Quantum Numbers Calculator
Enter a principal quantum number to see all valid sets of n, l, ml, and ms values with orbital names and electron counts.
Use the Quantum Numbers Calculator
Quantum Number Inputs
Determines the energy level and shell (1–7).
0 = s, 1 = p, 2 = d, 3 = f. Range: 0 to n−1.
Shell Summary
Quantum Number Rules
Principal
Positive integer ≥ 1. Sets energy level and shell.
Azimuthal
Integer from 0 to n−1. Defines orbital shape.
Magnetic
Integer from −l to +l. Specifies orbital orientation.
Spin
Either +½ (spin up) or −½ (spin down). Pauli exclusion.
Valid Quantum Number Sets
0 sets| # | n | l | ml | ms | Orbital | Spin |
|---|
Summary
Quantum numbers describe the state of each electron in an atom. The principal quantum number (n) sets the energy level, the azimuthal quantum number (l) defines the subshell shape, the magnetic quantum number (ml) specifies orbital orientation, and the spin quantum number (ms) indicates electron spin. Together they uniquely identify every electron via the Pauli exclusion principle.
How it works
- Enter the principal quantum number n (1–7).
- Choose a specific subshell (l value) or view all subshells for that n.
- The calculator lists every valid (n, l, ml, ms) combination.
- Each row shows the orbital name (e.g. 2p), orientation (ml), and spin (ms = +½ or −½).
- The summary table shows total electrons per subshell and per shell.
Use cases
- Verify which quantum number sets are allowed for a given energy level.
- Study for chemistry or physics exams on atomic structure.
- Find the number of orbitals and electrons in any subshell.
- Understand the Pauli exclusion principle through enumerated combinations.
- Cross-check electron configurations with quantum number rules.
- Teach or visualize quantum mechanics concepts interactively.