# Consider Compton scattering of a photon by a moving electron

• Albi Mema
In summary, the conversation discusses Compton scattering of a photon by a moving electron, where the photon and electron collide head-on. The wavelength of the scattered photon, λ', can be derived using the equations for energy conservation and momentum conservation, and it is shown that for high values of E (total energy of electron), the result reduces to λ' = hc/E(1 + m^2c^4λ/4hcE). The person speaking offers to guide the other person if they show their work, as there are multiple areas where mistakes can be made.
Albi Mema

## Homework Statement

Consider Compton scattering of a photon by a moving electron. Before the collision
the photon has wavelength λ and is moving in the +x-direction, and the electron is
moving in the −x-direction with total energy E (including its rest energy mc2). The
photon and the electron collide head-on. After the collision, both are moving in the
−x-direction (that is, the photon has been scattered by 180◦).
(a) Derive an expression for the wavelength λ′ of the scattered photon. Show that if
E ≫ mc2, where m is the rest mass of the electron, your result reduces to
λ′ =hc/E(1 +m^2c^4λ/4hcE)

## Homework Equations

Energy Coservation and Momentum Conservation law. Energy of a particle moving particle and energy of the photon.

## The Attempt at a Solution

Using the given equations above the same strategy as the one to find the Compton scattering is used. The problem is that the last formula is not the same as the one stated above.

I worked it out and got the quoted expression. Perhaps if you showed what you did, I will be able to guide you. There are several places where one can make a wrong turn.

## 1. What is Compton scattering?

Compton scattering is a phenomenon in which a photon (an elementary particle of light) collides with an electron, resulting in a change in the photon's energy and direction.

## 2. How does Compton scattering occur?

In Compton scattering, the photon transfers some of its energy to the electron, causing it to recoil and change direction. This results in a longer wavelength (lower energy) photon being scattered.

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

Compton scattering is important in understanding the behavior of photons and electrons, as well as in applications such as medical imaging and material analysis.

## 4. How does the motion of the electron affect Compton scattering?

The motion of the electron affects Compton scattering because it changes the amount of energy and momentum transferred to the electron during the collision, leading to a different scattered photon energy and direction.

## 5. What is the Compton wavelength?

The Compton wavelength is a fundamental constant in quantum mechanics that describes the size of an object (such as an electron) based on its mass and energy. It is related to the amount of energy and momentum transferred in Compton scattering.

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