# Consequences of proton size being smaller than thought to be?

1. Aug 6, 2010

### olee

Last edited by a moderator: Apr 25, 2017
2. Aug 6, 2010

### alxm

Well, we don't know for sure yet if that result is correct. But if we assume it is, the chemical effect? I can only assume you mean chemically, since this is the chemistry sub-board.

The answer to that is: No chemical consequences. It's too small an effect. Basically you don't need to take nuclear size into account whatsoever as far as chemistry is concerned. Usually it's treated as if it were infinitesimally small, and finite-size corrections are many orders of magnitude smaller than chemical energies. It's so small it couldn't even be measured accurately at all for an ordinary hydrogen atom. This result came from replacing the electron in helium with a muon.

For the physicists it's more interesting because there's a discrepancy between theory and experiment.

3. Aug 6, 2010

### olee

Thanks for the reply. The article says they used http://i38.tinypic.com/1zobuyq.png". Surely the proton size affects spectroscopy, does it not?
I'm interested in the fact that you mentioned that it's more interesting for physicists. I'm not debating, but I was wondering if you could explain why that is so.

Last edited by a moderator: Apr 25, 2017
4. Aug 6, 2010

### alxm

Right, meant to say hydrogen of course. Yes, it affects spectroscopy, but not enough that it can be measured, ordinarily. The measurement here is of the hydrogen Lamb shift, a very slight shift between the 2s and 2p levels of the atom. Which is an effect of quantum electrodynamics (vacuum polarization). Calculating it theoretically requires using the charge-radius of the proton. The muon is 200x heavier than the electron, so it's 200x closer to the nucleus and the effect of nuclear structure in its Lamb shift is correspondingly magnified. Here, they found a discrepancy - either the calculations which worked for hydrogen didn't work anymore, or the size of the proton was different.

This interesting for the physicists because the Lamb shift is an important test-case for QED. If the experimental results hold, then something is wrong with the QED calculations of the Lamb shift, and while I wouldn't go so far as to assume something's wrong with QED itself, it might mean there's some as-of-yet-unknown effect they haven't been taking into account.

Chemically it's not interesting because when you talk about an energy of chemical interest, such as the heat of formation of a molecule (even a simple one such as H2), then the experimental accuracy is lower (say, 7 decimals for H2, as opposed to the 10-12 decimals for the Lamb shift), and theory matches experiment without having to take QED effects into account.

Last edited by a moderator: Apr 25, 2017