N is the letter of the English alphabets that is used in quantum mechanics to signify or to symbolize the principal quantum number. Furthermore, the quantized energy states of microscopic reality of atomic electrons can be at the most represented by four quantum numbers. These are in the order of important, the principal quantum number, the orbital angular momentum quantum number, the magnetic quantum number, and the intrinsic spin quantum number.


The principal quantum number is the same quantum number of Bohr’s quantum theory of the atomic electrons. He theorized that the circular paths of atomic electrons called stationary orbits are a consequence of quantized angular momentum given by the product of N and Planck’s constant of action divided by 2p. Bohr’s quantum theory, which is also called the old quantum theory, works well, explaining the single electron of the hydrogen atom. But it failed abjectly explaining atoms with two or more electrons. For two or more atomic electrons, both Schrödinger and Heisenberg’s quantum theory can be used to describe the different quantized energy states of the atomic electrons, which can explain successfully both complex atomic spectra and molecular spectra. N can take only integer values starting with N=1. The orbital quantum number L is equal to N-1. For N=1, L=0. L=0 is called the s-orbital. For N=2, there are two values of L: L=0 and L=1. L=1 is called the p-orbital. Since the magnetic quantum number M is given by all integer values inclusively between +L and –L, the possible values of M for N=2, L=1 are +1, 0, -1 giving three distinct p-orbitals. In summary, using these index nomenclatures for N=1, 2, 3, and 4, the number of different energy states is simply the square of N. For N=1 there is only one energy state. For N=2 there are 4 energy states. For N=3 there are nine energy states. For N=4 there are 16 distinct energy states. For the hydrogen atom, most of these energy states are equal in values demonstrated by equal intensity of the line spectra determined by spectral analyses.