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# What is the Significance of Quantum Numbers in Physics?

Quantum number is defined as the value which is used to describe the available energy levels to the atoms and molecules. To describe the state of an electron in an atom/ion, there are 4 quantum numbers.

• Principal quantum number (n): Gives information about energy level.
• Azimuthal quantum number (l): Provides information about subshell and angular momentum.
• Magnetic quantum number (ml): Describes the orbital of subshell and magnetic moment.
• Spin quantum number (s): describes the spin of electron.

Here, before moving towards details, it is necessary to understand the way in which electrons get arranged in subshells. #### Principal Quantum Number

Principal quantum numbers is represented by the symbol ‘n’ and designates the electron shell of an atom. It also tells about the maximum distance b/w nucleus and electron. Its value is always an integer and can’t be zero or negative.

n = 1, 2, 3, ………

If n = 1, it indicates that electron is in lowest energy level or in ground state. If an electron jumps to higher energy level from ground state by gaining energy, then value of n increases and if electron returns back to ground level by emitting energy, then n decreases.

#### Azimuthal Quantum Number

It is also known as orbital angular momentum quantum number and is indicated by “l”. It describes the shape of an orbital. Its value depends upon the total number of angular nodes in an orbital. Its value is in range of 0 to (n-1), where n is principal quantum number, so clearly, azimuthal quantum number is dependent on principal quantum number. For example, if n = 3, then possible values of l are 0, 1 and 2. Azimuthal quantum number is related to angular momentum by the following relation:

L2 = ℏ2l (l + 1)

Under this condition, when l = 0, then electron is in s- subshell. For l = 1, 2, electron will reside in p and d subshells respectively. Hence for n = 3, there are 3 possible subshells, 3s, 3p and 3d.

#### Magnetic Quantum Number

This quantum number is indicated by “ml” and it indicates number of orbitals present in a subshell. Furthermore, orientation of these atomic orbitals is also determined by it. Its value depends upon azimuthal quantum number. Since the value of “ml” has a range of ( – l  to + l ), so indirectly it is also dependent on “n”.

For example, if n = 4, then clearly l = 3, then the possible values of “ml” are ( -3, -2, -1, 0, 1, 2, 3 ). Total number of orbitals of a subshell can be found by the formula (2l + 1). As in this example, l = 3 so number of possible “ml” values are 7. Orbitals are of various shapes for different sub-shells as shown below. Relation of magnetic quantum number with angular momentum is as:

Lz = ml

#### Spin Quantum Number

Electron spin quantum number is independent of previous quantum number values: n, l, and ml. The spin quantum number is indicated by “ms” and tells the direction of an electron in which it is spinning. Its possible values can be ( +1/2 and -1/2 ). “+1/2” indicates that electron has an upward spin and it is shown by ↑. Negative ½ means spin down or downward spin and is indicated by ↓. Ability of an atom to produce magnetic field is also determined by this quantum number. In an orbital, electrons must have opposite spins due to Pauli Exclusion Principle, that’s why an orbital can never contain more than two electrons. Relation of magnetic quantum number with angular momentum is as:

Sz = ms

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#### Summary Quantum numbers: An integer that indicates the number of the shell of the electron is the principal quantum number. Its value is 1 or higher (never 0 or negative). The angular momentum quantum number is an integer that is the orbital value of the electron (e.g., s=0, p=1). L is greater than or equal to zero and less than or equal to n-1. With integer values ranging from -l to l, the magnetic quantum number is the orbital orientation. Therefore, for the orbital p, where l=1, m could have values of -1, 0 , 1. The quantum number of the spin is a half-integer value that is either -1/2 (known as ‘spin down’) or 1/2 (known as ‘spin up’).