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Hund’s Rule

What is Hund’s Rule[1-4]

An atom consists of a nucleus around which electrons revolve in orbitals of different energy. According to the Aufbau principle, electrons fill the lowest energy level before filling up the higher ones. Thus, electrons are found in discrete atomic orbitals in an arrangement known as electron configuration. However, filling up of orbitals follows a particular set of guidelines known as Hund’s rule, which states that:

  • The sublevel of every orbital is singly occupied before it is doubly occupied.
  • All electrons in singly occupied sublevel have the same spin in order to maximize the spin.
Hund’s Rule

The rule has been named after German physicist Friedrich Hund, who formulated it around 1927.

Why Hund’s Rule is called the Rule of Maximum Multiplicity[2,3]

According to Hund’s rule, the lowest energy term in a given electronic configuration has the highest value of spin multiplicity. The electrons enter the sublevel orbitals so that the maximum number of unpaired electrons occupy them. All of them have identical directions of spins. This electron configuration is known as maximum multiplicity.

Hund’s Rule and Electron Configuration[1-3]

Electron configuration can predict the stability of an atom. If the valance orbitals are not filled, the atom will be unstable and combine with another unstable atom to form a chemical bond. When all the orbitals are filled, then the atom achieves a stable configuration. Such atoms do not have any empty orbital or unpaired electrons.

Examples of Hund’s Rule[1,3]

The different orbitals are designated as s, p, d, and f. The electrons fill in these orbitals according to Hund’s rule. The capacities of these orbitals are as follows:

s orbital – 2 electrons

p orbital – 6 electrons

d orbital – 10 electrons

d orbital – 14 electrons

Each of these orbitals has sublevels that can take two electrons, and different orbitals have different sublevels. They are as follows:

s orbital – 1 sublevel

p orbital – 3 sublevels

d orbital – 5 sublevels

d orbital – 7 sublevels

When the electrons fill them, each sublevel is filled with one electron with the same spin. Then, a second electron with an opposite spin completes the occupancy.

For example, the electron configuration for a carbon atom is 1s22s22p2. According to this designation, two electrons in each of the 1s and 2s orbital and 2 electrons in the 2p orbital. The 1s and 2s orbitals are completely filled, and the 2p orbital is partially filled. The two electrons present in 2p are in separate sublevels and have the same spin. If they are found in the same sublevel, then it will result in a violation of Hund’s rule.

Examples of elements with completely filled orbitals are helium, neon, argon, and xenon.

Hund’s Rule Example

Hund’s Rule and Pauli Exclusion Principle[3]

Pauli exclusion principle states that no two electrons can have the same set of four quantum numbers in a single atom. These quantum numbers are denoted by n, l, ml, and ms. Since an electron sublevel consists of two electrons, they will only differ in their spin quantum number ms. One electron will have an up spin (ms = +1/2), and the other electron will have a down spin (ms = -1/2). In other words, every electron has a unique (single) state.

Applications of Hund’s Rule[5]

Hund’s rule has a wide application in chemistry, especially in analytical chemistry, spectroscopy, and quantum chemistry.

References

  1. Chem.libretexts.org
  2. Hyperphysics.phy-astr.gsu.edu
  3. Chem.uci.edu
  4. Ch301.cm.utexas.edu
  5. Expii.com

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