Quantum Numbers:
The numbers used for completely characterizing each electron of an atom are known as Quantum numbers. Four such quantum numbers are found to be necessary for describing completely an electron. They are:
1. Principal Quantum number: It was proposed by Bohr. This number gives an average distance of the electron from the nucleus and corresponds to the principal energy level to which the electron belongs.
Thus, it gives an idea about the position of the electron around the nucleus and also refers to the size of the orbital. The higher the principal number is greater its distance from the nucleus, the greater its size, and also higher its energy.
Although theoretically, its value may be from 1 to µ, only values from 1 to 7 have so far been established for atoms of the known elements. These are designated either as 1, 2, 3, 4, 5, 6, 7, or K, L, M, N, O, P, Q respectively. The maximum number of electrons in the principal quantum number is given by 2n2.
2. Subsidiary or Azimuthal Quantum Number: It was proposed by Sommerfeld. The main energy levels are divided into sub-levels each being denoted by Subsidiary or Azimuthal Quantum Number (l). Electrons do not really travel in circular orbits. The volume in space where there is a high probability of finding an electron is called an Orbital.
The subsidiary quantum number (l) describes the shape of the orbital occupied by the electron. For a given value of the principal quantum number (n), the azimuthal quantum number (l) may have all integral values from 0 to (n-1), each of which represents a different sub-energy level ( subshell or sub orbit) and they are usually denoted by the letters, s, p, d, f, [s, p, d, f are spectroscopic terms, s= sharp, p=principal, d= diffuse and f = fundamental].
3. Magnetic Quantum Number: It was proposed by Lande. Each sub-shell is further sub-divided, the sub-divisions being denoted by a magnetic quantum number. The magnetic quantum number is determined by the way in which the lines in atomic spectra split under the influence of the magnetic field.
The magnetic quantum number determines the preferred orientations of orbitals in space. Suppose, m have values -l,…, -3, -2, -1, 0, +1, +2, +3,…..+l where l= Azimuthal quantum number. There are, therefore, (2l+1) possible values for magnetic quantum numbers.
4. Spin Quantum Number (s): When spectral lines of H, Li, Na, K, etc were observed by means of the instruments of high resolving power, each line of the spectral series was found to consist of a pair of lines known as Doublets or double-line structure. Here, it should be understood clearly that this doublet is different from line structure which consists of closely spaced fine lines.
To account for these doublets, Whlenbeck and Goud-Smith 1925 suggested that the electron, while moving around the nucleus in an orbit also rotates or spins about its own axis either in a clockwise direction or in an anticlockwise direction. Spin quantum number (s) can have two values such as +1/2 (corresponding to the spinning of the electron in the clockwise direction) and -1/2 (corresponding to the spinning of the electron in the anti-clockwise direction).
Clockwise and Anticlockwise spinning of the electron is represented as ↑ and ↓ respectively. An orbital at most can accommodate 2 electrons provided they have opposite spins. The spin quantum number is independent of other quantum numbers.
The Principal Quantum Number (n) refers to the size of the orbital and also the energy of the electron in it. The Azimuthal or Subsidiary Quantum Number (l) to the shape of the orbital. The magnetic Quantum number (m) to the orientation of the orbital in space and the Spin Quantum Number (s) to the direction of the spin of the electron about its own axis.