Does $ 4f $ orbital exist?

Hint: There are four quantum numbers namely Principle quantum number, Azimuthal quantum number, magnetic quantum number and spin quantum number. Based on these four quantum numbers and Pauli Exclusion Principle, we can determine the existence of an orbital and electronic configuration.

Complete answer:
We know that there are four quantum numbers namely Principle quantum number, Azimuthal quantum number, magnetic quantum number and spin quantum number.
So, the Principal quantum number is denoted by “n” and is the number of shells in which the electron is present.
 Azimuthal quantum number is denoted by “l” and it describes the sub-shell. Value of l varies from $ 0 $ to $ (n - 1) $ .
Magnetic quantum number is denoted by “m” and its value varies from $ - l $ to $ + l $ .
Spin quantum number is denoted by “s” and its value can be $ - \dfrac{1}{2} $ or $ + \dfrac{1}{2} $ .
We know that the azimuthal quantum number values are denoted with some letters such as:
 $ 0 - s $ , $ 1 - p $ , $ 2 - d $ , $ 3 - f $ and so on.
Now, the given orbital is $ 4f $ :
The principal quantum number, n, is $ 4 $ . Then, the value of the Azimuthal quantum number for this orbital can be from $ 0 $ to $ 3 $ .
The azimuthal quantum number for $ f $ Is 3 as given above and it lies in the permitted value range.
Hence, it satisfies all the above conditions, so we can say that $ 4f $ orbital exists.

Note:
Quantum numbers can also be used to determine the number of orbits, orbitals and orientation of electrons in an atom. We should also note that no two electrons in an atom can have the same set of quantum numbers. The two electrons present in a single orbitals have different spin quantum numbers.