Question

How many degenerate atomic orbitals are there that can be designated?
(i) 6p
(ii) 5d
(iii) 6f

Answer 1

Degenerate means that a set of orbitals or electron shells which are having the same energy value. The locations of the shells can be different around the nucleus.

The number of degenerate orbitals depends on Azimuthal Quantum Number. For example, the azimuthal quantum number is l = 1.

The total number of magnetic number of a sub-shell can process, i.e., no. of degenerate orbitals are from –l to +l or mathematically expressed as 2l+1.

Therefore, for p shell, there are 3 degenerate atomic orbitals ( -1 , 0 , +1 ) called $p_{x},p_{y},p_{z}$ and they all have exactly the same energy value.

To calculate number of orbitals one should know the following data :

The azimuthal quantum number (l) of  

i)        s sub-shell is 0  

ii)        p sub-shell is 1

iii)        d sub-shell is 2  

iv)        f sub-shell is 3

The total number of degenerate atomic orbitals of d sub-shell is 5 ( -2 , -1 , 0 , +1 , +2 ).