- #1

Opus_723

- 178

- 3

## Homework Statement

This isn't an assigned problem, but it's the on conceptual question in the chapter that's bugging me, regarding the Compton effect.

In the Compton Effect...(other questions)...The incoming photon's wavelength [itex]\lambda[/itex] is assumed to be known. The unknowns after the collision are the outgoing photon's wavelength and direction, [itex]\lambda'[/itex] and [itex]\theta[/itex], and the speed and direction of the electron, u[itex]_{e}[/itex] and [itex]\phi[/itex]. With only three equations- two components of momentum conservation and one of energy- we can't find all four. Equation (3-8) [Given in the book, see below] gives [itex]\lambda'[/itex]

*in terms of [itex]\theta[/itex]*. Our lack of knowledge of [itex]\theta[/itex]

*after*the collision (without and experiment) is directly related to a lock of knowledge of something

*before*the collision. What is it? (Imagine the two objects as hard spheres).

## Homework Equations

(3-8)

[itex]\lambda'[/itex]-[itex]\lambda[/itex] = [itex]\frac{h}{m_{e}c}[/itex](1-cos([itex]\theta[/itex])

## The Attempt at a Solution

When you have two hard spheres colliding, the angle is determined by whether it's a head-on collision or a glancing blow. Basically, they're not

*quite*lined up the way we usually treat them mathematically (point masses on the x-axis). Or, you could have objects that aren't spheres, in which case the deflection angle is determined by their geometry (imagine a collision between a sphere and a triangle). It could get even more complicated if the spheres were spinning. So maybe angular momentum plays a role?

None of these ideas seems helpful though. I can't think of what the "internal geometry" of a photon would be. Angular momentum... maybe, but I wouldn't know the first thing about what that would even mean in this case. Probably stretching the analogy too far.

The only other idea I had wasn't connected to the spheres analogy at all. It just occurred to me, that, if we treated the incoming light as a wave, the only property we haven't talked about is the phase of the wave at the point and moment of the collision. Now, I have no idea how that would translate to a photon, or if it's even meaningful for a photon. But it seems to be the only thing you could really change or measure in any way.

Mostly, I'm clueless.