Question

Does $4\mathrm{f}$ orbital exist?

Answer 1

1. Yes, $4\mathrm{f}$ orbital exists.
2. $4\mathrm{f}$ orbitals are the seventh $\mathrm{f}$ orbitals of the $4\mathrm{th}$ electron shell (energy level). $4\mathrm{f}$ orbitals are the first subset of $\mathrm{f}$ orbitals. This means $1\mathrm{st},2\mathrm{nd}$ and $3\mathrm{rd}$ electron shells have no $\mathrm{f}$ orbitals.