Question

What is the shape of f-orbital???

Answer 1

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

4F ORBITAL SHAPES

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:

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: