Question

Why do $2d,1d,$ and $3f$ orbitals not exist?

Answer 1

The number that was written before the orbital can be known as principal quantum number. It was represented by $n$ . It also corresponds to the energy level. First energy level consists of only s-orbital, second energy level consists of only s and p orbitals, third energy level consists of only s, p, and d-orbital.

Complete answer:
The region where there is a maximum probability of finding electrons is known as an orbital. There are different orbitals like s-orbital, p-orbital, d-orbital, and f-orbital.
The number of subshells in the first shell is one which is $1s$ and can accommodate only two electrons. The remaining sub-shells like $1p,$ and $1d$ can’t exist.
The number of subshells in the second shell are two, which are $2s$ and $2p$ can accommodate eight electrons. The remaining sub-shells $2d$ can’t exist.
The number of subshells in the third shell are three, which are $3s,3p,$ and $3d$ . These three sub-shells can accommodate eighteen electrons. the remaining sub-shells $3f$ does not exist.
The number of subshells in the fourth shell are four, which are $4s,4p,4d,$ and $4f$ . These four subshells can accommodate $32$ electrons.
Thus, due to the energy of the shell and the number of electrons that are able to occupy each orbital. The orbitals like $2d,1d,$ and $3f$ orbitals do not exist.

Note:
Shell corresponds to the energy level. Each shell consists of a sub-shell. Orbital is present in the subshell. First shell corresponds to one sub-shell. Second shell corresponds to two sub-shells. Third shell corresponds to three sub-shells. Fourth shell corresponds to four sub-shells.