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

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 $4 s , 4 p , 4 d ,$ and $4 f$ orbitals:

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

That tells us that the $n s$ 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 $4 f$ orbitals feel the least effective nuclear charge, and the $4 s$ orbitals feel the most effective nuclear charge.