I was wondering about something I was reading concerning light and its effect on electrons, and I was wondering during compton's effect how fast (not adding friction or other factors) will an electron move after being hit with a high energy photon wave?
E = mcc (c squared, of course). The c, the speed of light, is constant. So does greater mass produce greater speed? This sounds too simple. Actually, greater mass may create sluggishness. The energy probably is expressed in vectors, which, for starters, have magnitude and direction to take into account. Didn't Einstein equate speed with gravity, or am I really confused?
quote:Because the photons have such high energy, the interaction results in the electron being given enough energy to be completely ejected from its atom, and a photon containing the remaining energy being emitted in a different direction from the original, so that the overall momentum of the system is conserved. If the photon still has enough energy, the process may be repeated. Because of the overall reduction in energy of the photon, there is a corresponding increase in its wavelength. Thus overall there is a slight 'reddening' and scattering of the photons as they pass through the material. This scattering is known as Compton Scattering. In a material where there are free electrons, this effect will occur at all photon energies and hence all wavelengths.
From what I gather, the speed will not change because the increase in energy in one direction is offset by an increase in energy in another direction. In other words, if two electrons are hit by a photon wave, the electrons will be scattered and the net energy of the two electrons will balance each other to maintain the original speed.
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Sorry I didn't reply earlier, but it's been a while since I learned about the Compton effect and wanted to reply with a book in front of me.
p is the initial momentum of the photon p' is the momentum of the scattered photon pe is the momentum of the electron Θ is the angle (relative to the incident photon's path) of the scattered photon. Φ is the angle (relative to the incident photon's path) of the scattered electron.
p = p' cos Θ + pe cos Φ p' sin Θ = pe sin Φ
As you can see, the momentum (and therefore the velocity because p=mv, where m is mass and v is velocity) of the electon will vary with the angles at which it and the photon scatter. So, there is no single speed for all the electrons involved when you have a wave of photons and a collection of electrons. The speeds are very fast, close to the speed of light.
Serway, Moses, and Moyer's Modern Physics, 2nd Edition, page 82, for both the equations and the typical speeds.
"Because the electron typically recoils at speeds close to the speed of light, we must treat the collision relativistically."
What exactly "close to" is, they don't say, but I would imagine this means greater than 42,000,000 meters per second. Anything slower than this would produce a relativistic change of less than 1%.
