The Schrodinger wave equation for hydrogen atoms yields three quantum numbers, n, l, and m., where n is the principal quantum number, which determines the electron’s energy to a large extent. That also determines the average distance of an electron from the nucleus.
When the value of n increases, the electron gets farther away from the nucleus, and its energy increases. The portion of this energy is along with the electron’s orbital motion around the nucleus. This orbital motion is explained by the angular momentum of the electron, known as the angular momentum quantum number, and this quantum number is the appearance of a group of closely spaced lines in the hydrogen spectra.
But the n is the energy associated with the angular momentum of an electron that must be within its total energy. Therefore, the electrons in atoms are grouped into primary energy levels by n and energy sublevels given by l.
l gives the value of the subshell in which the electron is located. It determines the shape of the orbital where the electron is located. The value of n for that principal energy level is determined by the number of subshells within a principal shell.
So, l may have all possible whole number values from 0 to n-1, and the sublevels are designated as s,p,d,f,…. According to the value of l = 0,1,2,3,…..
An electron has an angular momentum; its motion may be likened to the flow of an electric current through a loop. Such a flow of current is known and creates a magnetic field. This field interacts with an external magnetic or electric field. As a result of this interaction, the electrons in a given energy sublevel orient themselves in a particular specific region of space around the nucleus. These regions of space are called orbitals.
The fourth quantum number, the spin quantum number, does not follow from the wave mechanical treatment. The electron’s intrinsic angular momentum or spin is specified by the quantum number s = ½. By this relation between the angular momentum quantum number l and the orbital angular momentum L, the spin angular momentum has a magnitude.
These components of s in the direction of the magnetic field B are specified by the quantum number ms, where ms = +1/2 or -1/2. The figure shows that the ms = +1/2 component has an upward orientation (↑) and the ms =-1/2 component orientation (↓).
