by John Walker
In discussions of special relativity, you occasionally encounter a claim like, “The effects of special relativity only matter to particle physicists and others working with extreme energies and velocities. Relativity has no consequences in everyday life.” Well, these days, anybody who relies upon the Global Positioning System (GPS) to navigate their car or the airliner in which they're travelling uses both special and general relativity, because without correction for their effects, GPS would be so inaccurate as to be useless. But GPS is a recent innovation, and the relativistic corrections are both complicated and hidden from the user in the software in the receiver and on board the satellites. But there's an effect of special relativity which was observed, if not understood, by the ancients: the yellow gleam of gold.
With an atomic number of 79, gold is in the last row of the periodic table containing stable elements, and only four stable elements (mercury, thallium, lead, and bismuth) have greater atomic number. With 79 protons in its nucleus, the electrons of the gold atom are subjected to an intense electrostatic attraction. Using the naļve Bohr “solar system” model of the atom for the moment, electrons in the 1s orbital, closest to the nucleus, would have to orbit with a velocity v of 1.6×108 metres per second to have sufficient kinetic energy to avoid “falling into” the nucleus. This is more than half the speed of light: c≈3×108 m/s, which, according to Einstein's equation:
increases the electron's mass (or, in more modern terminology, momentum) by about 20%. Quantum mechanics replaces the Bohr orbits with a probability distribution of the electron's position, with the Bohr orbit radius interpreted as the distance from the nucleus where the peak probability occurs. The relativistic increase in mass of the electron causes a relativistic contraction of its orbit because, as the electron's mass increases, the radius of an orbit with constant angular momentum shrinks proportionately.
From the Bohr model, you might expect this effect to be significant only for the innermost electrons, but due to quantum mechanics, it strongly affects electrons in s orbitals even in outer shells, because their probability density remains high near the nucleus. The higher angular momentum p, d, f, and g orbitals have their probability peaks farther from the nucleus, and hence are less affected by relativistic contraction.
The colour of metals such as silver and gold is mainly due to
absorption of light when a d electron jumps to an
s orbital. For silver, the
4d→5s transition has an energy
corresponding to ultraviolet light, so frequencies in the
visible band are not absorbed. With all visible frequencies
reflected equally, silver has no colour of its own; it's
silvery. In gold, however, relativistic contraction of
the s orbitals causes their energy levels to shift closer to
those of the d orbitals (which are less affected by relativity).
This, in turn, shifts the light absorption (primarily due to the
5d→6s transition) from the ultraviolet
down into the lower energy and frequency blue visual range. A
substance which absorbs blue light will reflect the rest of the
spectrum: the reds and greens which, combined, result in the
yellowish hue we call golden.
Warmly glowing gold,
What gives it that autumn hue?
Relativity.
Special relativity is also responsible for gold's resistance to
tarnishing and other chemical reactions. Chemistry is mostly
concerned with the electrons in the outermost orbitals. With a
single 6s electron, you might expect gold to be highly
reactive; after all, cęsium has the same 6s1
outer shell, and it is the most alkaline of natural elements: it
explodes if dropped in water, and even reacts with
ice. Gold's 6s orbital, however, is
relativistically contracted toward the nucleus, and its electron
has a high probability to be among the electrons of the filled
inner shells. This, along with the stronger
electrostatic attraction of the 79 protons in the nucleus, reduce
the “atomic radius” of gold to 135 picometres
compared to 260 picometres for cęsium with its 55
protons and electrons—the gold atom is almost 50% heavier, yet only a
little over half the size of cęsium. Only the most reactive
substances can tug gold's 6s1 electron out from
where it's hiding among the others, and hence not only the
colour of gold, but its immunity from tarnishing and corrosion
are consequences of special relativity.
What keeps that golden
twinkle bright?
Mass increase near
speed of light!
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This document is in the public domain.