 Before we get back to the atom, it's helpful to examine macroscopic orbital systems to see what varies with respect to energy, angular momentum, and orientation. In Newtonian mechanics, we can calculate the angular momentum, L, for an elliptical orbit and its energy, E. We see that there are no limits to the number of angular momentum values, L, that can be associated with any particular system energy, E. We also note that there are no restrictions on the orientation, or azimuth angle, for any angular momentum, L. Because we are dealing with a spherical system, with the bulk of the mass at the center, it is common practice to use spherical coordinates. R is the vector specifying the position of the electron relative to the proton, its length is the distance between the two, and the direction is the orientation of the vector pointing from the proton to the electron. Theta is the polar angle most closely related to angular momentum, and phi is the azimuthal angle associated with orientation. But when we move from matter systems to matter wave systems, we move from Newtonian equations to Schrodinger's equations. The relationships between energy, angular momentum, and orientation are quite different. With Schrodinger's equation for the hydrogen atom in spherical coordinates, we can separate the variables R, theta, and phi. Solving Schrodinger's equation yields multiple wave functions as solutions. They define an electron's probability density cloud. Energy is quantized into electron shells designated by the letter N. It determines the distance the electron is from the nucleus. These energy levels match the ones proposed by Bohr. For each energy level N, the associated angular momentum is also quantized into electron sub-shells designated by the letter L. It determines the shape of the orbital. And surprisingly, for each quantized angular momentum sub-shell, even the allowed orientations are quantized into orbitals and designated by the letters M sub-L. It determines the orientation of the orbital. In chemistry, an atomic orbital is defined as the region within an atom that encloses where the electron is likely to be 90% of the time. It is these radii, with their binding energies and interesting geometries, that give atoms their chemical properties.