# Electrons through quartz

1. Jun 25, 2008

### gareth

I'm wondering can electrons travel through quartz at any great distance.

I'm assuming since quartz is an insulator they will not be able travel any apreciable distance within the material.

Say if we got some extremely high energy electrons and fired them at a quartz slide, would any of them penetrate the slide.

My gut feeling is no, unless you're dealing with rediculously high energy electrons or a very thin plate of quartz.

Any thoughts?

2. Jun 25, 2008

### ZapperZ

Staff Emeritus
First of all, electrons tend to have a larger penetration depth through an insulator than they do through metals. This is because since metals have a larger density of free electrons, the electron-electron collision tends to be energy-absorbing. This is compared to electron-ion collision that predominantly occurs in insulators, in which the electron regains almost all of its original energy.

Secondly, yes, electrons can penetrate quartz through over a certain length, or even ordinary glass, for that matter (why just quartz?). It is very energy-dependent. For electrons with energy less than, say 5 keV, the penetration is of the order of microns. But if you have electrons with energy of a few MeV, it can be of the order of millimeters.

Zz.

3. Jun 26, 2008

### gareth

Thanks ZapperZ,

Could ou recommend a text, or maybe just tell me the equation, of the relationship between penetration depth of an electron and the energy?

I assume it will be similar to the equation describing the penetration depth of light into a material, but with a very shorter wavelength for the electron.

Gareth

4. Jun 26, 2008

### ZapperZ

Staff Emeritus
This isn't that trivial, since it can be model dependent. For example, there are models in which you have to do a Monte Carlo analysis to obtain the penetration depth, rather than settling for an analytical expression.

Having said that, there are models such as the Kanaya-Okayama[1] range relations that provide an almost phenomenological model for the dependence of the electron penetration depth as a function of several parameters, including the incident energy.

$$\lambda = \frac{0.0276AE^{1.67}}{Z^{0.89}d}$$

where $\lambda$ is the penetration depth, A is the atomic mass, E is the incident energy, Z is the average atomic number of the solid, and d density of the material.

Zz.

[1] K. Kanaya and S. Okayama, J. Phys. D v.5, p.43 (1972).

5. Jun 26, 2008

### gareth

I tried a few rough calculations but I'm definately missing something fundamental here;

Electrons have mass, so they can't go faster than c, so the maximum kinetic energy as calculated from 0.5mv^2 is around 0.26MeV. Surely this isn't the absolute limit for an electron. I could have sworn I saw papers qouting higher values than this.

What am I missing?

6. Jun 26, 2008

### ZapperZ

Staff Emeritus
This is now a different question. You need to look at relativistic energy calculation, and why 1/2 mv^2 doesn't work as v approaches c.

Zz.