Chapter 2
Gold: Why It Is Yellow
Why does gold shine yellow and not silver? Because Einstein’s relativity acts in its electron shell. Compare the orbitals with and without relativity.
Gold in one line: [Xe] 4f¹⁴ 5d¹⁰ 6s¹
Gold has atomic number 79: 79 protons in the nucleus and 79 electrons around it. How these electrons are distributed over the orbitals is written as the electron configuration. It looks complicated but is just a list. If you have read the ../../../en/atoms-and-molecules/hydrogen-atom/ chapter you already know the building blocks: number = shell, letter = shape, superscript = electrons.
Word by word
- [Xe] is shorthand for “all the inner shells as in the noble gas xenon”. That is 54 electrons in eleven sets of orbitals (1s to 5p). They are completely filled and do not change in chemical processes.
- 4f¹⁴: the 4th shell, f shape, 14 electrons. The f set is full and lies deep inside.
- 5d¹⁰: the 5th shell, d shape, 10 electrons. Also full, but just beneath the outside. These electrons decide the colour.
- 6s¹: the 6th shell, s shape, 1 electron. It is the only outer electron and makes the chemistry of gold.
Sum: 54 + 14 + 10 + 1 = 79. A set of orbitals can hold at most 2 (s), 6 (p), 10 (d) or 14 (f) electrons. Gold therefore has full d and f sets and only a half-empty s.
What the buttons above mean
Every button above the picture is a set of orbitals of gold, written as in the configuration (for example 5d10). The superscript tells how many electrons sit in it.
- Inner shells [Xe]: 1s to 5p, the eleven sets of the noble-gas core. Choose them to see how tiny the innermost shells are. The scale bar in the picture shows it: for the 1s orbital the picture is only a few picometres wide.
- Outer: 4f, 5d and 6s. This is where it is decided what gold looks like and how it reacts.
- Unoccupied: 6p. An orbital in which no electron sits in the ground state. It is only a possibility that the atom uses when energy is added.
- Orientation: for p, d and f there are several orbitals of the same shape pointing in different directions (3, 5, 7). They are equivalent for gold.
- Relativity: “With” is the realistic calculation. “Without” is a thought experiment: this is how gold would look if relativity did not exist. The crop stays the same so that you can see the difference.
Where in nature do these orbitals occur?
- s: everywhere. Hydrogen and helium, of which stars consist, and the outer electrons of the alkali metals (sodium glows yellow in street lamps).
- p: carbon, nitrogen and oxygen, the building blocks of life. Their directional orbitals form the bonds.
- d: the transition metals: iron (blood pigment, magnets), copper, gold. They are coloured, magnetic or good catalysts.
- f: the rare earths: neodymium magnets, red phosphors in screens (europium), amplifiers in fibre-optic cables (erbium). In gold the f set lies deep inside and shapes it only indirectly.
A heavy nucleus, fast electrons
The strong nucleus accelerates the electrons of the innermost shell to about 58% of the speed of light (speed ≈ Z / 137 of the speed of light). According to Einstein’s special relativity such a fast particle becomes heavier, and a heavier electron stays closer to the nucleus. The 1s orbital therefore shrinks by about one fifth (choose it above and compare “With” and “Without”).
The effect carries on outward. All s orbitals (and to a smaller degree the p orbitals) have to fit with the inner s orbitals and are pulled in with them. The 6s orbital with the single outer electron contracts markedly and drops in energy. The d and f orbitals do not shrink; they even expand a little, because the contracted inner shells screen the nuclear charge better.
The graph shows all shells of gold on a logarithmic axis. Each shell has its own hump: K right inside (very close to the nucleus), P on the outside (the single 6s electron). Without the logarithmic axis the inner shells would be invisibly small.
Why gold is yellow
The colour of a metal comes from which light it absorbs. In gold it is mainly light that lifts an electron from the full 5d set into the half-empty 6s. Because the 6s level drops relativistically and the 5d levels rise, the gap becomes smaller: in the metal it is measured at about 2.4 eV. That corresponds to light around 520 nm, blue-green to blue. This is absorbed, and the remaining light (red, orange, yellow) is reflected. That is why we see gold as yellow.
Without relativity the gap would be much larger. The absorbed light would lie in the ultraviolet, nothing would be missing in the visible, and gold would look silvery white like silver. This is the widely accepted explanation in the literature.
Gold, silver and copper compared
| Metal | Configuration | Onset of light absorption (d → s) | Colour |
|---|---|---|---|
| Copper (Z = 29) | [Ar] 3d¹⁰ 4s¹ | about 2.1 eV, roughly 590 nm | reddish |
| Silver (Z = 47) | [Kr] 4d¹⁰ 5s¹ | about 3.9 eV, in the ultraviolet | silvery |
| Gold (Z = 79) | [Xe] 4f¹⁴ 5d¹⁰ 6s¹ | about 2.4 eV, roughly 520 nm | yellow |
All three have the same outer arrangement (a full d shell and one s electron). Silver has no significant relativistic effects, so its gap is large. Gold, thanks to relativity, lies lower and absorbs blue light.
Why gold hardly rusts
The contracted 6s orbital is held firmly by the nucleus. Gold gives up its electron less readily than silver (first ionization energy 9.2 eV versus 7.6 eV) and even likes to accept one: its electron affinity of 2.3 eV is the highest among the metals. There are therefore compounds with negatively charged gold, for example caesium auride (CsAu). Gold hardly reacts with oxygen, acids or water and stays shiny for millennia. It is a noble metal. A relative is mercury (Z = 80): there too the 6s pair lies deep and barely bonds to neighbouring atoms, which is why mercury is liquid at room temperature.
How these pictures are made
The orbitals come from our own atomic calculation (density functional with exchange). It is solved once according to the laws of classical quantum mechanics and once with the corrections of relativity (scalar-relativistic, without spin–orbit coupling). The crop is chosen automatically for each orbital (see the scale in the picture) but kept identical for “With” and “Without”. The calculation is an approximation: orbital energies are not measured values, and spin–orbit coupling and electron correlation are missing. The direction and size of the relativistic shifts agree with more accurate calculations, though.
Think about it
What does “5d¹⁰” mean?
5 is the shell, d the shape (cloverleaf) and the superscript 10 the number of electrons. Five d orbitals with two electrons each are completely filled.
How many electrons does gold have outside the [Xe] core?
25: 14 in 4f, 10 in 5d and one in 6s. Together with the 54 of the core that makes 79.
Which orbitals contract because of relativity and which expand?
s orbitals (and to a lesser degree p orbitals) shrink because their electrons come close to the nucleus. d and f orbitals expand because the contracted inner shells screen the nuclear charge more strongly. You can see it in the numbers below the picture.
Why would gold be silvery without relativity?
The gap between 5d and 6s would be larger and the absorbed light would lie in the ultraviolet. Then nothing specific is missing from visible light, and the metal appears white like silver.
On to a molecule: water. Back: hydrogen atom.
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