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Concept 06 / 06Structure of Atom

Electronic Configuration: Aufbau, Pauli and Hund's Rules and Exceptions

The Aufbau principle and the (n + l) rule, the Pauli exclusion principle, Hund's rule of maximum multiplicity, writing configurations and orbital diagrams, extra stability of half-filled and fully-filled subshells (Cr, Cu), configurations of ions (4s removed first), and counting unpaired electrons and magnetic moment.

Figure 1
The ground-state arrangement of electrons in an atom is found from three rules. Aufbau principle. Electrons fill orbitals in order of increasing energy. For multi-electron atoms the order follows the (n+l)(n + l) rule: lower n+ln + l first, and for equal n+ln + l the lower nn first. The resulting sequence is 1s,2s,2p,3s,3p,4s,3d,4p,5s,4d,5p,6s,4f,5d,6p,7s,5f,6d,7p1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p, generated by the diagonal-arrow diagram in the figure. Pauli exclusion principle. No two electrons in an atom can have the same set of four quantum numbers. Hence an orbital holds at most two electrons, and they must have opposite spins. Hund's rule of maximum multiplicity. In degenerate orbitals (such as the three 2p2p orbitals), electrons occupy separate orbitals with parallel spins before any pairing occurs. Nitrogen is 1s22s22px12py12pz11s^{2}2s^{2}2p_{x}^{1}2p_{y}^{1}2p_{z}^{1}, with three unpaired electrons, not 2px22py12p_{x}^{2}2p_{y}^{1}. Parallel spins in separate orbitals reduce electron repulsion and gain exchange energy. Writing configurations. Use the noble-gas core: Fe (Z=26Z = 26) is [Ar] 3d64s2[\mathrm{Ar}]\,3d^{6}4s^{2}. By convention the final configuration is often written in order of nn (3d3d before 4s4s) even though 4s4s fills first. Exceptions from extra stability. Half-filled (d5d^{5}, f7f^{7}) and completely filled (d10d^{10}, f14f^{14}) subshells are especially stable, because of symmetric distribution and maximum exchange energy. So Cr (Z=24Z = 24): [Ar] 3d54s1[\mathrm{Ar}]\,3d^{5}4s^{1}, not 3d44s23d^{4}4s^{2}. Cu (Z=29Z = 29): [Ar] 3d104s1[\mathrm{Ar}]\,3d^{10}4s^{1}, not 3d94s23d^{9}4s^{2}. The same happens for Mo and Ag, Au, and several other heavier elements (with further irregularities among the lanthanides and actinides). Configurations of ions. For cations of transition elements, electrons are removed first from the outermost shell, which is 4s4s, before 3d3d: once 3d3d is occupied, the 4s4s electrons are higher in energy. So Fe2+\mathrm{Fe^{2+}} is [Ar] 3d6[\mathrm{Ar}]\,3d^{6} and Fe3+\mathrm{Fe^{3+}} is [Ar] 3d5[\mathrm{Ar}]\,3d^{5} (a stable half-filled set, which is why Fe3+\mathrm{Fe^{3+}} is favoured in air). Cu+\mathrm{Cu^{+}} is 3d103d^{10} and Cu2+\mathrm{Cu^{2+}} is 3d93d^{9}. For anions, add electrons in Aufbau order. Unpaired electrons and magnetism. Species with unpaired electrons are paramagnetic (attracted by a magnetic field); those with all electrons paired are diamagnetic. The spin-only magnetic moment is μ=n(n+2)\mu = \sqrt{n(n + 2)} BM, where nn is the number of unpaired electrons: 1.731.73, 2.832.83, 3.873.87, 4.904.90, 5.925.92 BM for n=1n = 1 to 55. Key Takeaways: - Aufbau order by (n+l)(n + l), ties broken by lower nn. - Pauli: at most 22 electrons per orbital, opposite spins. - Hund: occupy degenerate orbitals singly with parallel spins first. - Cr 3d54s13d^{5}4s^{1}; Cu 3d104s13d^{10}4s^{1} (half-filled and full stability). - Transition-metal cations lose 4s4s electrons before 3d3d. - μ=n(n+2)\mu = \sqrt{n(n + 2)} BM. - Pitfall: writing Fe2+\mathrm{Fe^{2+}} as 3d44s23d^{4}4s^{2}. Brain-Teaser 1: Write the configurations of Mn2+\mathrm{Mn^{2+}} and Zn2+\mathrm{Zn^{2+}} and predict their magnetic behaviour. Solution: Mn (Z=25Z = 25) is [Ar] 3d54s2[\mathrm{Ar}]\,3d^{5}4s^{2}; Mn2+\mathrm{Mn^{2+}} is [Ar] 3d5[\mathrm{Ar}]\,3d^{5} with 55 unpaired electrons, strongly paramagnetic, μ=35=5.92\mu = \sqrt{35} = 5.92 BM. Zn (Z=30Z = 30) is [Ar] 3d104s2[\mathrm{Ar}]\,3d^{10}4s^{2}; Zn2+\mathrm{Zn^{2+}} is 3d103d^{10}, all paired, diamagnetic, which is why zinc salts are colourless. Brain-Teaser 2: Which has more unpaired electrons: Fe3+\mathrm{Fe^{3+}} or Co2+\mathrm{Co^{2+}}? Which is more stable, Fe2+\mathrm{Fe^{2+}} or Fe3+\mathrm{Fe^{3+}}, and why? Solution: Fe3+\mathrm{Fe^{3+}} is 3d53d^{5} (55 unpaired); Co2+\mathrm{Co^{2+}} (Z=27Z = 27) is 3d73d^{7} (33 unpaired). Fe3+\mathrm{Fe^{3+}} has more. Fe3+\mathrm{Fe^{3+}} is more stable than Fe2+\mathrm{Fe^{2+}} (3d63d^{6}), because removing one electron from 3d63d^{6} gives the half-filled 3d53d^{5}, which explains why iron(II) salts are slowly oxidised in air. Brain-Teaser 3: An element has 22 electrons in its n=1n = 1 shell, 88 in n=2n = 2, 1313 in n=3n = 3 and 11 in n=4n = 4. Identify it and comment. Solution: Total 2424 electrons: chromium. Its n=3n = 3 shell holds 3s23p63d53s^{2}3p^{6}3d^{5} (1313 electrons) and the n=4n = 4 shell 4s14s^{1}. The single 4s4s electron reflects the stability of the half-filled 3d53d^{5} subshell, the classic exception to Aufbau order.

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