What does it mean for an electron orbital to be penetrating?

1 Answer
Jul 10, 2017

The high extent of penetration is characteristic of orbitals with lower angular momentum #l#, due to having the highest number of radial nodes for a given quantum level #n#.

This can be seen more easily if we examine the trend in the radial density distribution for the #4s, 4p, 4d,# and #4f# orbitals:

Graphed from H atom Wave Functions

If you notice, there is a little bump near #r = 0# (where the nucleus is) for the #4s# orbital. That tells us the #4s# orbital has some electron density near the nucleus, i.e. the #4s# orbital is core-like. This bump shifts away from the nucleus and disappears as we move to the #4p# and #4d# orbitals, and the #4f# orbital is nowhere near the nucleus.

That tells us that the #ns# orbitals are the most penetrating. They are the most core-like orbitals in the same quantum level #n#.

That is why the electrons within orbitals of lower angular momentum shield electrons within orbitals of higher angular momentum.

We can thus say that the #4f# orbitals feel the least effective nuclear charge, and the #4s# orbitals feel the most effective nuclear charge.