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Pauli’s Exclusion Principle



Pauli’s Exclusion Principle

 The nature of an electron, its position and energy, is fully implied only by mentioning the values of four quantum numbers ascribed to it.

Each electron is, therefore, fully characterised by a set of four quantum numbers (n) – giving the size of electron orbital, (l) – its shape, and (m) – the orientation or disposition of the orbital and (s) the spin of the electron.

Electrons having the same value of (n) , the principal quantum number, are said to belong to the same major energy level. However, the energies possessed by these electrons may yet be different owing to the different values of other quantum numbers assigned to them.

In fact, the major energy levels are made of sublevels, given by the value of azimuthal quantum number (l). A particular energy sublevel may be designated by s, p, d and f. Within each energy level, the various sublevels have slightly different energies which increase in the same order as the value of the azimuthal quantum number (l). Therefore, for the major energy level n = 4, which has an (s) orbital (l = 0), p orbitals (l = l), d orbitals (l = 2) and f orbitals (l = 3), the energy increases in the order:  s < p < d < f.

An electron with the principal quantum number (n) and azimuthal quantum number (l) has always lesser energy than that of an electron with principal quantum number (n + 1) and the same azimuthal quantum number (l) i.e., the energy of a 3s orbital is less than that of 4s orbital and energy of 4p orbitals is always more than the energy of 3p orbitals, and so on.

The other two quantum numbers namely magnetic and spin quantum numbers determine the maximum number of electrons that can be accommodated in orbitals of a sublevel. It is, therefore, the assignment of the four quantum numbers to the electrons which ultimately count to determine its energy and location in space within an atom.

Wolfgang Pauli put forward an ingenious principle which controls the assignment of values of four quantum numbers of an electron. It applies certain restrictions on the values of electrons in an atom and hence the name (exclusion principle).

Pauli exclusion principle is stated as: No two electrons in an atom can have the same set of four identical quantum numbers.

Even if two electrons have the same values for n, l and m, they must have different values of (s). Thus every electron in an atom differs from every other electron in total energy and, therefore, there can be as many electrons in a shell as there are possible arrangements of different quantum numbers.

The arrangements of electrons using permitted quantum numbers n, l, m and s are given in the following table (1):


Let us find out the maximum number of electrons that can be accommodated in an orbital. We have seen that the first shell (n = 1) has only one orbital i.e., 1s. The possible arrangements for the quantum numbers are only two in accordance with Pauli’s exclusion principle.



It follows, therefore, that a maximum of two electrons can be accommodated in an orbital and they must possess opposite spins.

Consider the second shell (n = 2), there being four orbitals, one s orbital (l = 0) and three p orbitals (l = 1), the possible number of electrons having different set of quantum numbers can be as follows :


The total number of electrons that can be accommodated in second shell is equal to 2 + 6 = 8. Similarly it can be shown that the maximum number of electrons in the third and fourth shells is equal to 18 and 32 respectively.

On the basis of the above direction and the Table(1) it follows that s sublevel may contain upto two electrons, (p) sublevel upto six, (d) sublevel upto ten and (f) sublevel may have upto fourteen electrons. Each sublevel can accommodate at the most twice the number of available orbitals at that sublevel.

Pauli’s exclusion principle is of immense value in telling the maximum number of electrons accommodated in any shell.

Reference: Essentials of Physical Chemistry /Arun Bahl, B.S Bahl and G.D. Tuli / multicolour edition.


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