Bulk gold has a very characteristic warm yellow shine to it, whereas almost all other metals have a grey or silvery color. Where does this come from?

I have heard that this property arises from relativistic effects, and I assume that it has to do with some distinct electronic transition energies in the gold atoms. But what changes with the "introduction" of relativistic effects, that then changes the energy of the frontier orbitals in such a drastic manner?

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    $\begingroup$ See also this related Physics.SE question (and answers): physics.stackexchange.com/questions/72368/… $\endgroup$ – Geoff Hutchison Sep 23 '14 at 16:03
  • $\begingroup$ Do you know, by the way, that not all orbitals are contracted due to relativistic effects? It is known that relativity contracts $s$ and most of $p$ orbitals and either contracts or expands orbitals of higher $l$ quantum number. $\endgroup$ – Wildcat Sep 24 '14 at 13:18
  • $\begingroup$ I heard somewhere (Science Channel, to be specific) that gold on an atomic level is actually pink. How does increasing the number of gold atoms make it golden? $\endgroup$ – Jason Chen Feb 25 '16 at 6:52
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    $\begingroup$ Wildcat, there are different levels of understanding of any topic. The ability to study and follow, for the most part, an answer like the one accepted is one level. The ability to then give a proper and thorough answer to your question in 600 characters or fewer, is quite a different level of understanding. This may be long-gone water under an ancient bridge at this point but I felt I had throw out my thoughts anyway. $\endgroup$ – airhuff Jan 19 '17 at 4:36
  • $\begingroup$ You could more information from fourmilab.ch/documents/golden_glow. $\endgroup$ – DARYL JOSEPH.G Apr 8 '17 at 3:22

Yes, this is a beautiful question.

As you said, in lower rows of the periodic table, there are relativistic effects for the electrons. That is, for core electrons in gold, the electrons are traveling at a significant fraction of the speed of light (e.g., ~58% for Au $\ce{1s}$ electrons). This contracts the Bohr radius of the 1s electrons by ~22%. Source: Wikipedia

This also contracts the size of other orbitals, including the $\ce{6s}$.

The absorption you see is a $\ce{5d->6s}$ transition. For the silver $\ce{4d->5s}$ transition, the absorption is in the UV region, but the contraction gives gold a blue absorption (i.e., less blue is reflected). Our eyes thus see a yellow color reflected.

There's a very readable article by Pekka Pyykkö and Jean Paul Desclaux that goes into more detail (if you subscribe to ACS Acc. Chem.Res.)

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    $\begingroup$ @GeoffHutchison I wish you could answer this in a way I can understand. I have a more general question of "why are some wavelengths reflects while others absorbed?" yet with all your voodoo terms and stuff I'm not even sure what's being said. $\endgroup$ – Griffin Sep 24 '14 at 13:14
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    $\begingroup$ @Griffin feel free to post other questions separately. They are hard to answer in comments. $\endgroup$ – Geoff Hutchison Sep 24 '14 at 14:04
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    $\begingroup$ I fear it too closely resembles this question. $\endgroup$ – Griffin Sep 24 '14 at 18:49
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    $\begingroup$ Adding to Geoff's source, I very much like this recent paper from Pyykkö with some updated data. $\endgroup$ – Nicolau Saker Neto Sep 28 '14 at 13:52
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    $\begingroup$ Even if there's a distribution of possible momenta (or velocities), that distribution still has an expectation value, which can be evaluated using quantum chemical methods. So yes, we can evaluate expected velocities (see @ron's answer) and we can compare this observable to various measurements. $\endgroup$ – Geoff Hutchison Apr 13 '16 at 14:25

See the footnotes I've included if you would like to see more of the detail behind a specific statement.

The figure below compares the reflectance spectrum for silver and gold (let's forget about aluminum, it's not relevant to this discussion; also keep in mind that where reflectance is low, absorbance is high and vice-versa).

enter image description here

The absorption (reduced reflectance) seen at lower wavelengths by silver and gold is caused by an electron transition (caused by the absorption of light) between their 4d -> 5s and 5d -> 6s orbitals respectively. Silver absorbs (reflects less) in the ultraviolet, no visible light is appreciably absorbed. Therefore, if we shine white light on silver, none of the visible wavelengths are absorbed, they are all reflected and silver appears as a shiny, white metallic substance. In fact, jewelers say that silver is the whitest of the metals. On the other hand, gold absorbs (reflects less) blue light in the visible region. When white light shines on gold, the blue light is absorbed and yellow light is reflected (see this article on complementary colors for more detail on how removing certain colors from white light produces different colors). So our question becomes, why is gold's 5d -> 6s electronic transition shifted into the visible region?

S electrons are strongly attracted to the nucleus because their probability density is higher near the nucleus than other types of orbitals (p, d, f, etc.). Simple Bohr theory tells us that these strongly attracted s electrons in atoms with a large number of protons (heavy nuclei) would have to travel at a considerable fraction of the speed of light to avoid "falling into" the nucleus (1). Special relativity takes things a step further and explains that, for these heavy nuclei with their s electrons traveling over half the speed of light, the electron mass will increase and as mass increases (2), orbital radius decreases (3).

Further, as the orbital radius decreases and the electron is closer to the nucleus it becomes more stabilized and the energy of the orbital decreases. As the various s electrons (and to a lesser degree p electrons, but d and f electrons don't have enough electron density close to the nucleus so they are not directly affected by these relativistic effects and their orbits are not contracted) move closer to the nucleus, the other non-s (or p) electrons are better screened from the nucleus. So although the various s orbitals are contracted and placed at lower energy, the various d and f orbital radii shift further out and occur at higher energy due to this increased screening effect.

Hence, in the gold atom, we would expect the 5d orbital to be raised in energy (screening effect) and the 6s orbital to be lowered in energy (relativistic orbital contraction effect). The net effect is a smaller energy separation between these two orbitals and a red-shift in the 5d -> 6s absorption to the lower energy (compared to the absorption of silver which is not subject to the same magnitude of relativistic effects) blue region of the spectrum, resulting in a yellowish color for light reflected from gold.

(1) The ratio of the speed of an electron traveling in the first Bohr orbit to the speed of light is given by the handy equation

$$v_\mathrm{rel} = \frac{Z}{137}$$

where $Z$ is the atomic number of the element under consideration and 137 is the speed of light in atomic units, also known as the fine structure constant. Consequently a 1s electron in silver ($Z=47$) will travel around $47/137 = 34\%$ the speed of light, while a similar electron in gold ($Z=79$) will travel at $58\%$ the speed of light.

(2) The relativistic mass of an electron is given by

$$m_\mathrm{rel} = \frac{m_\mathrm{e}}{\sqrt{1-(v_\mathrm{rel}/c)^2}}$$

where $m_\mathrm{e}$, $v_\mathrm{rel}$ and $c$ are the electron rest mass, the velocity of the electron, and the vacuum speed of light respectively. The following figure provides a graphical representation of the result.

enter image description here

(3) The following equation relates the ratio of the relativistic radius of the first Bohr orbit $R_\mathrm{rel}$ to the normal radius $R_0$, to the relativistic velocity of the electron

$$\frac{R_\mathrm{rel}}{R_0} = \sqrt{1-\left(\frac{v_\mathrm{rel}}{c}\right)^2}$$

As the relativistic velocity of the electron increases, the orbital radius contracts (the above ratio becomes smaller). For silver, the first Bohr radius contracts ~6%, while for gold the contraction is ~ 18%.

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    $\begingroup$ If the effect only relies on the atomic number of the nucleus, how come it is not observed for lead, thallium or mercury? $\endgroup$ – tschoppi Sep 23 '14 at 13:58
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    $\begingroup$ I know that the effect does manifest itself for mercury, but in other ways. See, "Why does Mercury have low melting and boiling points?". I suspect that other heavy atoms show the effect in some way as well. Since the electron configuration of mercury, lead and thallium is different from that of gold, the 5d-6s transition may no longer be the "operative" absorption. $\endgroup$ – ron Sep 23 '14 at 14:07
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    $\begingroup$ In particular, mercury, lead, thallium, etc. don't have partially filled 6s orbitals. So a 5d-6s transition is impossible. As @ron said, the relativistic effects show up in different ways (e.g., liquid mercury, low melting lead, inert pair, etc.) $\endgroup$ – Geoff Hutchison Sep 23 '14 at 14:10
  • $\begingroup$ Is this difference in Ag and Au due to lanthanoid contraction? $\endgroup$ – John Feb 19 at 20:51

This effect comes from the band structure of the metal, not atoms. In simplest terms (see, e.g. Ashcroft & Mermin, Solid State Physics, chapter 1) the electrons in the conduction band have a plasma frequency $\omega_{p}^{2} = 4\pi n e^{2}/m$ - this is a collective excitation of the metal. For Cu (reddish) you start exciting the plasmons around 2eV (red), while for Ag you don't hit it until 4eV (near UV). Au is a bit higher than Cu, but still in the visible.

If you want an excellent mirror across the visible, you need to use Ag, not Au - Au will absorb the blue.

EDIT - additional information.

Coming from a solid state background, I'll add some more on band theory. Again, following Ashcroft and Mermin's discussion of noble metals (Chapter 15):

In the case of copper (and the other noble metals) at least six bands are required (and six turn out to be enough) to accommodate the eleven additional electrons. ... For almost all waver vectors k the six bands can be seen to separate into five lying in a relatively narrow range of energies from about 2 to 5 eV below E_F, and a sixth, with an energy anywhere from about 7eV to 9eV below E_F. ... It is conventional to refer to the set of five narrow bands as the d-bands, and the remaining set of levels as the s-band. However, these designations must be used cautiously, since at some values of k all size leves are close together and the distinction between d-band and s-band levels is not meaningful. The nomenclature reflects the fact that at wave vectors where the levels do clearly group into sets of five and one, the five are derived from the five orbital atomic d-levels, in the sens of tight binding...

So it is tempting to jump on the d-band desciption and say, hey, since there are relativistic effects in Au, than that must carry over into the band structure. I'm really not convinced. Yes, while the levels may well derive from d-levels of the atom, that does not mean that the resulting band structure is or is not different from a non-relativistically impacted band structure. As an example, look at the Fermi surfaces of Cu, Ag, and Au as plotted in Ashcroft and Mermin (Fig. 15-5) - they are all free-electron like, except that contact is made along <111> directions. It is very difficult to differentiate the Fermi surfaces of Cu and Au, while Ag is different (actually more free-electron like). This shows up in the table of Belly-to-Neck areas of the Fermi surface (from De Haas-van Alphen oscillations), where Cu=27, Au=29, and Ag=51.

When you overlap the orbitals to make bands, all that matters is their relative placement with respect to the Fermi energy. In the big picture, Cu, Ag, and Au are all very similar - it is just that our eyes are sensitive to just the small energy region where their plasma frequencies differ, so we see a big difference.

If you are going to ascribe Au's golden color to relativistic effects on the orbitals, than I'm going to have to ask how Cu has such a similar band structure without the relativistic effects.

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    $\begingroup$ While you accurately describe the how, the why part is kind of lacking at the moment. I do not want to deter you, and I like the way the answers are diverse. But I feel you have not addressed the underlying reason. $\endgroup$ – tschoppi Sep 23 '14 at 13:56
  • $\begingroup$ Copper, silver and gold all have $\ce{d->s}$ transitions (yes, in the band structure). Copper has a $\ce{3d->4s}$ transition, which is also in the visible - based on the poor shielding of the $\ce{3d}$ electrons. So yes, if we're comparing silver to gold, the appearance is definitely relativistic, and you can look through the linked paper above for more science. $\endgroup$ – Geoff Hutchison Sep 23 '14 at 16:09
  • $\begingroup$ I'm happy to hear the physics perspective, but yes, the relativistic effects in Au do carry over into the band structure. For example, if you do DFT band structure calculations with Au, you must use relativistic core potentials. $\endgroup$ – Geoff Hutchison Sep 23 '14 at 16:10
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    $\begingroup$ @GeoffHutchison - I think we come at it from different perspectives. While, no doubt, the wave functions of Au are influenced by relativistic effects, and in DFT or tight binding you need to use an appropriate relativistic-corrected potential, the fact remains that the end result of the band structure calculation looks remarkably like that of the other noble metals. A band structure calculation using improper orbitals will, of course, not result in the actual bands. But, the actual band structure may not owe a lot in general form and function to whether there are relativistic effects at play. $\endgroup$ – Jon Custer Sep 23 '14 at 16:20
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    $\begingroup$ @JawadAlShaikh - the plasma frequency is above the visible (for humans), so Ag does a good job of reflecting at high efficiency across the entire visible spectrum so what is reflected is pretty much what hits the mirror in terms of color balance. Consider a mirror made of silver vs one made of gold (or copper). $\endgroup$ – Jon Custer Oct 20 '17 at 17:08

protected by orthocresol May 17 '17 at 17:38

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