# Question 38976

Apr 27, 2016

There are two types of nodes: angular nodes and radial nodes.

#### Explanation:

An angular node is a planar or conical surface.

A radial node is a spherical surface surrounding the nucleus.

For a given orbital:

• $\text{number of nodes} = n - 1$
• $\text{number of angular nodes} = l$
• "number of radial nodes" = n – l – 1

For a $4 s$ orbital

n = 4; l = 0

• $\text{number of nodes} = 4 - 1 = 3$
• $\text{number of angular nodes} = 0$
• "number of radial nodes" = 4 – 0 – 1 = 3

A $4 s$ orbital has three radial nodes. A $4 s$ orbital has 3 radial nodes (the red vacancies between the blue occupied shells).

For a $4 {p}_{z}$ orbital

n = 4; l = 1

• $\text{number of nodes} = 4 - 1 = 3$
• $\text{number of angular nodes} = 1$
• "number of radial nodes" = 4 – 1 – 1 = 2

A $4 p$ orbital has one angular node and two radial nodes. (from fineartamerica.com)

The $4 {p}_{z}$ orbital has an angular node in the $x y$ plane, with a small spherical node close to the nucleus and a larger one further out.

For a $4 {d}_{x y}$ orbital

n = 4; l = 2

• $\text{number of nodes} = 4 - 1 = 3$
• $\text{number of angular nodes} = 2$
• "number of radial nodes" = 4 – 2 – 1 = 1#

A $4 {d}_{x y}$ orbital has two angular nodes and one radial node. (from fineartamerica.com)

The $4 {d}_{x y}$ orbital is the one on the top left, but it is easier to see the nodes in the $4 {d}_{x z}$ orbital at top centre.

The latter has two angular nodes (the $x y$ and $y z$ planes) and a radial (spherical) node.