Quantum Numbers - Practice Questions & MCQ

Quantum numbers:

They are the set of four numbers which explain the state of electron i.e., location, energy, type of orbital, orientation of orbital, etc. in an atom. Various quantum numbers are as follows:

1. Principal quantum number(n)

2. Azimuthal quantum number(l)

3. Magnetic quantum number(m)

4. Spin quantum number(s)

Principal quantum number(n):

It represents the principal shell of an atom. It can have integral values except zero like 1,2,3,.... Also denoted as K,L,M,.....etc.

Maximum number of electrons in a principal shell can be 2n² where n is principal quantum number.

This quantum number gives information about :

• Distance of electron from nucleus i.e., size of electron cloud.
• Energy of electron in any shell in unielectronic species

$\mathrm{E}_{\mathrm{n}}=-\frac{1312 \times \mathrm{Z}^2}{\mathrm{n}^2} \mathrm{~kJ} / \mathrm{mol}$

Where, Z is atomic number and n is principal quantum number.

•  In case of multielectronic species, the energy of an electron is given by Aufbau's Principle, which we shall be studying later.

Azimuthal quantum number(l):

It gives us an idea of the three dimensional shape of the orbitals.

Azimuthal quantum number represents the subshell or subenergy shell in an atom.

l has values from 0 to (n-1).

e.g. for n=2 ; l= 0, 1

Subshell notation for l = 0, 1, 2, ..... is s, p, d ...

Maximum number of electrons that can be accomodated in a subshell with azimuthal quantum number 'l' is given by [2(2l+1)]:

e.g. for s subshell = 2; for p subshell = 6.

Magnetic quantum number(m):

It gives us information about the spatial orientation of the orbitals in the subshell with respect to the standard set of coordinate axes.

Every value of m represents a possible orientation of the orbital

It represents the number of orbitals present in a subshell.

m has values ranging from -l to +l including zero.

For eg: for ‘s’ subshell :

1. The value of l is 0

2. m has value=0 

It means that there is only one possible orientation for the s orbital

For ‘p’ subshell :

1. Value of l is 1

2. m has value= -1, 0, +1

It means that there are three possible orientation for the p orbital

Spin quantum number(s):

Electron in an orbital can spin in either clockwise or anticlockwise direction. The spin quantum number has no classical analogue and any spin direction can be assigned +1/2 and the opposite spin will be automatically assigned -1/2. These values of +1/2 or -1/2 are not fixed for a particular spin direction. 

Thus, an electron can have only two possible values of this quantum number, either $+\frac{1}{2}$  or $-\frac{1}{2}$ respectively.