Does 2d orbital exist in an atom?

Does 2d orbital exist in an atom?

2d orbital can’t exist in an atom. We can explain it from its subsidiary quantum number and principal quantum number (n). The value ℓ gives the sub-shell or sub-level in a given principal energy shell to which an electron belongs. Because the quantum number n must be superior to angular momentum quantum number. In the 2nd energy level, electrons are placed only in the ‘s’ and ‘p’ sublevels, so there is no ‘d’ orbital.

For n=2, ℓ=0, 1

i.e. The second principal energy level consists of two sub-shell which is 2s (ℓ=0) and 2p (ℓ=1). So, 2d orbital can’t exist.

Thus, for n = 1, only l = 0 gives a valid wave function, for n = 2, you can only have l = 0, 1 (‘s’ and ‘p’), and so on. This form follows from the obligation that the wave function needs to be square integral.