How many spherical nodes are in a 3d_(xy) orbital?

May 20, 2017

A spherical node is otherwise known as a radial node. Radial nodes are given by

$n - l - 1$,

where $n - 1$ is the total number of nodes, and $l$ is the number of angular nodes. (Ordinarily, $n$ is the principal quantum number, and $l$ is the angular momentum quantum number.)

So, the number of radial nodes is:

$\textcolor{b l u e}{n - l - 1}$

$= 3 - 2 - 1 = \textcolor{b l u e}{0}$

Hence, there are zero spherical nodes in the $3 {d}_{x y}$ orbital.

How many angular nodes are there?