How many d orbitals are there?

Aug 3, 2017

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

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

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

${m}_{l} = \left\{- l , - l + 1 , 0 , l - 1 , l\right\}$

$= \left\{- 2 , - 1 , 0 , + 1 , + 2\right\}$

And you can see that there are $2 l + 1 = 5$ 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 $l$?)