# What is the difference between nodal surfaces and nodal planes?

Jan 27, 2016

A nodal surface is also called a radial node, which is a hollow spherical region in which electrons cannot be. A nodal plane is also called an angular node, which is either a plane where electrons cannot be, or a conic surface (${d}_{{z}^{2}}$ orbital).

Radial nodes (or nodal surfaces) can be found using the principal quantum number $n$ and the angular momentum quantum number $l$, using the formula $\setminus m a t h b f \left(n - l - 1\right)$.

• $n$ goes as $1 , 2 , 3 , . . . , N$ where $N$ is an integer, and $n$ tells you the energy level.

• $l$ goes as $0 , 1 , 2 , . . . , n - 1$, and $l$ tells you the shape of the orbital. $l$ is $0$ for an $s$ orbital, $1$ for a $p$ orbital, $2$ for a $d$ orbital, etc.

For instance, for a $1 s$ orbital:

• $l = 0$
• $n - l - 1 = 1 - 0 - 1 = \setminus m a t h b f \left(0\right)$ radial nodes.

For a $2 s$ orbital:

• $l = 0$ again
• $n - l - 1 = 2 - 0 - 1 = \setminus m a t h b f \left(1\right)$ radial node.

We can see the single radial node here as a white hollow sphere's cross-section:

Angular nodes (or nodal planes) can be found simply by determining $l$. For a $2 p$ orbital, $l = 1$, so there is $\setminus m a t h b f \left(1\right)$ angular node. However, $n - l - 1 = 2 - 1 - 1 = 0$, so it has $\setminus m a t h b f \left(0\right)$ radial nodes.

On the other hand, a $3 p$ orbital is distinctly different in that although it has $\setminus m a t h b f \left(1\right)$ angular node, it actually also has $\setminus m a t h b f \left(1\right)$ radial node; $n - l - 1 = 3 - 1 - 1 = 1$. We can see the radial node create a spherical "pocket" in the upper and lower lobes.