Question

4d, 5p, 5f and 6p orbitals are arranged in the order of decreasing energy. The correct option is :
a.) 5f > 6p > 5p > 4d
b.) 6p > 5f > 5p > 4d
c.) 6p >5f > 4d > 5p
d.) 5f > 6p > 4d > 5p

Answer 1

Hint:. Higher is the value of the sum of Principal quantum number and Azimuthal quantum number, greater will be the energy of the orbital.
And in any case the value of sum is equal, then the orbital with higher value of ‘n’ will have higher energy.

Complete step by step answer:
We know that the energy of an orbital can be given by the sum of Principal quantum number (n) and Azimuthal quantum number (l).
Higher is the value of the sum of Principal quantum number and Azimuthal quantum number, greater will be the energy of the orbital.
We know that the value of n is an integer.
Further, we have s, p and d notations for various values of l.
If l = 0; then s orbital
l = 1; then p orbital
l = 2; then d orbital
l = 3; then f orbital
l = 4; then g orbitals
So, from here we can have the value of ‘l’ and find their sum.
Thus, for the various options given to us, let us find their total as-
For 5f :-
‘n’ = 5 ; l = 3
(n + l) = 8

For 6p :-
‘n’ = 6 ; l = 1
(n + l) = 7

For 5p :-
‘n’ = 5 ; l = 1
(n + l) = 6

For 4d :-
‘n’ = 4 ; l = 2
(n + l) = 6
We can see that 5p and 4d have the same value, in that case; the orbital with lower value of ‘n’ will have lower energy.
So, the order for decreasing energy can be written as-
5f > 6p > 5p > 4d
So, the correct answer is “Option A”.

Note: The Principal quantum number designates the main shell in which the electron entered in an atom. Its value can be any integer with a positive value starting from 1.
The Azimuthal quantum number describes the shape of the given orbital. The value of azimuthal quantum number is obtained from principal quantum number.
‘l’ = n - 1