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Relativity sounds like physics for spaceships and black holes, not chemistry. But inside heavy atoms, electrons move so fast that Einstein’s theory of special relativity measurably changes their behaviour. The consequences are surprisingly familiar: gold is yellow instead of silvery, mercury is a liquid at room temperature, and your car’s lead–acid battery produces its voltage partly because of relativity. This article explains how relativity enters chemistry and what it does.
Why electrons in heavy atoms move so fast
In an atom, an electron’s typical speed increases with nuclear charge. For a 1s electron, the speed is roughly:
v ≈ Z × c ÷ 137
where Z is the atomic number and c is the speed of light.
- Hydrogen (Z = 1): v ≈ c/137, less than 1% of light speed. Relativity barely matters.
- Gold (Z = 79): v ≈ 79/137 ≈ 0.58c, well over half the speed of light.
- Mercury (Z = 80): v ≈ 0.58c.
At such speeds, relativistic effects become significant.
What relativity does to electrons
1. s orbitals (and p₁/₂) contract
According to special relativity, a particle’s effective mass increases as it moves faster. For a 1s electron in gold, the increase is about 20%. A heavier electron orbits closer to the nucleus, so the 1s orbital contracts.
Because all s orbitals of an atom must remain mathematically independent of one another (orthogonal), the contraction spreads outward: the outer s orbitals contract too, including the valence 6s orbital. They’re also stabilised (lowered in energy), so their electrons are held more tightly.
2. d and f orbitals expand
The contracted s and p orbitals shield the nucleus more effectively. The d and f orbitals, which don’t penetrate close to the nucleus, feel less nuclear attraction. They expand and rise in energy.
3. Spin–orbit coupling grows
Relativity also strengthens the interaction between an electron’s spin and its orbital motion, splitting some energy levels. This becomes very important for the heaviest elements.
These effects grow roughly with Z², so they’re small for light elements, noticeable for the fifth period, and large for the sixth period and beyond, peaking around gold.
Why gold is yellow
Silver and gold are in the same group, with similar outer configurations: silver [Kr] 4d¹⁰ 5s¹ and gold [Xe] 4f¹⁴ 5d¹⁰ 6s¹. Yet silver is silvery-white and gold is yellow.
Metals reflect light when electrons absorb and re-emit it. In silver, the gap between the filled 4d band and the partly filled 5s band corresponds to ultraviolet light, so all visible colours are reflected equally: silver looks white.
In gold, relativity lowers the 6s level and raises the 5d level, narrowing the gap. It now corresponds to about 2.4 eV, in the blue part of the spectrum. Gold absorbs some blue light and reflects the rest, which looks yellow.
Calculations show that without relativity, gold would look silvery like silver. See why is gold yellow?
Why gold is so unreactive
The contracted, stabilised 6s electron in gold is held unusually tightly:
- Gold’s first ionisation energy (890 kJ/mol) is much higher than silver’s (731 kJ/mol), even though gold’s atom is heavier.
- Gold has a surprisingly high electron affinity (about 223 kJ/mol) and can even form the auride ion, Au⁻, in caesium auride (CsAu), behaving somewhat like a halogen.
This helps explain why gold is one of the most noble (unreactive) metals, resisting corrosion for thousands of years. See most expensive elements.
Why mercury is a liquid
Mercury ([Xe] 4f¹⁴ 5d¹⁰ 6s²) has a filled 6s² subshell. Relativity contracts and stabilises the 6s orbital so much that the two 6s electrons are held very tightly and are reluctant to take part in metallic bonding between mercury atoms.
With weak bonding between atoms, mercury atoms behave a bit like those of a noble gas. Its melting point is −38.8 °C, making it the only metal that’s liquid at room temperature. Its neighbours in the same period, gold (1,064 °C) and thallium (304 °C), are solids.
Detailed calculations published in 2013 showed that without relativistic effects, mercury would melt at roughly 82 °C, like a typical soft metal. Relativity lowers its melting point by more than 100 °C. See lowest melting point element and liquid elements at room temperature.
The inert pair effect
In groups 13–15, the heavier elements often prefer an oxidation state two lower than the group’s maximum:
- Thallium prefers +1 over +3.
- Lead prefers +2 over +4.
- Bismuth prefers +3 over +5.
The pair of 6s electrons is stabilised and contracted by relativity, so it’s harder to remove or use in bonding: the “inert pair”. Lead(IV) compounds, such as lead(IV) oxide, are strong oxidising agents because lead readily returns to +2. See post-transition metals and how to predict the charge of an ion.
Relativity in your car battery
A lead–acid car battery works by reducing lead(IV) oxide to lead(II) sulfate while oxidising lead metal. A 2011 computational study found that of the roughly 2.1 volts produced by each cell, about 1.7 volts comes from relativistic effects, because relativity makes lead(IV) such a strong oxidising agent. The same calculations suggested that a similar battery made with tin (a lighter element in the same group) produces far less voltage, which is part of why tin-acid batteries aren’t used. In other words, cars start partly thanks to Einstein.
Other relativistic effects
- Platinum and gold catalysis: relativistic effects influence why these metals are such good catalysts for certain reactions.
- Thallium’s toxicity and chemistry are affected by the stability of Tl⁺.
- Tungsten and heavier elements show bond strengths and structures that non-relativistic calculations get wrong.
- Colours of heavy-metal compounds are often shifted.
Superheavy elements: will they still fit the table?
For the heaviest elements (Z above about 100), relativistic effects become so large that they may change their chemistry compared with lighter members of the same group:
- Copernicium (112), below mercury, is predicted to be even more noble and volatile, possibly behaving almost like a noble gas.
- Flerovium (114), below lead, may be surprisingly unreactive for the same reason.
- Oganesson (118), formally a noble gas, is predicted to be a solid at room temperature and possibly semiconducting.
Experiments on these elements are extremely difficult because only a few atoms can be made at a time, and they decay within seconds or less. See how new elements are made and heaviest element.
Key takeaways
- In heavy atoms, inner electrons move at a large fraction of the speed of light, so relativity matters.
- Relativity contracts and stabilises s orbitals and expands d and f orbitals.
- Gold’s yellow colour and nobility, and mercury’s low melting point, are largely relativistic effects.
- The inert pair effect in thallium, lead and bismuth comes from the relativistic stabilisation of 6s electrons.
- Relativity even contributes most of the voltage of a lead–acid battery, and may reshape the chemistry of superheavy elements.
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