Hund's Rule - Definition, Examples, Practice Problems & FAQs 

There was a man named Ravi who used to run his own shop. Now, he has expanded his business and opened 5 more shops of his own. He wanted a few more employees to run his other shops efficiently. He asked people around him to work with him, and 6 people came to him to work in the 5 shops that Ravi has.

Ravi decided to fill one person in a single shop first so that all the shops run smoothly, one person is left out, he kept that man with the other employee in one of the shops so that he can help the other person.

We are not interested in Ravi’s shop and his business. But, we are interested in the chemistry of electrons and how the filling of electrons takes place while writing the basic electronic configuration of elements. Just like Ravi's thoughts, while filling the electrons in orbitals, electrons first occupy singly and then their pairing starts.

There are various rules for filling electrons but in this article, we will study Hund's rule of maximum multiplicity.

What do you think, out of unpaired and paired electrons, which are more stable in an electrical configuration?

During the filling of electrons in subshells first, single electrons are assigned to all then orbitals then pairing takes place. In this article, we’ll learn about the significance of how to fill electrons in the orbitals. 

Table of Contents

• Hund’s Rule of Maximum Multiplicity
• Electronic Configurations of Elements Following Hund’s Rule
• Application of Hund's Rule
• Practice Problems
• Frequently Asked Questions - FAQs

Hund’s Rule of Maximum Multiplicity

The Hund's rule states that the atom/ion with the highest spin multiplicity value has the lowest energy. According to the Hund’s rule, electron pairing in the degenerate orbitals can't happen until each degenerate orbital is singly occupied. So, no electron pairing takes place in the degenerate orbitals of a subshell until each degenerate orbital is occupied by one electron with parallel spin. 

Half-filled and fully filled orbitals make the atoms more stable, i.e., configurations are the most stable. 

The electrons will want to stay as far apart as possible to decrease coulomb repulsion. This is possible when electrons occupy distinct orbitals. Electrons in the same orbital are stacked on top of one another, maximising repulsion.

The identical spin orientation ensures that there is no chance of two electrons occupying the same orbital (Pauli exclusion), reducing coulomb repulsion at the same time.

Electrons are negatively charged particles that make up an atom. The attraction and repulsion principle governs these charged particles, as it does all other charged particles. As we all know, like charges repel one another while opposite charges attract each other. The electrons partly occupy an orbital first, based on this concept, to reduce repulsion between them.

Every electron has two spin quantum numbers to select from: or , and the spin around the axis is governed by the number chosen. To maintain optimal stability of the partially filled orbitals, the unpaired electrons in an orbital of a subshell tend to have the same spin.

We can say, the higher the value of spin multiplicity, the more stable the electronic configuration.

Calculation of spin multiplicity: 

Maximum spin multiplicity =  

S = total spin 

E.g- for configuration) 

S = or  

Spin multiplicity of = =  

Electronic Configurations of Elements Following Hund’s Rule

On the basis of Hund’s rule, the electronic configurations of elements are written: 

Electronic configuration of oxygen: Oxygen has an atomic number of eight and an electronic configuration of . The lower energy level 1s shell gets filled first, followed by subshells 2s and 2p, according to Aufbau's principle.

Because an s-subshell has just one orbital, it is easy to fill. Whereas there are three orbitals in the p-subshell, the filling of these orbitals happened on the basis of Hund's rule. The three p-orbitals are filled individually initially, and then one orbital is paired.

Electronic configuration of chlorine: Chlorine has an atomic number of 17 and an electronic configuration of chlorine is .

To achieve optimum stability, the atom seeks to fill the 3p orbitals with single electrons first according to Hund's rule. The first three 3p orbitals are singly occupied and then pairing happens and two orbitals are paired up to have outer configuration. 

Application of Hund's Rule

• When it comes to filling the orbitals of the shells with electrons, almost every element follows Hund's rule of maximum multiplicity. The rule's ultimate purpose is to increase the stability of negatively charged particles.

• Hund's rule is useful for determining an atom's lone pair of electrons as well as its valency.

• It is often used in spectroscopy to create an element's atomic spectra.

• Hund's rule, along with other ideas, is employed in quantum chemistry research.

Related video: Hund's rule (55:11 / 1:02:01)

Practice Problems

Q 1. The correct configuration of the nitrogen atom is: 

1. Both A and B

Answer: (D)

Solution: According to Hund's rule, no electron pairing takes place in the orbitals in a subshell until each degenerate orbital is occupied by one electron with a parallel spin. This is not mandatory to start filling any orbital by the upward arrow; we can start filling orbitals of any subshell by the downward arrow and make sure after the distribution of one electron to each orbital, pairing should start with electrons of opposite spin. So, both options A and B are correct. 

Q 2. In which of the following subshells Hund's rule is not applicable?

1. s-subshells
2. p-subshells
3. d-subshells 
4. f-subshells 

Answer: (A)

Solution: s-subshells contain only one orbital. For subshells p, d and f, we should take care that the orbitals are first singly occupied with parallel spin and then pairing shall start.

Q 3. According to which of the following rule(s), the orbitals are filled?

1. Pauli exclusion principle 
2. Aufbau rule
3. Hund’s rule of maximum multiplicity
4. All of the above

Answer: (D)

Solution: These concepts dictate that orbitals are filled in ascending energy order according to Aufbau’s principle. According to Hund's rule, no electron pairing takes place in the degenerate orbitals in a subshell until each degenerate orbital is occupied by one electron with a parallel spin. According to Pauli’s exclusion principle, It is impossible for two electrons in the same orbital to share the same set of all four quantum numbers. So, to decide the filling of electrons in orbitals, we have to follow all the rules mentioned in the options. So all of the given options are correct.

Q 4. The spin multiplicity of configuration is: 

1. 1
2. 5
3. 8
4. 10

Answer: (A)

Solution: 

Spin multiplicity =  

S = Total spin 

for configuration: 

S = or  

Spin multiplicity = =  

Frequently Asked Questions-FAQs

Q. Can we write exactly the correct configurations of all elements by only Hund's rule?

Answer: No, for writing electronic configuration of elements generally we need to follow all the rules including the Aufbau rule, Hund’s rule and Pauli exclusion principle.

Q. Is the outermost electronic configuration of elements along a group of the periodic table always the same?

Answer: Not always, we can observe this in many cases,

For example, Helium and Neon , they are in the same group but the outer electronic configuration of these two are not the same.

We can observe many cases in transition metal series also.

Q. 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 of a subshell until each orbital is occupied by one electron with parallel spin.

Q. What are 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 options for exchanging the more the stability of an atom. 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 when the electrons get paired in an orbital. The more the paired electrons, the more the atom’s stability. The number of pairs is maximum in fully filled orbitals, hence it is more stable compared to partially filled orbitals.

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