Quantum Number Calculator

Quantum Number Calculator

Explore the electronic structure of atoms by calculating allowed quantum states for a given shell.

Last updated: March 2026 | By ForgeCalc Engineering

Represents the main energy level (shell).

Total Orbitals (n²)1
Max Electrons (2n²)2
Allowed Subshells (l)
s
l = 0
1 Orbitals
2 Electrons

What are Quantum Numbers?

Quantum numbers describe the values of conserved quantities in the dynamics of a quantum system. In atomic physics, four quantum numbers are used to completely describe the state of an electron in an atom.

These numbers define the energy, shape, orientation, and spin of the electron's orbital. According to the Pauli Exclusion Principle, no two electrons in an atom can have the same set of four quantum numbers.

The Four Quantum Numbers

Principal (n)

Determines the size and energy of the orbital. n = 1, 2, 3...

Angular Momentum (l)

Determines the shape of the orbital. l = 0 to (n-1).

Magnetic (mₗ)

Determines the orientation of the orbital in space. mₗ = -l to +l.

Spin (mₛ)

Determines the direction of electron spin. mₛ = +½ or -½.

Frequently Asked Questions

Why is n limited in this calculator?

In ground-state atoms, electrons only occupy shells up to n=7. Higher shells are theoretically possible but rare in stable matter.

What do the letters s, p, d, f mean?

They stand for 'sharp', 'principal', 'diffuse', and 'fundamental', terms used by early spectroscopists to describe spectral lines.

How many electrons can fit in one orbital?

Exactly two. One with spin +½ and one with spin -½.

What is the Aufbau principle?

It states that electrons fill lower-energy subshells before moving to higher ones (e.g., 1s before 2s).

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