Question

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

Answer 1

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.