Fundamental concepts in chemistry: What are quantum numbers and explain the four types of quantum numbers?

Quantum numbers can be defined as a set of numbers which describes the shape, energy, spin and orientation of an electron in an orbital. There are four types of quantum number and an electron in an atom can be completely described by its four quantum numbers which are given as follows

(i) Principal quantum number

(ii) Azimuthal quantum number

(iii) Magnet quantum number

(iv) Spin quantum number

1. Principal quantum number:

The principal quantum number explains the distance of electron from the nucleus and the energy level at which the electron revolves around the nucleus. It is denoted by ‘n”. The value of principal quantum number for any electron can be 1, 2, 3, 4 ….n, but never be zero. The placement of any electron in orbits or shells (K, L, M, N and O) is according to the energy levels which are explained by principal quantum number (n). Greater the value of principal quantum number (n), greater will be the distance of electron from nucleus. For example

When

            n = 1, it represents the first energy level called K shell and the electron is revolving in K shell around the nucleus.

When

            n = 2, it represents the second energy level called L shell, thus the electron is revolving in L shell.

When

            n = 3, it represents the third energy level called M shell; therefore the electron is revolving in M shell.

When

            n = 4, it represents the fourth energy level called N shell and electron is revolving in it.

When

            n = 5, it represents the fifth energy level called O shell.

2. Azimuthal quantum number:

The azimuthal quantum number explains the shape and existence of electron in orbital or sub-shell within the orbit or shell. It is denoted by ‘l” and it has values 0, 1, 2, 3 for different orbital.

When

            l = 0, it represents S orbital.

When

            l = 1, it represents p orbital.

When

            l = 2, it represents d orbital.

When

            l = 3, it represents f orbital.

The S, p, d and f are sub-shells or orbital within the shell or orbits and stands for

            S = sharp

            p = principal

            d = diffused

            f = fundamental

The azimuthal quantum number can be related to principal quantum number to explain the position of electron as follows

When

            n = 1, it is K shell then l = 0, thus it is sub-shell ‘1S”. Where 1 is taken from the value of principal quantum number (n = 1) which represents the first energy level.

When

          n = 2, it is second energy level L shell then azimuthal quantum number can have two values given as follows

            l = 0 and n = 2 then it represents sub-shell 2S.

            l = 1 and n = 2 then it represents sub shell 2p.

When  

            n = 3, the value of azimuthal quantum number can be

            l = 0, for sub-shell 3S.

            l = 1, for sub-shell 3p.

            l = 2, for sub-shell 3d.

When

            n = 4, the value of azimuthal quantum number can be

            l = 0, for sub-shell 4S.

            l = 1, for sub-shell 4p.

            l = 2, for sub-shell 4dp.

            l = 3, for sub-shell 4f.     

3. Magnetic quantum number:

The magnetic quantum number explains the concept of degenerate orbital which are the orbital having same energies but different shapes. Note that each degenerate orbital can compensate two electrons at a time. This quantum number actually explains the ways in which s, p, d and f orbital arrange themselves along X, Y and Z axis in the presence of magnetic field. It is denoted by m and it has values –l, 0, +l. The magnetic quantum number can be related to azimuthal quantum as follows

When

            l = 0, m = 0, thus S orbital have no degenerate orbital and it can possess only two electrons at a time.

When

            l = 1, m = -1, 0, +1, which means that p orbital have three degenerate orbital and each degenerate orbital can compensate two electron thus p orbital can have total of six electrons at a time.

When

            l = 2, m = -2, -1, 0, +1, +2, which means that d orbital have five degenerate orbital therefore it can possess ten electrons at a time.

When

            l = 3, m = -3, -2, -1, 0, +1, +2, +3, which means that f orbital have seven degenerate orbital and it can compensate fourteen electrons at a time.

4. Spin quantum number:

The spin quantum number describes the direction of spin of electron. It is denoted by ‘ms and it has only two values +1/2 and -1/2 as all the electron revolves around the nucleus either in clockwise direction or anticlockwise direction. The clockwise motion of an electron is represented by +1/2, while the anticlockwise motion of an electron is represented by -1/2.

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