Azimuthal Quantum Number: Definition, Quantum Numbers & Types

Quantum Numbers can be defined as a number assigned to the electrons in an atom and they describe the characteristics and properties associated with them. The state of an electron can be defined using the parameters of the orbital used. The characteristics of the orbital can be expressed using the numbers: 

• Principal Quantum Number 
• Azimuthal Quantum Number 
• Magnetic Quantum Number 
• Spin Quantum Number 

These quantum numbers indicate the location of an electron in an atom. Pauli’s Exclusion Principle suggests that every electron in an atom has a unique set of quantum numbers. Quantum numbers help in determining the approximate location of an electron and the electronic configuration of an atom. They also help to understand the characteristics of an atom. The different quantum numbers of electrons in an atom can be represented as a wave function complying with the Schrodinger equation.

Key Terms: Quantum Numbers, Azimuthal Quantum Numbers, Electrons, Orbits, Atoms

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Quantum Numbers and Their Types

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An atom consists of a nucleus and of electrons that revolve in atomic orbits around the nucleus. An atom can consist of a large number of orbitals of different shapes, sizes, and orientations. Smaller size orbitals indicate a higher chance of finding the electron nucleus. The shape and orientation of the orbital indicate the probability of finding the electron in a certain direction and area of the atom as compared to others. 

Atomic orbitals can be differentiated from one another by their quantum numbers. Each orbital is associated with three quantum numbers which are the Principal Quantum Number ‘n’, Azimuthal Quantum Number ‘l’, and Magnetic Orbital Quantum Number ‘m₁’. Another quantum number is also important to understand the angular momentum of the electron as it spins. This quantum number is a vector quantity and can take two values +½ and -½. The different quantum numbers and their significance are as follows:

• Principal Quantum Number ‘n’: It defines the shell along with the size and energy of the orbital. This quantum number takes values n=1,2,3,......As the value of the Principal Quantum Number increases, the size of the orbital increases
• Azimuthal Quantum Number ‘l’: Also called Orbital Angular Momentum Quantum Number or Subsidiary Quantum Number, it indicates the three-dimensional shape of the orbital.
• Magnetic Quantum Number ‘m₁’: This quantum number indicates the orientation of the orbital in comparison to the defined standard coordinate axis.
• Spin Quantum Number ‘mₛ’: It is a vector quantity indicating the spin of the electron on the orbital.

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What is Azimuthal Quantum Number?

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The Azimuthal Quantum Number helps to determine the orbital angular momentum and also defines the shape of the orbital in three-dimensional space. It is also known as orbital angular momentum quantum number or subsidiary quantum number. For a particular value of ‘n’, the value of l can range from 0 to n-1. For example, if n=1, l=0. When n=2, the values of l are 0 and 1. When n=3, the values of l are 0,1, and 2.

Azimuthal Quantum Number

There are one or more sub-shells for each shell. For each principal shell, there are multiple sub-shells. For example, for the first shell n=1, there is only one sub-shell indicated by l=0. For the second shell n=2, there are two sub-shells indicated by l=0,1. Similarly, for different values of n, there are different values of l which are represented by different symbols. The table below shows the sub-shell notation for l values 0 to 5 along with the value of the Magnetic Quantum Number.

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History

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Azimuthal Quantum Number was carried over from Bohr Model of the Atom, and was introduced by Arnold Sommerfeld. The Bohr model was inspired from the spectroscopic analysis of the atom in combination with the Rutherford Atomic Model. The lowest quantum level was found to have an angular momentum of zero.

• Sommerfeld refined Bohr's semi-classical model by replacing circular orbits with elliptic ones. 
• Spherical orbitals were similar (in the lowest-energy state) to a rope oscillating in a large "horizontal" circle.
• Azimuthal quantum number (l)=0 corresponds to the s orbital. Shape of s orbital is spherical.

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Need of Quantum Numbers

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The quantum numbers characterize the configuration of an electron in an atom. There may be multiple orbitals in an atom that can accommodate a maximum of 2 electrons with an orientation opposite to each other. Due to the spinning of electrons in an atom, a small magnetic field is created. 

If two electrons are paired in an orbital, their spin values cancel each other and the atom becomes diamagnetic. However, in the case of unpaired electrons, there is a net spin as spins do not cancel each other. These atoms are known as paramagnetic atoms and they have a small magnetic field. Quantum numbers are useful for the following reasons:

• To determine the electronic configuration of an atom.
• To find the location of the electrons in the atom.
• To understand the properties like ionization energy and atomic radius of an atom.

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Things to Remember

• Quantum Numbers are numbers assigned to the electrons in an atom that describe the characteristics of the atom.
• The four quantum numbers are Principal Quantum Number, Azimuthal Quantum Number, Magnetic Quantum Number, and Spin Quantum Number.
• Azimuthal Quantum Number points toward the shape of the orbital of an atom in three-dimensional space.
• Azimuthal Quantum Number is denoted by ‘l’ and it can take values from 0 to (n-1) where ‘n’ is the Principal Quantum Number of the electron.
• Quantum numbers are useful in determining the electronic configuration of the atom along with the shape, size, and orientation of the electrons in the atom.

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