# principal quantum number and azimuthal quantum number

## Quantum Numbers:

There are four quantum numbers which describe the electron in an atom but I will explain two zodiac signs. They are denoted by the letters n, m, and s called the principal quantum number, azimuthal quantum number, magnetic quantum number, and spin quantum number, respectively.

### Principal Quantum Number (n):

This quantum number describes the motion of an electron in an orbit and stands for the number shell or orbit. In other words, it is a rough measure of the size of the orbit. The large the value of n, the greater is the volume of the bulk of the electronic density, n may have integral value i.e., 1, 2, 3, 4, 5, …….. it may take the value up to 7 correspondings roughly to seven horizontal rows of the Periodic Table. The valve of n describes the binding force and distance between the nucleus and the orbit in which an electron moves. The lower value of n corresponds to lower energy, while the higher value of n corresponds to the higher energy. The energy level K, L, M, N, N, O, P and Q correspond to n = 1, 2, 3, 4, 5, 6 and 7, respectively.

The value of n also determines the number of breaks and discontinuities in the electron cloud. These breaks are also called nodes. The number of breaks is given by n – 1 and is denoted by  called azimuthal quantum number.

### Azimuthal Quantum Number (ℓ):

This quantum number describes the shape of an orbit. Its value corresponds to the value of n and is given by n – 1. It is also called secondary quantum number. The value of ‘’ tells whether the orbit is spherical, is like a dumbbell, sausage-shaped or even more complicated. It means that ‘’ is associated with a certain value of angular momentum. The large the value of , the more complicated will be the shape of the electronic cloud. The angular momentum is given by the quantum number explains the fine structure of the spectral lines in the hydrogen spectrum, thus lending support to the Sommerfeld’s assumption that the orbits are somewhat elliptical rather than being circular. The values of  and the number of orbitals are given in Table 1.5.
The resolution of a single line into two or more than two lines indicates that there are various sublevels in an energy level, in which an electron revolves. The energy is also quantized in various sublevels. The main energy shell thus can be considered as being made up of one or more energy sublevels. According to Sommerfeld modification, the electron in any particular energy level could either have a circular orbit or a number of elliptical orbits about the nucleus. The number of sublevels is always aqual to the value of n. For example, when n = 1,  = 0, this means that the main energy level and sublevel coincide with each other. When n = 2, l = 0 or 1, which means that there are two sublevels in the second energy level, one having an elliptical shape and the other circular shape. Similarly, when n = 3,  = 0, 1, 2. This means that there are three sublevels, one having a circular shape and the two other with elliptical shapes.
When n = 4,  can have four values (0, 1, 2, 3) corresponding to 4 sublevels, one with circular and three with elliptical shapes. Thus it is seen that the number of sublevels for a given principal quantum number is equal to the value of that quantum number. So if l = 0, 1, 2 or 3 the electrons are said to be in the s, p, d or f sublevels after the spectral names called sharp, principal, diffused or fundamental, respectively.