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

Aug 12, 2017

The total number of nodes in general is given by

$\text{Number of Nodes} = n - 1$,

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,

$\text{Number of Angular Nodes} = l$

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

$\textcolor{b l u e}{\overline{\underline{| \stackrel{\text{ ")(" ""Number of Radial Nodes" = n - l - 1" }}{|}}}}$

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?