# How does 2s orbital differ from 1s?

May 28, 2018

A $2 s$ orbital has one more radial node.

The number of total nodes is

$n - 1$,

where $n$ is the principal quantum number ($n = 1 , 2 , 3 , . . .$).

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

$n - l - 1$.

But for $s$ orbitals, $l = 0$, so $n - 1 = n - l - 1$ for $s$ orbitals. Therefore, since $n$ increased by $1$, $2 s$ orbitals have one more node, and it is of the radial kind.

Knowing that, if the following radial distribution functions consist of either the $1 s$ or the $2 s$, which is which?

HINT: if the radial part of the wave function, ${R}_{n l} \left(r\right)$ goes to zero, so does the radial probability density, which is proportional to ${R}_{n l}^{2} \left(r\right)$.