Compton scattering and momentum

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Discussion Overview

The discussion revolves around the problem of determining the directions of a photon and an electron after a collision, specifically in the context of Compton scattering. Participants explore the implications of known momentum values before and after the collision, as well as the conservation laws applicable to the scenario.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions whether it is possible to determine the directions of the electron and photon after the collision given certain momentum values.
  • Another participant asserts that knowing the momentum after the collision implies knowledge of their directions, as momentum is a vector quantity.
  • A different viewpoint suggests that only the absolute value of momentum after the collision is known, while the vector for the photon before the collision is available.
  • One participant argues that the problem is over-specified, indicating that there is too much initial information with only two unknown quantities, which complicates finding a solution.
  • Another participant proposes that knowing the momentum of the electron allows for the calculation of its kinetic energy, which can then be used to infer the energy and direction of the scattered photon.
  • There is a clarification that if the momentum of the scattered photon is known, its energy can be determined, which could help find the direction of the electron.
  • One participant highlights the importance of knowing the momentum or energy of the incoming photon to solve for the unknowns in the conservation equations.
  • Another participant acknowledges a missed detail regarding the initial conditions and confirms that the information provided is sufficient to solve the problem, provided the values are consistent with energy conservation.

Areas of Agreement / Disagreement

Participants express differing views on the sufficiency of the given information to determine the directions of the particles after the collision. While some believe the available momentum data is adequate, others highlight potential inconsistencies and the need for additional information.

Contextual Notes

Participants note that the problem involves multiple unknowns and equations related to momentum and energy conservation, which may not yield a unique solution without careful consideration of the initial conditions.

johann1301
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If a photon collides with an electron not moving, and you know the momentum of the photon before and after, and the electrons momentum, is it possible to know the direction of the electron and the photon after the collision?
 
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If you know the momentum of the electron and the photon _after_ the collision, then by definition you know their directions!

Momentum is a vector quantity!
 
You only know only the absolute value of the momentum after the collision. You know the vector of the photon before.
 
In general, your situation has no solution because it is over-specified: too much initial information, with only two unknown quantities.

[added later: see my next post below]

All of the momentum vectors lie in a plane, therefore we need to use only two components of momentum, e.g. x and y. We have three equations for conservation of x-momentum, y-momentum, and energy. In order to guarantee a solution, we need three unknown quantities.
 
Last edited:
If we know the momentum of e we know the Ke of e, and then we you know, by difference, the energy Es of the scattered photon ps.
If we know Es then we know the direction of ps and from this we can get the direction of e,
isn't it so?
 
bobie said:
If we know the momentum of e we know the Ke of e, and then we you know, by difference, the energy Es of the scattered photon ps.

He already knows (is given) the momentum of the scattered photon, therefore he already knows its energy.

I just now noticed that he didn't say that he knows the momentum (or energy) of the incoming photon. If indeed he doesn't know that, then that is his third unknown quantity, and he can solve the momentum and energy conservation equations to find:

  • the momentum (and energy) of the incoming photon
  • the direction (angle) of the outgoing photon
  • the direction (angle) of the outgoing electron
 
johann1301 said:
If a photon collides with an electron not moving, and you know the momentum of the photon before and after, and the electrons momentum, is it possible to know the direction of the electron and the photon after the collision?
jtbell said:
I just now noticed that he didn't say that he knows the momentum (or energy) of the incoming photon
It's complementary, jitbell, I missed the second bit and you the first.
The information he has is more than enough
 
Oops, I missed the "before." Yes, he can use your procedure, provided that the three values of momentum are indeed consistent with conservation of energy (which he should confirm, as a first step).

If you give three "random" values for the momenta, in general they won't work because energy won't be conserved.
 

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