Question

How many radial nodes are in a given atomic orbital as a function of `n` and `l`?

Answer 1

The total number of nodes in general is given by

`"Number of Nodes" = n - 1`,

where `n` is the principal quantum number, and `n = 1, 2, 3, 4, . . .`, given as the numerical coefficient for the orbital.

The angular momentum quantum number `l` specifies the number of angular nodes. Each `l` corresponds to a given orbital shape: `s, p, d, f, g, h, i, k, . . .`, and `l = 0, 1, 2, 3, 4, 5, 6, 7, . . . , n-1`. That is,

`"Number of Angular Nodes" = l`

Since there are only two types (radial, angular), it follows that:

`color(blue)(barul(|stackrel(" ")(" ""Number of Radial Nodes" = n - l - 1" ")|))`

CHALLENGE: Given the above radial density distribution, how many radial nodes are in each orbital? Can you show what it is, mathematically? If there were radial nodes in a radial density distribution, can you describe what you would see occur in the graph?