Quantum Number Calculator

Find the orbitals and electron capacity of a shell.

Max electrons 18

Number of orbitals 9

Number of subshells 3

Formula: max electrons = 2n²; orbitals = n²

Step-by-step with your numbers:

1. Values used:

2. Principal quantum number n = 3

4. Max electrons = 18

5. Number of orbitals = Principal quantum number n squared = 3 x 3 = 9

6. Number of subshells = 3

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The principal quantum number n sets how many orbitals and electrons a shell can hold.

The math behind it

A shell has n subshells, n² orbitals, and holds up to 2n² electrons (two per orbital).

n = 3 → 9 orbitals, up to 18 electrons.

Why two electrons per orbital?

The Pauli exclusion principle allows two opposite spins.