Hunds Rule - Definition, Examples, Uses, Spin Multiplicity, FAQs

Hund's Rule Of Maximum Multiplicity

Hund’s Rule of Maximum Multiplicity states that pairing of electrons in the orbitals belonging to the same subshell does not take place until each orbital contains one electron first. All the singly occupied orbitals have electrons with parallel spins. According to this rule, electrons distribute themselves in different orbitals of equal energy in such a way that the number of unpaired electrons is maximum. This arrangement provides greater stability to the atom because it minimizes electron–electron repulsion.

What Is Hund's Rule?

Hund's rule states that:

1. For a particular electronic configuration, the electron having the maximum spin multiplicity has the lowest energy. The multiplicity can be depicted as ( 2S+1), where S represents the total spin angular momentum of the electrons.

2. For a particular multiplicity, the term with the maximum value of total orbital angular momentum quantum numbers (L) occupies the lowest energy.

3. In an atom having the outermost subshell half-filled or less, for a particular term, the level with the lowest value of the total angular momentum quantum number (J) lies in the lowest energy. If the outermost shell is more than half-filled, the level with the highest value of J is the lowest in energy.

Where, total angular momentum quantum number, J = L + S

Example Of Hund's Rule Of Maximum Multiplicity

For example, a nitrogen atom’s electronic configuration would be 1s²2s²2p³. The same orbital will be occupied by the two 2s electrons, although different orbitals will be occupied by the three 2p electrons in accordance with Hund’s rule.

Let's consider carbon as an example.

The electronic configuration for carbon atoms: 1s²2s²2p²:

Here, the two 2s electrons will occupy the same orbital, whereas the two 2p electrons will be in different orbitals (and aligned in the same direction) in accordance with Hund's rule. Consider also the electronic configuration of oxygen. Oxygen has 8 electrons.

The electronic configuration can be written as 1s²2s²2p⁴.

The first two electrons will be paired up in the 1s orbital; the next two electrons will be paired up in the 2s orbital. The remaining 4 electrons must be placed in the 2p orbitals. According to Hund’s rule, all orbitals will be singly occupied before being doubly occupied. Therefore, two p orbitals get one electron, and one will have two electrons. Hund's rule also stipulates that all of the unpaired electrons must have the same spin. In keeping with convention, the unpaired electrons are drawn as "spin-up".

Spin Multiplicity Meaning

In spectroscopy and in quantum chemistry, the multiplicity of an energy level can be calculated by using 2S+1, where S indicates the total spin angular momentum. States of electrons with multiplicity 1, 2, 3, 4, and 5 are respectively called singlets, doublets, triplets, quartets, and quintets.

Spin Multiplicity Rule

According to the spin multiplicity rule, for a given electron configuration, the lowest energy term is the one with the greatest value of spin multiplicity. This indicates that if two or more orbitals of equal energy are available, electrons will occupy them singly before filling them in pairs.

Uses Of Hund’s Rule

Hund's rule of maximum multiplicity is a rule that is based on the observation of atomic spectra. This observation is used to predict the electronic configuration of the ground state of an atom or molecule with one or more open electronic shells. For example, from boron through neon, the electron filling order of the 2p orbitals follows Hund's Rule of maximum multiplicity. It has wide applications in atomic chemistry to predict the electronic configuration and spin of an electron, quantum chemistry, spectroscopy, etc.

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Some Solved Examples

Example.1 The 71^st electron of an element X with an atomic number of 71 enters the orbital:

1) 6p

2) (correct)5d

3) 4f

4) 6s

Solution

The 71st electron will having an atomic number 71, will enter 5d.

Hence, the answer is option (2).

Example.2 Which law indicates the pairing of electrons in the same orbital?

1) Newton’s first law

2) (correct)Hund’s rule

3) Aufbau principle

4) Pauli exclusion principle

Solution

Hund’s rule states that “pairing of electrons in the orbitals belonging to the same subshell (p, d or f) does not take place until each orbital belonging to that subshell has got one electron each. It is singly occupied”.

Hence, the answer is option (2).

Example. 3 Nitrogen has the electronic configuration $1 \mathrm{~s}^2, 2 \mathrm{~s}^2, 2 \mathrm{p}_{\mathrm{x}}^1, 2 \mathrm{p}_{\mathrm{y}}^1, 2 \mathrm{p}_{\mathrm{z}}^1$ and not $1 \mathrm{~s}^2, 2 \mathrm{~s}^2, 2 \mathrm{p}_{\mathrm{x}}^2, 2 \mathrm{p}_{\mathrm{y}}^1, 2 \mathrm{p}_{\mathrm{z}}^0$ which is determined by

1) Aufbau's Principle

2) Pauli's exclusion principle

3) (correct)Hund's rule

4) Uncertainty Principle

Solution

The above is determined by Hund's rule of maximum multiplicity, which says that pairing will not start until all the degenerate orbitals are singly occupied first.

Hence, the answer is option (3).

Example.4 Which of these orbitals has the highest penetration effect?

1) (correct)1s

2) 2p

3) 3d

4) 4s

Solution

Penetration effect of electron -

Due to the different shapes and orientations of different orbitals, the penetration effect decreases from 1s to f.

n(s)>n(p)>n(d)>n(f)

Hence, the answer is option (1).

Question 5: Which of the following options does not represent the ground state electronic configuration of an atom?
1) $1 s^2 2 s^2 2 p^6 3 s^3 3 p^6 3 d^8 4 s^2$

2) $1 s^2 2 s^2 2 p^6 3 s^2 3 p^6 3 d^{10} 4 s^1$

3) $1 s^2 2 s^2 2 p^6 3 s^2 3 p^6 3 d^5 4 s^1$

4) (correct) $1 s^2 2 s^2 2 p^6 3 s^2 3 p^6 3 d^9 4 s^2$

Solution:

Aufbau Principle -

In the ground state of the atoms, the orbitals are filled in order of their increasing energies.

Electrons fill the orbitals in the order of increasing energy. By that rule, 3d orbit should fill up before 4s.

Hence, the answer is option (4).

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