# - Compton Scattering - Electron Momentum

• phil ess
In summary, the problem involves an x-ray photon of initial energy 1x10^5 eV colliding with a free electron at rest and being scattered at right angles into the +y direction. The components of momentum of the recoiling electron can be found by using the Compton equation and conservation of energy. However, in this particular attempt at a solution, the assumption of the electron recoiling at 45 degrees leads to a violation of momentum conservation. Further analysis is needed to determine the correct recoil angle for the electron.
phil ess
URGENT - Compton Scattering - Electron Momentum

## Homework Statement

An x-ray photon of initial energy 1x10^5 eV traveling in the +x direction is incident on a free
electron at rest. The photon is scattered at right angles into the +y direction. Find the components of momentum of the recoiling electron.

Lots

## The Attempt at a Solution

Since the photon recoils at 90 degrees, I'm assuming that the electron recoils at 45 degrees, so the x and y components of its momentum are equal. Then I just need to find the momentum of the electron after collision:

Ephoton = 1.602x10^-14 J = hc/lambda => lambda1 = 1.2398x10^-11 m

Then using the compton equation:

delta lambda = (h/melectron*c)(1-cos 90) = 3.5135x10^-12 m

Which gives the final energy of the photon via:

lambda2 = lambda1 + delta lambda = 1.59115x10^-11 m
Ephtoton' = hc/lambda2 = 1.2484x10^-14

Then the energy lost by the photon is gained by the electron, whose total energy becomes:

Eelectron' = rest energy + photon energy = melectron*c^2 + (1.602-1.2484)x1-^-14 = 8.5407x10^-14

The energy gained by the electron is in the form of kinetic energy, so we can find its speed:

KE' = (1.602-1.2484)x10^-14 = 1/2 melectron*v^2 => v = 8.811x10^7 m/s

Finally the relativistic momentum of the electron is given by:

p=gamma mv
E=gamma mc^2

=> v/c=pc/E => pelectron' = Ev/c^2 = 8.3729x10^-23

But the momentum of the initial photon is:

pphoton = h/lambda1 = 5.3437x10^-23

So momentum is not conserved? I have tried this problem so many times my head hurts! Can anyone see where I've gone wrong? Any help is greatly aprreaciated!

Hi phil ess,

phil ess said:

## Homework Statement

An x-ray photon of initial energy 1x10^5 eV traveling in the +x direction is incident on a free
electron at rest. The photon is scattered at right angles into the +y direction. Find the components of momentum of the recoiling electron.

Lots

## The Attempt at a Solution

Since the photon recoils at 90 degrees, I'm assuming that the electron recoils at 45 degrees,

I don't think you can assume this. The recoil angle for the electron is something you'll need to find while doing the problem.

so the x and y components of its momentum are equal. Then I just need to find the momentum of the electron after collision:

Ephoton = 1.602x10^-14 J = hc/lambda => lambda1 = 1.2398x10^-11 m

Then using the compton equation:

delta lambda = (h/melectron*c)(1-cos 90) = 3.5135x10^-12 m

Which gives the final energy of the photon via:

lambda2 = lambda1 + delta lambda = 1.59115x10^-11 m
Ephtoton' = hc/lambda2 = 1.2484x10^-14

Then the energy lost by the photon is gained by the electron, whose total energy becomes:

Eelectron' = rest energy + photon energy = melectron*c^2 + (1.602-1.2484)x1-^-14 = 8.5407x10^-14

The energy gained by the electron is in the form of kinetic energy, so we can find its speed:

KE' = (1.602-1.2484)x10^-14 = 1/2 melectron*v^2 => v = 8.811x10^7 m/s

Finally the relativistic momentum of the electron is given by:

p=gamma mv
E=gamma mc^2

=> v/c=pc/E => pelectron' = Ev/c^2 = 8.3729x10^-23

But the momentum of the initial photon is:

pphoton = h/lambda1 = 5.3437x10^-23

So momentum is not conserved? I have tried this problem so many times my head hurts! Can anyone see where I've gone wrong? Any help is greatly aprreaciated!

## 1. What is Compton scattering?

Compton scattering is a phenomenon in which a photon (usually an X-ray or gamma ray) collides with an electron, transferring energy and changing the direction of the photon's path.

## 2. How does Compton scattering affect electron momentum?

Compton scattering can cause a change in the momentum of the electron, as it absorbs the energy from the photon and moves in a different direction.

## 3. What is the significance of Compton scattering in physics?

Compton scattering is an important phenomenon in understanding the interactions between photons and electrons. It provides evidence for the dual nature of light as both a particle and a wave, and it also has applications in fields such as medical imaging and materials science.

## 4. Can Compton scattering be used to determine the energy of a photon?

Yes, the change in energy and direction of the photon after Compton scattering can be used to calculate the initial energy of the photon.

## 5. How is Compton scattering related to the Compton wavelength?

The Compton wavelength is a fundamental constant in quantum mechanics that is related to the momentum of a particle. Compton scattering is one of the phenomena that demonstrates the effects of the Compton wavelength on the behavior of photons and electrons.

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