# Electronic configuration-Aufbau Principle, Hund’s rule, Pauli’s exclusion Principle- Explanation, solved examples

Which property of elements is most useful to categorize them in a group according to their similar chemical & physical properties?

According to Dalton's theory, an atom is the simplest unit of matter that can participate in any chemical reaction. From further research, we concluded that mainly electrons determine the chemical behaviour of an atom. The electronic configuration of atoms is very useful in understanding the periodic table, and their chemical and physical behaviour. Some sets of rules are defined to write the correct electronic configuration of any element.

## What is electronic configuration?

Electrons are filled in orbitals of an element under a set of rules based on the parameters of energy, indistinguishability and orientation.

Rules for Filling Electrons in Orbitals

• Aufbau's principle
• Pauli’s exclusion principle
• Hund’s rule for maximum multiplicity

## Aufbau’s principle

Electrons are filled in various orbitals in order of their increasing energies. Orbitals having the lowest energy are filled first. The sequence of orbitals in order of their increasing energy is

• Energies of subshells of single-electron species

Note: Energy of single-electron species depends only on the principal quantum number (n).

Order of Energy, 1s < 2s = 2p < 3s = 3p = 3d < 4s = 4p = 4d = 4f < …

• Energies of subshells of multi-electron species

Note: Energy of single-electron species depends on the principal quantum number (n) & azimuthal Quantum Number (l).

The energy of orbitals depends on (n+l) rule.

 Letter code (subshell) Value of l s 0 p 1 d 2 f 3
 subshell Value of l Value of n (n+l) 1s 0 1 1 2s 0 2 2 2p 1 2 3 3s 0 3 3

Note: if two subshells with the same (n+l) value, subshell with lower ‘n’ value has lower energy

Order of Energy, 1s < 2s < 2p < 3s < 3p < 3d < 4s < 4p < 4d < 4f < …

## Pauli’s Exclusion Principle

No two electrons in an atom can have the same set of all four quantum numbers.

Hund’s rule of maximum multiplicity

No electron pairing takes place in the orbitals in a sub-shell until each orbital is occupied by one electron with parallel spin. Exactly half-filled and fully filled orbitals make the atoms more stable, i.e., p3, p6, d5,d10,f7&f14 configuration is the most stable.

Maximum spin multiplicity = 2|S|+1

|S| = Modulus of the maximum spin of an atom

## Exceptional electronic configurations:

Cr24=1s2,2s22p6,3s23p63d5,4s1
Cu29=1s2,2s22p6,3s23p63d10,4s1
Pd46=1s2,2s22p6,3s23p63d10,4s24p64d10,5s0

Atomic Structure - Electronic Configuration | JEE | NEET | Aakash EduTV

## Practice problems:

Q1. Calculate maximum spin multiplicity of d5 & d6configuration respectively

A.  6 & 7
B.  6 & 6
C. 6 & 5
D.  5 & 6

Solution: d5 ; number of unpaired electron = 5

Maximum spin multiplicity = 2|S|+1 = 2|2|+1= 5

Q2. Which is correct order of energy of subshells in hydrogen atom

A. 1s < 2s < 2p<3s < 3p < 3d
B. 1s < 2s = 2p<3s = 3p = 3d
C.  1s < 2s = 2p<3s < 3p = 3d
D. 1s = 2s < 2p=3s < 3p < 3d

Solution: Energy of subshells for single-electron species only depend on principle quantum number (n). So, the energy of 2s = 2p and 3s = 3p = 3d

So, 1s < 2s = 2p<3s = 3p = 3d

Q3. For an electron with angular quantum number ℓ = 2, the magnetic quantum number m can have:

A. An infinite number of values
B. Only one value
C. One of two possible values
D. One of five possible values

Solution: As per the existing rule, the values of magnetic quantum number (m) can range between -l to +l

So the number of values of magnetic quantum number (m) = 2l + 1

= (2*2) + 1

= 5

Q4. An atom have d7 configuration. Calculate the maximum number of electrons having same spin

A. 5
B. 6
C. 7
D. 8

Solution: only 5 electrons can have same spin

Video:

Question 1. Can we write exactly the correct configurations of all elements by strictly following (n + l) rule, Pauli exclusion principle, Hund's rule?
Answer: No, we can see many configurations which don’t obey these rules (specially Aufbau). Eg. Cr, Cu, Pd, Pt etc.

Question 2. Is the outermost electronic configuration of elements along a group of the periodic table always the same?
Answer: Not always, we can observe in many cases,

Eg- He - 1s2 but Ne - 1s2,2s22p6

We can observe the same in many cases in transition metal series.

Question 3. Is it necessary to start filling any orbitals with an upward arrow?
Answer: No, you can start filling orbitals with upward or downward spin but make sure, no electron pairing takes place in the orbitals in a sub-shell until each orbital is occupied by one electron with parallel spin.

Question 4. What is exchange energy and pairing energy?
Answer: Exchange energy is the energy released when two or more electrons with the same spin exchange their positions in the degenerate orbitals of a subshell. The more the options for exchange, the more is the electron’s stability. The number of exchange pairs is maximum in half filled orbitals, hence it is more stable compared to partially filled orbitals.

Pairing energy refers to the energy released with paired electrons sharing one orbital. More the paired electrons, more is the electron’s stability. The number of pairs is maximum in fully filled orbitals, hence it is more stable compared to partially filled orbitals.

Related topics:

 Isotopes Isobars, Isotones & Isodiaphers Discovery of neutron Rutherford atomic model Thompson’s Atomic Model Atomic number and Mass number Quantum numbers