Question

What is the total number of orbitals possible at the `n = 4` energy level?

Answer 1

hmmm...
Back to the Aufbau principle, and the Madelung Rule I think...

Explanation:

I assume there will be no Level 5 included, so it stops at 4p,,,

Therefore:
In every level, there are:
one `s`-orbital;
three `p`-orbitals (n=2 onwards) ;
five `d`-orbitals (n=3 onwards) ;;
seven `f`-orbitals (n=4 onwards) ;
etc.

Therefore:
1 x `1s`
1 x `2s`
3x`2p`
1 x`3s`
3x`3p`
1 x`4s`
5x`3d`
3x`4p`

Total: 1+1+3+1+3+1+5+3 = 18 orbitals.....

Image credits: https://en.wikipedia.org/wiki/Aufbau_principle