# Azimuthal Quantum Number: Characteristics of the Orbital, Azimuthal Quantum Number, Azimuthal or Subsidiary Quantum Number (For CBSE, ICSE, IAS, NET, NRA 2022)

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- Quantum numbers are numbers allocated to all the electrons in an atom and they describe certain characteristics of the electron.

## Characteristics of the Orbital

- 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 & Spin Quantum number.

## What is Azimuthal Quantum Number?

- Other than principal quantum number (n) , spectroscopic notation, magnetic quantum numbers (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.

### Azimuthal Quantum Number

- Definition: The quantum number associated with the angular momentum of an atomic electron.
- The Azimuthal Quantum Number also termed as the orbital angular momentum quantum number, orbital quantum number or second quantum number, and is symbolized as ℓ.
- n − 1. Where n refers to the principal quantum number. When ℓ is equal to zero, you have an “s orbital” and when it is equal to 1, this is called the “p orbital.” as shown in the figure above.
- This number describes the shape of the orbital and determines the orbital angular momentum.

## 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 to the solar system, except 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 ℓ. Values of are from zero to n-1.

### For S-Orbital, ℓ = 0

- S orbital is simplest in all and it is in spherical shape. It has only one orbital which is S.

### For P-Orbital, ℓ = 1

- P orbital is dumbbell shaped three orbital:

### For D-Orbital, ℓ = 2

- For f-orbital, ℓ = 3 which is more complex than d, it has 7 orbitals.
- With the help of the value of azimuthal quantum number one can determine the total number of energy sub-levels in a given energy level.