Quantum Numbers

The quantum numbers are nothing but the details that are required to locate an electron in an atom. In order to specify energy, size, shape and orientation of the electron orbital, three quantum numbers are required these are discussed below.

The principal quantum number (n)

The electrons inside an atom are arranged in different energy levels called electron shells or orbits. Each shell is characterized by a quantum number called principal quantum number. This is represented by the letter "n" and "n" can have values, 1,2,3,4 etc.  

The subsidiary or azimuthal quantum number (l)

According to Sommerfield, the electron in any particular energy level could have circular path or a variety of elliptical paths about the nucleus resulting in slight differences in orbital shapes with slightly differing energies due to the differences in the attraction exerted by the nucleus on the electron. This concept gave rise to the idea of the existence of subenergy levels in each of the principal energy levels of the atom. This is denoted by the letter "l" and have values from 0 to n-1. Thus, if n=1, l=0 only one value (one level only) s level.  

Magnetic quantum number (m)

In a strong magnetic field a sub-shell is resolved into different orientations in space. These orientations called orbitals have slight differences in energy. This explains the appearance of additional lines in atomic spectra produced when atoms emit light in magnetic field. Each orbitals is designated by a magnetic quantum number m and its values depends on the value of "l" . The values are -"l" through zero to +"l" and thus there are (2l+1) values. Thus when l=0, m= 0 (only one value or one orbital) l=1, m= -1, 0, +1 (3 values or 3 orbitals)  

Spin quantum number (s)

The electron in the atom rotates not only around the nucleus but also around its own axis and two opposite directions of rotation are possible (clock wise and anticlock wise). Therefore the spin quantum number can have only two values +1/2 or - 1/2. For each values of m including zero, there will be two values for s.