# Question #65790

Jul 2, 2015

A 4f-orbital has 3 nodes.

#### Explanation:

There are actually two types of nodes an orbital can have, radial nodes and angular nodes.

As you know, a node denotes a region that surrounds a nucleus in which you have zero probability of finding an electron.

The two types of nodes that exist will thus be regions in which you have no electron density, with the mention that

• a radial node is a sperical surface;
• an angular node is usually a flat plane (but it could also be a conical plane);

The number of angulal nodes is given by the angular momentum quantum number, $l$

$\text{no. of angular nodes} = l$

The number of radial nodes is given by both the angular momentum quantum number, and by the principal quantum number, $n$

$\text{no. of radial nodes} = n - l - 1$

Therefore, the taotal number of nodes an orbital has is given by

$\text{total no. of nodes} = \cancel{l} + n - \cancel{l} - 1 = n - 1$

In your case, the 4f-orbital will have a total of

$\text{no. nodes} = 4 - 1 = 3$, out of which

$l = 3$ $\to$ angular nodes;
$n - l - 1 = 4 - 3 - 1 = 0$ $\to$ radial nodes.