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When you fill three 2p boxes for nitrogen with one arrow each instead of pairing two, you are applying a rule Friedrich Hund found by studying light from atoms. He lived for more than a century and shaped how chemists think about both atoms and molecules. This post covers his life, what the rule says and why, worked examples you can check, the usual mistakes, and what to learn from his way of working.
Who was Friedrich Hund?
A profile in the Indian Academy of Sciences journal Resonance (2022) gives the outline. Hund was born in Karlsruhe on 4 February 1896. He studied mathematics, physics and geography at Marburg and Göttingen, at first planning to be a school teacher, and served in the First World War. He then did his doctorate in Göttingen under Max Born, finishing in 1922, and worked with Born until 1925.
He later held chairs at Rostock, Leipzig (from 1929, alongside Peter Debye and Werner Heisenberg), Jena, Frankfurt and finally Göttingen, where he retired in 1964 but kept lecturing on the history of quantum theory. He died in Göttingen on 31 March 1997, aged 101. The Deutsche Biographie records the same places of birth and death.
Where did Hund's rule come from?
In 1925 Hund published Zur Deutung verwickelter Spektren, insbesondere der Elemente Scandium bis Nickel (On the interpretation of complicated spectra, especially of the elements scandium to nickel) in Zeitschrift für Physik. The spectra of transition metals contain thousands of lines. Hund worked backwards from them to the energy order of the states of each atom.
The Resonance profile summarises his two main findings: the state with the highest spin multiplicity has the lowest energy, and among those, the one with the largest orbital angular momentum is lowest. School chemistry uses the first one.
NCERT's Structure of Atom chapter states it as Hund's rule of maximum multiplicity: "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". So pairing starts with the 4th electron in p, the 6th in d and the 8th in f. The chapter links the rule to exchange energy, which is largest when parallel spins are as many as possible.
Worked example: counting unpaired electrons
Nitrogen, 1s² 2s² 2p³. Three 2p electrons go into three separate 2p orbitals with parallel spins: 3 unpaired. Total spin S = 3 × ½ = 3/2, so the multiplicity 2S + 1 = 4.
Oxygen, 2p⁴. The fourth p electron must pair: 2 unpaired.
Mn²⁺, 3d⁵. Five d electrons, one per d orbital: 5 unpaired.
Fe²⁺, 3d⁶. The sixth pairs: 4 unpaired.
Now use the spin-only formula from NCERT's d- and f-block chapter, μ = √[n(n + 2)] Bohr magnetons, where n is the number of unpaired electrons:
n = 3 (N atom): μ = √15 = 3.87 BM
n = 4 (Fe²⁺): μ = √24 = 4.90 BM
n = 5 (Mn²⁺): μ = √35 = 5.92 BM, the value NCERT's own Example 4.8 gives for atomic number 25.
If you ignored Hund's rule and paired nitrogen's electrons, you would predict only 1 unpaired electron. Magnetic measurements are one way chemists check which is right.
What mistakes do students make with Hund's rule?
Pairing too early. Fill every box in the subshell once before adding a second arrow.
Mixing spins in singly filled boxes. The single electrons must have parallel spins.
Applying it across subshells. The rule is about orbitals of equal energy. Whether 4s or 3d fills first is the Aufbau order, a separate rule.
Ions from the wrong orbital. For Fe²⁺, remove the two 4s electrons first, leaving 3d⁶.
Hund's rule works together with the exclusion principle of Wolfgang Pauli and the four quantum numbers. If orbital diagrams are hard to picture, the Fermi Simulation Lab has interactive simulations for ideas that are easier to see than read.
What else did Hund do?
He moved from atoms to molecules. In his 1966 Nobel lecture, Robert Mulliken called him "my friend Friedrich Hund", recalled meeting him in Göttingen in 1925, and wrote that molecular orbital theory "has long been known as the Hund-Mulliken theory in recognition of the major contribution of Professor Hund in its early development." Our post on Robert Mulliken covers that side. Resonance also credits Hund with an early paper on quantum tunnelling in 1927.
What can you take from how he worked?
Find order in messy data. Thousands of spectral lines became a short rule.
State the rule simply. That is why it is still taught a century later.
Keep moving to the next problem. From atoms he went straight on to molecules.
Next step: write orbital diagrams for carbon, phosphorus and Cr³⁺, count unpaired electrons, and work out each spin-only magnetic moment.
