Question

How many `d` orbitals are there?

Answer 1

Well, that is given by `2l+1`, the degeneracy of the set of orbitals belonging to a particular subshell defined by `l`.

Take the `3d` orbitals for example. They have `l = 2`:

And as such, their magnetic quantum numbers are in the set

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

`= {-2, -1, 0, +1, +2}`

And you can see that there are `2l+1 = 5` of these orbitals, each corresponding to a unique orientation.

---

In the absence of an external field, what is the degeneracy of `p` orbitals? `f` orbitals? (What are their angular momenta `l`?)