Quantum Number Calculator

Calculate and Understand Atomic Quantum Numbers

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Principal Quantum Number (n)

Calculate allowed energy levels and shell numbers.

Energy Level Properties: -

Angular Momentum Quantum Number (l)

Calculate allowed subshell values for a given principal quantum number.

Allowed l values: -

Magnetic Quantum Number (ml)

Calculate allowed magnetic quantum numbers for a given l value.

Allowed m values: -

Understanding Quantum Numbers

Principal Quantum Number (n)

The principal quantum number (n) determines the main energy level or shell of an electron:

  • n = 1: K shell
  • n = 2: L shell
  • n = 3: M shell
  • n = 4: N shell

It can take positive integer values: n = 1, 2, 3, ...

Angular Momentum Quantum Number (l)

The angular momentum quantum number (l) describes the subshell and determines the shape of the orbital:

  • l = 0: s orbital (sharp)
  • l = 1: p orbital (principal)
  • l = 2: d orbital (diffuse)
  • l = 3: f orbital (fundamental)

Allowed values: 0 ≤ l ≤ (n-1)

Magnetic Quantum Number (ml)

The magnetic quantum number (ml) determines the orbital orientation in space:

  • For s orbitals: ml = 0
  • For p orbitals: ml = -1, 0, +1
  • For d orbitals: ml = -2, -1, 0, +1, +2

Allowed values: -l ≤ ml ≤ +l

Spin Quantum Number (ms)

The spin quantum number (ms) represents the electron's intrinsic angular momentum:

  • ms = +½ (spin up ↑)
  • ms = -½ (spin down ↓)

This follows the Pauli Exclusion Principle.

Quantum Number Rules

Principal Quantum Number (n)

n = 1, 2, 3, 4, ...

Maximum electrons = 2n²

Angular Momentum (l)

l = 0 to (n-1)

Subshell electrons = 2(2l + 1)

Magnetic Quantum Number (ml)

ml = -l to +l

Number of orbitals = 2l + 1