Question

Differentiate between the principal quantum number (n) and the angular quantum number (l). In your answer discuss what each represents, the letter designation, and the values it may have.

Type Answer And No Plagiarism!

Answer 1

A large no of orbitals are present in an atom and these orbitals have different shapes, size and orientation. Quantum numbers are basically used to describe the various orbitals.

Each orbital is designated three quantum numbers :

1. Principal quantum no (n)

2. Angular quantum no. (l)

3. Magnetic quantum no (m_l)

PRINCIPAL QUANTUM NUMBER

The principal quantum no. basically identifies the SHELL. It determines the size and to large extent the energy of orbital. 'n' is a possitive integer with value of n= 1, 2, 3.........

With the increase in value of 'n' the size of an orbital increases, in other words electron will be located away from the nucleus. Also, as 'n' increases, the number of allowed orbitals increases (given by n²). All the orbitals that have same value of 'n' are present in single shell of atom. Shells are represented by following letters:

n= 1 2 3 4 .......

Shell= K L M N .......

Since energy is required in shifting away the negatively charged electron away from possitively charged nucleus, the energy of the orbital increases with increase of 'n'.

ANGULAR QUANTUM NUMBER

It is also known as orbital Azimuthal quantun no. or orbital angular momentum. It basically defines the shape of the orbital. For a given value of 'n' , l can have values ranging from 0 to n-1, that is, for a given value of n, the possible value of l are 0, 1, 2, ......... (n-1)

For example, n=1 the only possible value of l is 0

For n=2, the possible values of l are 0 and 1.

Difference between n and l

Each shell consists of one or more sub-shells. The no. of sub-shells in a principal shell is equal to the value of 'n'. For example, in the first shell (n=1), there is only one subshell which corresponds to l=0. There are two sub-shells (l=0, 1) in the second shell (n=2), three sub-shells (l=0, 1, 2) in third shell (n=3) and so on.

Sub-shells corresponding to different values of l are:

l 0 1 2 3 4 5 .........

notation for subshell s p d f g h .........

Possible values of 'n' and 'l'

n	l	sub-shell notation
1	0	1s
2	0	2s
2	1	2p
3	0	3s
3	1	3p
3	2	3d
4	0	4s
4	1	4p
4	2	4d
4	3	4f