Relativity is Golden, but how?

[peter grimes]

OK, I've heard a few times that special relativity explains why Au has such a unique color and anti-tarnishing properties compared with similar metals in the periodic table.

Last night I read through this piece on it:
https://www.fourmilab.ch/documents/golden_glow/

[snip]
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.
[snip]
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.
[snip]

But there are some things I don't understand.

1. If the relativistic contraction of the s orbital causes the electron to speed up, shouldn't the relativistic addition of mass increase the distance from the nucleus, not decrease it? Or am I misapplying the idea of the conservation of angular momentum here?

2. Am I understanding that the protonic mass of the nucleus is what's causing the acceleration of the electrons? Why don't other larger atoms do this as well? The article mentions 4 other heavier stable metals, but why don't these experience the same relativistic effects? Does it have to do with the density or distribution of the protons vs. neutrons?

3. If the outer valence is difficult to interact with, how does gold make a solid to begin with? Shouldn't each Au atom's electron clouds be repulsing eachother, precluding formation of molecules? How can you get so many gold atoms to cling together long enough to make a gold bar? How can alloys be formed using gold?

It's been 25 years since I took chemistry, so it's probably safest to assume I don't remember any of it

 

[dutchfire]

Ugh, atomic physics Hopefully uppi will be able to weigh in on this. One note though:

Relativistic mass as a concept is crap, you should not use it. I honestly haven't seen it used in any serious literature. One of the problems is that if you want to keep some Force=Mass*Acceleration equation, then you need to introduce different masses acceleration along the direction of motion and orthogonal to it.
Instead, Einstein's equation is usually written as E=gamma mc^2, with gamma = 1/sqrt(1-v^2/c^2). So things that are going faster have a higher gamma factor, increasing their energy.

 

[uppi]

OK, I've heard a few times that special relativity explains why Au has such a unique color and anti-tarnishing properties compared with similar metals in the periodic table.

Last night I read through this piece on it:
https://www.fourmilab.ch/documents/golden_glow/

But there are some things I don't understand.

1. If the relativistic contraction of the s orbital causes the electron to speed up, shouldn't the relativistic addition of mass increase the distance from the nucleus, not decrease it? Or am I misapplying the idea of the conservation of angular momentum here?

The classical argument would go like this:
L = m * r x v
where L is the total angular momentum, r is the radius, m is the mass and v the speeed (x denotes the cross product).
So if L is supposed to be constant and the mass gets larger, the radius (or the speed) has to decrease to maintain L.

However, the 6s state has no orbital angular momentum at all, so the argument falls flat on its face. (Incidentally, the lack orbital angular momentum of the s-states is the main reason why the Bohr model can't be right). Trying to explain the shift of the 6s state by appealing to the Bohr model and conservation of angular momentum is very much a doomed effort.

You would have to use the Dirac theory (with QED corrections) to explain the shift of the 6s state. These are relativistic theories, so the statement is more or less correct, but the explanation is not.

2. Am I understanding that the protonic mass of the nucleus is what's causing the acceleration of the electrons? Why don't other larger atoms do this as well? The article mentions 4 other heavier stable metals, but why don't these experience the same relativistic effects? Does it have to do with the density or distribution of the protons vs. neutrons?

It is not the protonic mass, but the charge of the nucleus that is responsible for the attraction ("simple" electromagnetic attraction between a positive charge and a negative one). As the charge of every proton is the elementary charge, it is a simple conversion away from the protonic mass, though.

The number of neutrons have an effect on the spectrum but at the scales relevant here, this can be neglected. Different colors are separated by frequencies on the order of 100THz and different isotopes have shifts of GHz for the heavy ones.

The other atoms exhibit the same relativistic effects as well, but in their case it doesn't work out that the 5d states are close to the 6s state. You could say that it is coincidence that this happens for gold. If the shift was larger (which it is for heavier atoms), you would get different effects.

3. If the outer valence is difficult to interact with, how does gold make a solid to begin with? Shouldn't each Au atom's electron clouds be repulsing eachother, precluding formation of molecules? How can you get so many gold atoms to cling together long enough to make a gold bar? How can alloys be formed using gold?

The electron clouds do not repel each other, because as whole, gold atoms are neutral: The charge of the electrons cancels out the charge of the nucleus.

The arguments for the inertness of gold only apply to ionic bonding: Bonds where an electron is given up by one atom to join the other. Gold crystals and alloys are held together by metallic bonding, where the electrons are shared by (in principle) all the atoms. So there is no "tugging out" here and the argument does not apply.