What’s the difference between a p-orbital of the second shell and a p-orbital of the third shell? Thank you!

1 Answer
Sep 25, 2017

The number of radial nodes, which are spherical nodal shells.


Recall that

  • the principal quantum number #n# gives the energy level of the orbital.
  • the angular momentum quantum number #l# labels the shape of the orbital (#s,p,d,f, . . . #).

Well, the total number of nodes (regions where electrons cannot be found) is given by #n - 1#, and the number of angular nodes (nodal planes or conical nodes) is given by #l#.

By subtraction, the number of radial nodes (spherical nodal shells) is given by:

#overbrace(n - 1)^"Total nodes" = overbrace((n - l - 1))^"Radial nodes" + overbrace(l)^"Angular nodes"#

So having an orbital of one higher #n# increases the number of radial nodes.

#bb2p -> n - l - 1#

#= bb2 - 1 - 1 = ul(bb0 " radial nodes")#

#bb3p -> n - l - 1#

#= bb3 - 1 - 1 = ul(bb1 " radial node")#

And this can be visually seen:

http://chemwiki.ucdavis.edu/

http://www.villierspark.org.uk/

Circled in green is the #3p#'s radial node. They still both have one angular node (nodal plane).

This is also seen in radial density distributions:

Graphed from H atom wavefunctions

The radial node shows up at the point where the graph dips down to #bb(a_0r^2R_(nl)^2(r) = 0)#, with #r > 0# (but not at #r -> oo#).

That shows where the orbital wave function goes to zero (here, close to #6a_0#), which indicates the distance away from the nucleus where electrons cannot be found.