# Quantum numbers

Four numbers describe each electron in an atom. n is the shell (size and energy), l is the subshell shape, mₗ is the orbital direction and mₛ is the spin, +½ or −½.

Chemistry (university) · Part 01: Atomic structure and periodic trends · Card 4 of 10 · Last updated 2026-10-19

## Analogy

Like an address: building (n), floor type (l), room (mₗ) and which of two beds (mₛ).

## Example

**Allowed values**

n = 1, 2, 3 ...
l = 0 to n − 1
mₗ = −l to +l
mₛ = +½ or −½

## In practice

Quantum numbers tell you why shell n = 2 holds 8 electrons and shell n = 3 holds 18.

## Practice

### Flashcards

- **What does the quantum number n describe?** The shell: its size and main energy level.

## Questions people ask

### What values can l take for n = 3?

For n = 3, l can be 0, 1 or 2, which is always 0 up to n − 1. These match the s, p and d subshells. So the third shell contains one s, three p and five d orbitals, which gives 9 orbitals and room for 18 electrons.

### Why are there only two spin values?

Experiments show an electron behaves as though it has a tiny built-in magnet that can point in only two directions, called spin up and spin down. We label them +½ and −½. No third direction is ever seen, so mₛ has just two values.

## Related concepts

- [Wave-particle duality](https://studyvisually.com/learn/science/chemistry-university/chemistry-university-part-1/chemistry-university-part-1-concept-3)

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