The five different orientations of orbitals in the 3 d subshell are shown in the figure below. One of these orbitals lies in the XY plane of an XYZ coordinate system and is called the 3 d xy orbital. The fourth orbital in this subshell lies along the X and Y axes and is called the 3 d x 2 - y 2 orbital. Most of the space occupied by the fifth orbital lies along the Z axis and this orbital is called the 3 d z 2 orbital. Before we can use these orbitals we need to know the number of electrons that can occupy an orbital and how they can be distinguished from one another.
Experimental evidence suggests that an orbital can hold no more than two electrons.
To distinguish between the two electrons in an orbital, we need a fourth quantum number. Thus, it takes three quantum numbers to define an orbital but four quantum numbers to identify one of the electrons that can occupy the orbital. The allowed combinations of n , l , and m quantum numbers for the first four shells are given in the table below. For each of these orbitals, there are two allowed values of the spin quantum number, s . The Relative Energies of Atomic Orbitals Because of the force of attraction between objects of opposite charge, the most important factor influencing the energy of an orbital is its size and therefore the value of the principal quantum number, n .