h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

The nature of the Fine Structure Constant and the dynamics of the hydrogen atom, including the absorption spectra and the mechanism which underlies the discrete energy levels, can be fully explained using classical mechanics based on one simple postulate:-

If velocity itself is assumed to be affected by relativity in relation to phenomena involving interactions between an orbiting object and a stationary observer, such as for example centrifugal force and angular momentum, a model for the hydrogen atom emerges.

Sounds interesting. Is this anything to do with Randell Mill's Classical Quantum mechanics?

Not really. - For one thing, based on the postulate that I outlined, the radius of the atom is not the Bohr radius, but is smaller by a factor of Alpha. This works out to be the Compton radius divide by two pi or 3.86159*10^-13.

The radius remains constant for all energy levels of the atom. This has important implications because it means that energy levels are accompanied by a change in velocity, not in position as is required by Quantum theory.

Such discontinuities of position, albeit shrouded in terms of probability density functions, are central to quantum theory and are cited as an example of quantum wierdness. There is nothing weird about the energy levels changing due to changes in velocity.

So how do you account for the indisputable fact that heavy atoms are much bigger than light atoms?

I don't - I am only concerned at this stage with the hydrogen atom and in particular the size of the hydrogen atom at different levels of excitation.

There is some anecdotal evidence that the size does not vary with the excitation level of the orbiting electron. If it did - as is suggested by both the Bohr and Schroedinger models, then it is reasonable to expect that the rate at which hydrogen permeates through a membrane, such as the skin of a balloon or the walls of a pressure vessel would be lower if the excitation levels were higher.

If this was the case then the leakage rate could be reduced by raising the excitation level of the atoms using say a UV lamp. I do not believe that this happens, strongly suggesting that the radius and hence the size ot the hydrogen atom remains constant for all excitation levels.

The trouble is, is that despite your saying that you are only concerned with the excited levels of the hydrogen atom, that these *must* become occupied as we traverse the periodic table. This is regardless of whether the velocity or the orbital size increases. Trouble is, as you do this, the atoms get bigger. By your reckoning, with increased charge on the nucleus, we'd expect them to get smaller.

Actually not - they stay the same - as the orbital velocity of the electron approaches the speed of light the radius of the orbit is asymptotic to the value 3.86159*10^-13.

As I said I have only considered hydrogen in detail, but I think what may be happening with atoms of higher mass is that as each such orbital path is filled additional electrons they are forced into a different orbital path of the same radius but in a different plane.

If this were the case, the density of metals would be directly proportional to the atomic number. Which they aren't. This doesn't reflect reality in any meaningful way. And reality is registering loud and clear on my radar here.

I am not sure that I follow your reasoning here.

Well, of the orbit size doesn't increase, atoms would remain the same size regardless of atomic number. They don't do this. If they remained the same size, emtails would have the same internuclear distance and similar atomic packings of different metals would have a fixed ratio of density to atomic number. This isn't the case.

'emtails'??

'metals', I mean

I don’t think we know the physical dimensions of any atoms. Unfortunately we have no tools for directly measuring the size of an atom so we can only infer physical size from observing the way that atoms interact and this will vary with their structure.

It is not clear that the internuclear distance is a function of the physical size - it could equally be related to the strength of the electrical interaction between the atoms.

However within any one type of atom the structure does not vary. This means that there exists the possibility to determine whether the size varies with excitation level.

Yes we do, and yes we have. The tool is called a Scanning Tunnelling Microscope. And its very good at imaging atomic orbitals.

I do not think that STM directly images the structure and therefore the physical size of the atom.

If the strength of the interactions between atoms and not the physical size determines such things as the internuclear distance then it could equally be imaging this apparent size.

The internuclear distance is determined by the point at which the repulsion of the electron clouds balances the bonding strength. Atoms are not billard balls, they are squashy things like overripe tomatoes, and their size will vary depending upon the conditions they find themselves in. To all intents and purposes, the internuclear distance is as good a measure of the atomic size as we are ever likely to find.

BTW: STM images the density of states per unit volume at any point on a solid surface. This will vary, but when it varies in a 2-dimensional lattice structure then I think it's perfectly reasonable to assume it's the underlying atoms that cause this variation, don't you?

I don't disagree with that, but the question then is what property of the atom is it that is being imaged. It probably bears a relationship to the physical size, but it is almost certainly also a function of other factors such as the charge distribution and structure.

In any event - back to hydrogen. I can find no evidence that the size of the atom varies with energy level. This is consistent with the theory that its radius is constant, which is an inevitable consequence of the postulate that certain velocity terms are relativistic.

The Fine Structure Constant is then the ratio of this relativistic velocity to the actual velocity which latter then turns out to be 99.997337% of c for the lowest energy level.