What is the shape of f-orbital???
Personally, I’ve never really known which one was which until now… turns out they’re right on wikipedia.
Curated from Wikipedia, these are the \(4 f\) orbitals. Row-wise, these have corresponding magnetic quantum number \(ml\) values in the set
n = 4 ORBITAL RADIAL NODES
The radial density distribution of the \(4f\) orbitals could be compared with the \(4s, 4p,\) and \(4d\) orbitals:
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: