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Rules for Filling of Orbitals in an Atom


An atom in its lowest energy state is said to be in the normal state or the ground state. The ground state is the most stable state for the atom. The filling of orbitals in the ground state is determined by the following rules:


According to this rule, the electrons are added progressively to the various orbitals in their order of increasing energies, starting with the orbital of lowest energy.

Increasing order of energies of various orbitals is:

1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s,

4d, 5p, 6s, 4f, 5d, 6p, 7s, …… .



This principle was discovered by Wolfgang Pauli in 1925. This principle states that: No two electrons in an atom can have same values for all the four quantum numbers.

A direct implication of this principle is that it is not possible to accommodate more than two electrons in an orbital. This can be easily understood as follows:

All the electrons in a particular orbital have same values of principle(quantum number (n), azimuthal quantum number (l) arid magnetic quantum number (m1). For example, all the electrons in 3s orbital have n = 3, l = 0 and m1 = 0. Therefore, in order to have unique sets of quantum numbers they must have different values of spin quantum number (ms) But we know ms can have only two values +1/2 and -1/2 . Hence, in an orbital only two electrons can be accommodated, one spinning clockwise ( ms = + l) and the other spinning anticlockwise ( ms = -l). From the above discussion it follows that s-sub-shell (containing only one orbital) can have a maximum of 2 electrons

p-sub-shell (containing three orbitals) can have a maximum of 6 electrons

d-sub-shell (containing five orbitals) can have a maximum of 10 electrons

f-sub-shell (containing seven orbitals) can have a maximum of 14 electrons.



This rule states that the pairing of electrons in the orbitals of a particular sub-shell (p, d or f ) does not take place until all the orbitals of the sub-shell are singly occupied. Moreover, the singly occupied orbitals must have the electrons with parallel spins.

The basis of this rule is that two electrons in a particular orbital feel greater repulsion and hence while filling orbitals of equal energy pairing of electrons is avoided as long as it is possible. Moreover, the singly occupied orbitals should have electrons with parallel spin because this corresponds to state of lower energy. This can be explained in terms of magnetic effects of electron spin. This rule helps us in writing the ground state configurations of those atoms which have partially filled p, d or f sub-shells in them. The application of these rules has been illustrated in the following electronic configurations.