What is the shape of f-orbital???

1 Answer
Jun 22, 2017

Personally, I've never really known which one was which until now... turns out they're right on wikipedia.

4F ORBITAL SHAPES

https://en.wikipedia.org/wiki/Atomic_orbital

Curated from Wikipedia, these are the #4f# orbitals. Row-wise, these have corresponding magnetic quantum number #m_l# values in the set #{-3,-2,-1,0,+1,+2,+3}#.

n = 4 ORBITAL RADIAL NODES

The radial density distribution of the #4f# orbitals could be compared with the #4s, 4p,# and #4d# orbitals:

Graphed from H atom Wave Functions

Regarding their nodes, we can see that:

  • The #f# orbitals in the same quantum level have less radial nodes than other orbitals of lower angular momentum #l# (where the function dips down to #y = 0# on the above graph).

  • In contrast, these also have more angular nodes than the #d#, #p#, and #s# orbitals in the same quantum level (not seen in the above graph), as they have the highest #l# here.

POOR CAPACITY FOR ELECTRON SHIELDING

From the above graph, they are also the least effective at electron shielding, as they are the least penetrating orbitals in their quantum level; the radial electron density tapers off before getting near the nucleus, and so the #4f# electrons are usually not near the nucleus.

For example, this is what gives rise to the lanthanide contraction, where the #6s# electrons penetrate the core significantly and relativistically contract due to traveling close to the speed of light, but the #4f# electrons shield poorly.

This can be observed in the 3rd row transition metals, which have only SLIGHTLY larger atomic radii than the respective 2nd row transition metals:

http://images.flatworldknowledge.com/