# Azimuthal Quantum Number

A quantum number for an atomic orbital is called azimuthal quantum number. This number describes the shape of the orbital and also determines the orbital angular momentum.

Other than principal quantum number (n), spectroscopic notation, magnetic quantum number (m) and the spin quantum number (s) – the azimuthal quantum number is another set of quantum numbers which describe the unique quantum state of an electron.

It is also termed as the orbital angular momentum quantum number, orbital quantum number or second quantum number, and is symbolized as ℓ.

## Brief History

Arnold Sommerfeld posited the term azimuthal quantum number from the Bohr model of the atom. The Rutherford-Bohr model or Bohr model, depicts the atom as a small, positively charged nucleus surrounded by electrons that travel in circular orbits around the nucleus – similar in structure to the solar system, but with attraction provided by electrostatic forces rather than gravity.

The Bohr model has its existence from spectroscopic analysis of the atom in combination with the Rutherford atomic model. Angular Momentum was found to be ‘0’ at the lowest level of quantum. Orbits with zero angular momentum were termed as ‘pendulum’ orbits.

### Azimuthal or Subsidiary Quantum Number

Azimuthal quantum number describes the shape of orbital. It is denoted by . Values of are from zero to n-1.

For s-orbital, ℓ = 0

For p-orbita, ℓ = 1

For d-orbital, ℓ = 2

For f-orbital, ℓ = 3

With the help of the value of azimuthal quantum number we can determine the total number of energy sub-levels in a given energy level.

### Angular Momentum Quantum Numbers

• Intrinsic (or spin) angular momentum quantum number, or simply spin quantum number