Electronic Configuration

The distribution of electrons in different orbitals is known as its electronic configuration. This characterizes each electron in an atom. The electronic configuration is expressed by indicating the principal quantum number and its respective orbital along with the number of electrons present in it. For example the notation 3p_x¹ indicates that in the third principal shell there is one electron in the 'p_x' orbital.

Sometimes the electronic configuration is also described by box notation form i.e., putting an arrow for single electron in a box or a pair of arrows for two electrons in a box. The direction of the arrows gives the orientation of its spin.

Further the box is labelled on top by writing the symbol of the orbital.

Rules for Filling the Orbitals

Aufbau principle

The principle states that the electron in an atom are so arranged that they occupy orbitals in the order of their increasing energy. Since the energy of a 'n' orbital in the absence of any magnetic field depends on the 'n' and 'l' quantum number values, the order of filling orbitals with electrons may be obtained from the (n + l) rule of Bohr Bury's rule.

According to this principle the orbital with the lowest energy will be filled first. The orbital having lower (n + l) value has lower energy. However for orbitals whose (n + l) values are equal, the orbital having lower value of 'n' has lower energy. It is important to remember that because of this rule, this sequence of energy levels pertains to energy level up to '3p' and thereafter, '4s' orbitals comes first instead of '3d'. Thus, the orbitals should be filled in the order:

1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s

Fig: 3.19 - A simple way to determine the relative energies of different orbitals

Pauli's exclusion principle

The Paulis exclusion principle states, that no two electrons in an atom can have the same values of all the four quantum numbers. If one electron in the atom has the quantum numbers n = 1, l = 0, m = 0 and s = +1/2, no other electron can have the same four quantum numbers. In other words, we cannot place two electrons with the same value of 's' in a '1s' orbital.

Secondly, each orbital can accommodate a maximum of two electrons only if their spins are of opposite directions. Each sub shell holds a maximum of two electrons in an orbital. It can be thus concluded that

It can be inferred that the maximum number of orbital in each shell is n² and the maximum number of electrons is 2n².

Hund's rule of maximum multiplicity

It states that when more than one orbital of equal energies are available then the electrons will first occupy these orbitals separately with parallel spins. The pairing of electrons will start only after all the orbitals of a given sub level are singly occupied. This is because electrons with parallel spins tend to be as far apart as possible to minimize the electrostatic repulsion.

For example, the three electrons that are filled into the three 'p' orbitals can be represented in two different ways:

Based on these rules the electronic configuration of some of the important elements can be written as follows:

In the electronic configuration of elements Na to Argon the filled sub shells can be represented by the inert gas notation e.g., Ne as shown:

After argon the first orbital to be filled is '4s' followed by '3d' as shown for Ca.

In some cases the actual configuration differs slightly from the expected ones e.g., Cu (atomic number 29) and Cr (atomic number 24) because of the extra stability of half-filled and completely filled sub shell configuration.

The extra stability of half-filled and completely filled sub shell configuration is due to the following two reasons:

a) Symmetry of orbitals

The configurations in which all the orbitals of the same subshell are half-filled or completely filled involves symmetrical distribution of electrons. Symmetry of electronic distribution leads to extra stability. Example:

or

b) Exchange energy

In an atom, the electrons present in various orbitals of the same subshell tend to exchange their positions which is associated with very small amount of energy. Half-filled and completely filled subshell configurations allow maximum exchange of electrons to take place. Therefore, such configurations have maximum stability e.g., molybdenum (half-filled '4d' orbitals) and silver (completely filled '4d' orbitals).

For cations the electronic configuration is written by determining the number of electrons. The number of electrons is found by subtracting the number of positive charges on the cation from the atomic number.

For example,

Na⁺, atomic number = 11, number of positive charges = 1

Number of electrons in Na⁺ = (11 - 1) = 10

Electronic configuration is 1s² 2s² 2p_x² 2p_y² 2p_z² .

For anions the electronic configuration is written by determining the number of electrons. The number of electrons is found by adding the number of negative charges on the anion to the atomic number.

For example,

Cl^-, atomic number = 17, number of negative charges = 1

Number of electrons in Cl^- = (17 + 1) = 18

Electronic configuration is 1s² 2s² 2p_x² 2p_y² 2p_z² 3s²3p_x² 3p_y² 3p_z²

The ions and atoms having the same number of electrons are termed as isoelectronic e.g., O^2-, Na⁺, Al³⁺, Mg²⁺ and Ne (each containing ten electrons).

Problem

10. How many sublevels are possible in each energy level?

Solution

The total number of sublevels or sub-shells possible in each energy level is equal to the numerical value of 'n'. Thus 'n' = 1 energy level can have only one sublevel which is 'l' = 0 or the 's' orbital, 'n' = 2 energy level can have two sublevels corresponding to 'l' = 0 (s) and 'l' = 1(p).

Similarly 'n' = 3 energy level can have 3 sublevels 's', 'p' and 'd'.