Why is Mercury a Metal?

June 26, 2008

I’ve been working with a mercury pressure gauge these past few weeks, which has lead to the inevitable question: why is mercury, of all the metals, a liquid at room temperature? Instead of passing the buck or shrugging my shoulders, I decided to find out. It should be noted that this topic has been covered before and in better detail here and here.

The simple (and surprising answer) is that it’s all about relativity. As you may know, relativity tells us that as the velocity of an object increases, the mass increases by

Clearly, for small velocities, the mass increase will be insubstantial. That’s why you don’t notice such changes in the real world: if you go out for a run, you don’t expect your mass to increase (that would totally be negate the point!). But for very fast things, this relativistic effect can be substantial.

Atoms are such ‘fast things.’ The average radial velocity of a 1s electron for a given atom is

Where Z is the atomic number (basically, the number of protons). So, if you get out your handy dandy periodic table and look up mercury, you’ll see that it has an atomic number of 80. Plug that into the above equation and you end up traveling at 58.4% the speed of light. That’s pretty fast, and you’ll start to notice some effects. Such as the fact that the relativistic mass of the electron is 1.27 times larger than the rest mass. Now take Bohr’s equation for the radius of a hydrogen atom (which is analogous to finding radius of the 1s orbital of any atom)

The only part we’re concerned with here is the me, the mass of the electron. As you can see, because the mass is in the denominator, increasing the mass will decrease the radius. So you have a substantial contraction of the 1s orbital. Because all the s orbitals must be orthogonal (you’ll have to take quantum chem to learn the reasoning behind that one), the 2s, 3s, …, 6s orbitals also contract. So, the bonding orbital of Hg, the 6s orbital, is much smaller than would be classically expected, and therefore less available for bonding. Add to that the fact that the orbital is completely filled, and Hg doesn’t have much of a reason to be making bonds at all. Therefore, the major forces holding the Hg together are van der Waals forces (the result of the dynamic polarization of atoms and the concurrent electric attraction). These forces are exceedingly weak. Weak force yields weak bonds yields lower heat of fusion yields liquid mercury.

Who would have thought that such a simple question could yield such deep science? I know I wouldn’t have.

But NOW YOU KNOW!

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One Response to “Why is Mercury a Metal?”

  1. dave in the west said

    oh snap. this might just be enough to inspire me to look into this again. Damnit Dave!!!

    Pretty interesting stuff. I always did find the structure/physics of the atom to be interesting. Keep on keepin.

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