This question is tricky because distance and location are not well defined within the electron cloud. So for the sake of explanation, let us assume that the question is "Which has a region maximum probability closest to the nucleus?"
I could not find an answer in print for the 4f vs 6s. However, I did find an answer comparing the 3d and 4s. I believe that an understanding of a comparison between the 3d and 4s can be extended to a comparison between the 4f and 6s.
The most probable distance of the 3d is less than the 4s. Therefore, we could extend this and say that most likely the 4f sublevel would have a distance of maximum probability closer than the 6s.
You did not ask why so I will not go into an explanation.
I would think the s orbital, because it is closer to the nucleus, and because the outer energy level holds more energy than the inner ones.
4f is a valid orbital.
4f orbital
three nodes
4f
They are further away from the nucleus and easier to remove (requires less energy), i.e. first ionization is less.
The element cerium has a single electron in the 4f orbital. Its electron configuration is [Xe] 4f1 5d1 6s2.
in 5s it is filled but in 4d or 4s its half
Lanthanides are in the '4 f ' block (of the so-called 'secundairy transitionals', atom number 58 to 71) filling up 4f orbital (1 to 14 electrons)
Atoms used to be thought to look like little solar systems. Now they are thought to be nesting shells of probability density functions known as orbitals. The S1 and P1 orbitals are the first two filled with other S and P orbitals following along with the various D and F orbitals. The S orbitals are essentially spheres with the P orbitals looking like infinity signs.Aside: A probability density function maps out where the electron is most likely to be in relation to the nucleus of the atom - not that it is there, just likely to be.
The first orbit only has an S orbital. The S orbital can hold 2 electron. The second orbit has s and p orbitals. The p orbital can hold 8 electrons The third orbit has s, p, and d orbitals. The d orbital hold 10 electrons giving a total of 18. However the 3d orbital has a higher energy level than 4s so the 4s orbital is filled with electrons before you can put electrons in the 3d orbital. The fourth orbital has s,p,d,and f. The f orbital can hold 14 electrons. This gives a total of 32 electrons. However the 4f orbital is higher in energy than the 5s, 5p, and 62 orbitals. Therefore these orbitals must be filled first. The fifth, sixth and seventh orbitals are similar to the fourth.
3 nodes in 4f