This result comes from the manner in which the orbitals are determined for particular orbitals.
First, the principal quantum number nn is determined. This decides to which shell the orbital belongs. nn can have any positive integer value starting with 1.
Next, the angular momentum quantum number, ll must be specified. ll can be any value from zero up to n-1n−1.
An orbital is a pp=orbital if it has an angular momentum quantum number, ll equal to 1 (which implies that these orbitals first exist for quantum level n=2n=2, and are found for every value of nn after that).
Finally, for determining orbitals, the one remaining quantum number to be specified is the magnetic quantum number, m_lml. Like each quantum number, there are restrictions on the values m_lml can possess. In this case it is -l, -l+1, -l+2,..., 0, 1, 2, ...l-1.
Therefore, putting all this together: if l=1, (so we are referring to a p-orbital, the possible value for m_l are only -1, 0, and +1. These three possible values create the orbitals known as p_x, p_y, and p_z as the only possibilities, regardless on the value of n.
