# Azimuthal Quantum Number

Quantum numbers are numbers allocated to all the electrons in an atom and they describe certain characteristics of the electron. The characteristics of the orbital are used to define the state of an electron completely and are expressed in terms of three numbers as Principal quantum number, Azimuthal quantum number and Magnetic quantum number and Spin Quantum number.

## What is Azimuthal Quantum Number? 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 can be defined as,

The quantum number associated with the angular momentum of an atomic electron.

It is also termed as the orbital angular momentum quantum number, orbital quantum number or second quantum number, and is symbolized as ℓ. This number describes the shape of the orbital and also determines the orbital angular momentum. An example of the angular quantum momentum number would be a p orbital that is associated with an azimuthal quantum number equal to 1.

## 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