What is the maximum number of f orbitals in any single energy level in an atom?

1 Answer
Jun 1, 2017

Recall that the angular momentum quantum number l gives the shape of an orbital. It corresponds as:

l" "" ""type"
0" "" "s
1" "" "p
2" "" "d
3" "" "f
vdots" "vdots

The number of orbitals of a given shape is given by the degeneracy, 2l+1. So, there are

2l+1 = 2(3) + 1 = color(blue)bb(7)

(n-2)f orbitals for a given principal quantum number n. This is also represented in the number of magnetic quantum numbers m_l.

m_l = {-l, -l + 1, . . . , 0, . . . , l - 1, l}

So in the case of (n-2)f orbitals,

m_l = {-3,-2,-1,0,+1,+2,+3}

and there are color(blue)bb(7) such m_l values, each corresponding to one of the (n-2)f orbitals.