# Metals, X-rays, and plasma frequency

1. Apr 15, 2006

### pervect

Staff Emeritus
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/physics/PlasmaFrequency.html

or whether some other mechanism was involved.

2. Apr 17, 2006

### Tide

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

3. Apr 17, 2006

### inha

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

Last edited: Apr 17, 2006
4. Apr 17, 2006

### pervect

Staff Emeritus
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/HBASE/tables/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 :-(.

5. Apr 17, 2006

### pervect

Staff Emeritus
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?

6. Apr 17, 2006

### 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.

7. Apr 17, 2006

### Gokul43201

Staff Emeritus
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...

8. Apr 18, 2006

### pervect

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