Metals, X-rays, and plasma frequency

In summary, plasmon frequencies are orders of magnitude lower than x-ray frequencies, so the plasma frequency given by the MKS equation for copper is too low. The effective mass of an electron in copper should be higher, and the permittivity value should be lower, in order for copper to be transparent to EM radiation at high UV frequencies.
  • #1
pervect
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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.
 
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  • #2
Have you tried calculating the electron plasma frequency for some typical metals?
 
  • #3
you wouldn't be correct. plasmon energies are several orders of magnitude lower than the x-ray range.
 
Last edited:
  • #4
Tide said:
Have you tried calculating the electron plasma frequency for some typical metals?

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

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

1. What are metals and how do they differ from other elements?

Metals are a type of element on the periodic table that are characterized by their high electrical and thermal conductivity, luster, and malleability. They are different from other elements because they have a high number of free electrons, which allows them to easily conduct electricity and heat.

2. What are X-rays and how are they used in science and medicine?

X-rays are a type of electromagnetic radiation that have a shorter wavelength and higher energy than visible light. In science, they are used for imaging techniques such as X-ray crystallography to determine the structure of molecules. In medicine, they are used for diagnostic imaging to see inside the body and diagnose medical conditions.

3. What is the plasma frequency and how does it affect the behavior of metals?

The plasma frequency is the frequency at which electrons in a metal oscillate in response to an applied electric field. This frequency is unique for each metal and is affected by factors such as temperature and density. The behavior of metals is influenced by the plasma frequency, as it determines how easily electrons can move through the metal and how it interacts with light.

4. How are X-rays used to study the properties of metals?

X-rays are commonly used in materials science to study the properties of metals. They can be used for techniques such as X-ray diffraction, which can reveal information about the crystal structure of a metal, and X-ray fluorescence, which can determine the elemental composition of a metal. X-ray absorption spectroscopy is also commonly used to analyze the electronic structure of metals.

5. What are some potential applications of plasma frequency research?

Research on plasma frequency has many potential applications, including in the development of new materials with improved properties, such as increased conductivity or better light absorption. It can also be used in the design of electronic devices, as well as in the study of plasma physics and astrophysics.

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