What is the difference between them?

I think radial nodes and spherical nodes are the same, and angular and planar nodes are the same.


Finally, how many spherical nodes are there in a $2p$ orbital?


The wave function $\Psi(r,\theta,\phi)$ of a one-electron (hydrogen-like) atom is seperable as the product of a radial function $R(r)$ and an angular function $Y(\theta,\phi)$

$\Psi(r,\theta,\phi) = R(r)Y(\theta,\phi)$

If $R(r_1) = 0$, there exists a radial node. The radial node is a sphere with radius $r_1$. Therefore the terms "radial node" and "spherical node" are the same.

$Y(\theta,\phi)$ is further seperable as

$Y(\theta,\phi) = P(\theta)F(\phi)$

If either $P(\theta)$ or $F(\phi)$ is zero for a given respective angle value, there is an angular node. However, a angular node is not necessarily a planar node. An angular node could be a planar node or a conical node.

$F(\phi)$ being zero corresponds to a planar node.

$P(\theta)$ being zero corresponds to either a conical node or a planar node (some think of the planar case as a specical case of conical, with apex angle being 180 degrees)

Overall, there will be $n-1$ nodes.

$l$ nodes will be angular

$n-l-1$ nodes will be radial (spherical)

  • $\begingroup$ Does this mean that all p orbitals have planar nodes and in d, only $d_{z^2}$ has conical node while others have planar node. I am clear about radial/spherical nodes. Thanks. $\endgroup$
    – pikachu
    Mar 27 '15 at 18:18
  • $\begingroup$ yes, px, py, pz each have one planar node. Dz2 has 2 conical nodes and the other d orbitals have 2 planar nodes winter.group.shef.ac.uk/orbitron/AOs/3d $\endgroup$
    – DavePhD
    Mar 27 '15 at 18:24

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