# Quantum Numbers

QUANTUM NUMBERS

In an atom a large number of electron orbitals are permissible. These orbitals are designated by a set of numbers known as quantum numbers. In order to specify energy, size, shape and orientation of the electron orbital three quantum numbers are required. These are, principal quantum number, azimuthal quantum number and magnetic quantum number.

These quantum numbers arise as a natural consequence during the solution of the Schrodinger wave equation. In order to designate the electron, an additional quantum number called spin quantum number is needed to specify spin of the electron. Thus, each orbital in an atom is designated by a set of three quantum numbers and each electron is designated by a set of

four quantum numbers. These quantum numbers are discussed below:

THE PRINCIPAL QUANTUM N UMBER (n)

This is the most important quantum number as it determines to a large extent the energy of an electron. It also determines the average distance of an electron from the nucleus. It is denoted by the letter n. This quantum number tells us in which principal energy level or shell the electron is present. It can have any whole number value such as 1 , 2, 3, 4, …… , etc. The energy levels or energy shells corresponding to these numbers are designated as K, L, M, N……. etc. As the value of n increases, the electron gets farther away from the nucleus and its energy increases. The higher the value of n, the higher is the electronic energy. For hydrogen and hydrogen-like species, the energy and size of the orbital are determined by principal quantum number alone.

THE ORBITAL ANGULAR MOMENTUM, QUANTUM N UMBER OR AZIMUTHAL QUANTUM NUMBER (/)

This quantum number determines angular momentum of the electron. This is denoted by l. The value of l gives the sub-level or sub-shell in which the electron is located. It determines the three dimensional shape of the orbital in which the electron is located. The number of sub-shells within a principal shell is determined by the value of n for that principal energy level. Thus, l  may have all possible whole number values from 0 to n-1 for each principal energy level. For a given value of n, l can have n values. The various sub-levels are designated as s, p, d, f depending upon the value of I, as follows:

Value of 1 à                                      0          1          2          3          4          5          6