Hund’s Rule Definition and Examples

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Hund's Rule Definition and Example
Hund’s rule states that electrons fill a suborbital singly and with the same spin before they form doubles with opposite spins.

In chemistry and atomic physics, Hund’s rule states that electrons fill a suborbital as singles before they start forming doubles and that all of the singles in the suborbital have the same spin. The rule gets it name for German physicist Friedrich Hund, who formulated it around 1927.

What Is Hund’s Rule?

Hund’s rule describe the order in which electrons fill subshells and the spin quantum number of each electron:

  1. The orbitals of a subshell fill with single electrons before any subshells get double electrons (with antiparallel spin).
  2. The single electrons in subshells have the same spin, so as to maximize total spin.

Basically, the lowest or most stable atomic state is the one that maximizes the total spin quantum number. Spin is either ½ or -½, so single electrons with the same value satisfies the rule. Another name for Hund’s rule is the “bus seat rule” because people choose separate seats on a bus before they start pairing up.

Giving the single electrons in the orbitals the same spin minimizes electrostatic repulsion between electrons. While not entirely accurate, the classical example is that electrons orbiting an atom all in the same direction meet less often than if some went in one direction and some went in the opposite direction. Basically, single electrons in subshells have parallel spin because it is the most stable configuration.

Relationship to the Aufbau Principle and Pauli Exclusion Principle

The Aufbau principle and Hund’s rule both describe how electrons fill orbitals, but the Aufbau principle explains the order in which electrons fill orbitals, while Hund’s rule describes how, exactly, electrons fill those orbitals.

The Aufbau principle states that electrons fill the subshells of the lowest energy orbital before moving on to higher energy subshells. For example, electrons fill the 1s subshell before any electrons enter the 2s subshell. This way, electrons achieve the most stable electron configuration.

Hund’s rule describes the way these electrons fill the lowest energy subshell, where electrons half-fill subshells with electrons having the same spin before that subshell gets two electrons. Those two electrons have opposite spin values due to the Pauli exclusion principle.

The Pauli exclusion principle states that a maximum of two electrons can occupy an orbital and they have opposite or antiparallel spin values because no two electrons in an atom have the exact same quantum numbers.

Aufbau Rule Examples

Nitrogen Atom

The electron configuration of a nitrogen atom (Z=7) is 1s2 2s2 2p3. Using Hund’s rule, show how electrons fill the subshells.

Here, the 1s and 2s subshells are filled. The 2p subshell is only half-filled. So, the electrons in the 1s and 2s subshells are pairs and antiparallel, while the 3 electrons in the 2p subshell are separate from each other and have the same spin:

Hund's Rule for Nitrogen

Oxygen Atom

Oxygen follows nitrogen on the periodic table (Z=8). Its electron configuration is 1s2 2s2 2p4. The filling of the 1s and and 2s subshells is the same as for nitrogen, but there is an additional electron in the 2p subshell. First, fill each subshell with a single electron. Add the additional electron to make a pair and make it antiparallel to the first electron:

Hund's Rule for Oxygen

Importance of Hund’s Rule

Hund’s rule is important because it shows how electrons organize into subshells. This identifies the valence electrons (the unpaired ones), which are the electrons that participate in chemical reactions and account for much of an atom’s chemical properties. For example, the electron configuration reflects an atom’s stability. An atom with only one unpaired electron is highly reactive, while one with no unpaired electrons is stable. The valence shell also indicates the magnetic properties of an atom. If there are unpaired electrons, the atom is paramagnetic and attracted to a magnetic field. If all of the electrons are paired, the atom is diamagnetic and is weakly repelled by a magnetic field.

References

  • Cottingham, W. N.; Greenwood, D. A. (1986). “Chapter 5: Ground state properties of nuclei: the shell model”. An Introduction to Nuclear Physics. Cambridge University Press. ISBN 0-521-31960-9.
  • Engel, T.; Reid, P. (2006). Physical Chemistry. Pearson Benjamin-Cummings. ISBN 080533842X.
  • Goudsmit, S. A.; Richards, Paul I. (1964). “The Order of Electron Shells in Ionized Atoms”. Proc. Natl. Acad. Sci. 51 (4): 664–671. doi:10.1073/pnas.51.4.664
  • Klechkovskii, V.M. (1962). “Justification of the Rule for Successive Filling of (n+l) Groups“. Journal of Experimental and Theoretical Physics. 14 (2): 334.
  • Miessler, G.L.; Tarr, D.A. (1999). Inorganic Chemistry (2nd ed.). Prentice-Hall. ISBN 0138418918.