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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 well-defined orbits. The electrons reside in orbitals of sublevels of different energy. According to the Aufbau principle, electrons fill the lowest energy sublevel before filling up the higher ones. Thus, electrons are found in discrete atomic sublevels in an arrangement known as electron configuration. However, filling up of orbitals in the sublevels follows a particular set of guidelines known as Hund’s rule, which states that:

  • Every orbital is singly occupied before it is doubly occupied.
  • All electrons in singly occupied orbitals 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 chemical bonds. 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 sublevels are designated as s, p, d, and f. The maximum number of electrons that they can take are as follows:

s-sublevel – 2 electrons

p-sublevel – 6 electrons

d-sublevel – 10 electrons

f-sublevel – 14 electrons

Each of these sublevels is divided into orbitals and each orbital can take a maximum of two electrons. The number of orbitals as follows:

s-sublevel – 1 orbitals

p-sublevel – 3 orbitals

d-sublevel – 5 orbitals

f-sublevel – 7 orbitals

When the electrons fill them, each orbital is initially filled with one electron. All the unpaired electrons have 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 configuration, there will be two electrons in each of the 1s and 2s sublevels, and 2 electrons in the 2p sublevel. The 1s and 2s sublevels are completely filled, and the 2p sublevel is partially filled. According to Hund’s rule, these two electrons will occupy separate orbitals and have the same spin. If they are found in the same orbital, then it will result in a violation of Hund’s rule.

Examples of elements having completely filled subshells 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 designated by n, l, ml, and ms. Since orbital 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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