Question

Question #38976

Answer 1

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:

• `"number of nodes" = n-1`
• `"number of angular nodes" = l`
• `"number of radial nodes" = n – l – 1`

For a `4s` orbital

`n = 4; l = 0`

• `"number of nodes" = 4-1= 3`
• `"number of angular nodes" = 0`
• `"number of radial nodes" = 4 – 0 – 1 = 3`

A `4s` orbital has three radial nodes.

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

For a `4p_z` orbital

`n = 4; l = 1`

• `"number of nodes" = 4-1= 3`
• `"number of angular nodes" = 1`
• `"number of radial nodes" = 4 – 1 – 1 = 2`

A `4p` orbital has one angular node and two radial nodes.

(from fineartamerica.com)

The `4p_z` orbital has an angular node in the `xy` plane, with a small spherical node close to the nucleus and a larger one further out.

For a `4d_(xy)` orbital

`n = 4; l = 2`

• `"number of nodes" = 4-1= 3`
• `"number of angular nodes" = 2`
• `"number of radial nodes" = 4 – 2 – 1 = 1`

A `4d_(xy)` orbital has two angular nodes and one radial node.

(from fineartamerica.com)

The `4d_(xy)` orbital is the one on the top left, but it is easier to see the nodes in the `4d_(xz)` orbital at top centre.

The latter has two angular nodes (the `xy` and `yz` planes) and a radial (spherical) node.