rules
Each electron has unique quantum numbers (Pauli exclusion)
Maximum 2 electrons per orbital (opposite spins)
n² total orbitals in shell n
2n² maximum electrons in shell n
Understanding Quantum Numbers
What are Quantum Numbers?
Quantum numbers are a set of four numbers that completely describe an electron in an atom. They serve as the "address" of each electron, specifying its energy, orbital shape, orientation, and spin direction. No two electrons can have identical quantum numbers (Pauli exclusion principle).
Why are They Important?
- •Predict electron configuration and chemical properties
- •Explain atomic structure and bonding
- •Understand periodic table organization
- •Describe electron behavior in atoms
Quantum Number Relationships
n: 1, 2, 3, 4, ... (energy levels)
l: 0 to (n-1) (subshells)
mₗ: -l to +l (orbital orientations)
mₛ: +½ or -½ (spin directions)
Angular Momentum
Orbital: L = √[l(l+1)] ℏ
Spin: S = √[s(s+1)] ℏ = (√3/2) ℏ
where ℏ = h/2π = 1.055 × 10⁻³⁴ J⋅s
Electron Capacity Examples
⚛️ Shell n=1 (K)
Subshells: 1s
Orbitals: 1 (1²)
Max electrons: 2 (2×1²)
First and smallest shell
⚛️ Shell n=2 (L)
Subshells: 2s, 2p
Orbitals: 4 (2²)
Max electrons: 8 (2×2²)
Contains s and p orbitals
⚛️ Shell n=3 (M)
Subshells: 3s, 3p, 3d
Orbitals: 9 (3²)
Max electrons: 18 (2×3²)
First shell with d orbitals