Metals, X-rays, and plasma frequency

pervect

I was wondering if it would be fair to say that the frequency at which x-rays start to penetrate a metal would be the plasma frequency associated with the electron density of the metal, i.e. the frequency given by

http://scienceworld.wolfram.com/phys...Frequency.html

or whether some other mechanism was involved.

Tide

Have you tried calculating the electron plasma frequency for some typical metals?

inha

you wouldn't be correct. plasmon energies are several orders of magnitude lower than the x-ray range.

pervect

Using the MKS formula at

http://www.everything2.com/index.pl?node_id=1529021

and using N = 8.47 * 10^28 / m^3 for copper

http://hyperphysics.phy-astr.gsu.edu.../fermi.html#c2

I am currently getting 2.6*10^15 hz

This seems to probably be a bit low, in the UV range. But I don't know what the effective mass of an electron in copper should be, nor do I know what the permittivity value should be - they probably shouldn't be the free-space values I used for both.

I also don't really know when copper starts transmitting x-rays, for that matter :-(.

pervect

What's a plasmon?

It looks like the estimate in terms of plasma frequency misses the mark by a few orders of magnitude from remarks that have been made - any ideas of how can it be "fixed up" to get within, say, one order of magnitude?

inha

plasmons are charge density fluctuations (collective excitations) in metals. same stuff but treated quantum mechanically taking the proper electronic structure into account. I don't think you can get much closer since in a lot of metals the electron effective masses aren't too far from the bare electron mass.

Gokul43201

If you are trying to calculate the frequency at which a metal starts to become transparent to radiation, that would be the plasma frequency. Most metals are transparent at high UV frequencies.

So, to correct the statement in your OP :
...it would be fair to say that the frequency at which EM radiation starts to penetrate a metal would be the plasma frequency associated with the electron density of the metal...

pervect

OK, that answers the question, thanks. And it nicely explains why the semiconductor people have trouble building UV mirrors, too.