How many $d$ orbitals are there?

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Answer 1 · 2017-08-03T18:09:59

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 $l = 2$ :

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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 $l$ ?)

How many dd orbitals are there?