How Does the Compton Effect Explain Photon-Electron Collisions?

[Extherium]

In the Compton effect, a 0.100nm photon strikes a free electron in a head-on collision and knocks it into the forward direction. The rebounding of the photon recoils it directly backward. Use conservation of (relativistic) energy and momentum to determine:
a) the kinetic energy of the electron, and
b) the wavelength of the recoiling photon.
Assume the electron's kinetic energy is given by the non-relativistic formula.

For starters, I've found the following information about the photon.
Energy = 1.986*10^-15 J
Momentum = 6.626*10^-24 N.S

The main reason I'm having trouble with this question is because the photon recoils directly backwards and there is no angle change. I would be right otherwise, because I could use the Compton eqaution, but we never went over a question like this.

I'm just not sure how to find any of the relevant information about the photon as well as the electron after the collision, like the momentum or energy transferred to the electron. I know there are a few other general formula's that I could use to determine various aspects of the photon or electron afterwards, but they involve using values relevant to the photon/electron after collision. So I'm pretty much stuck.

 

[Extherium]

Ahhh nevermind!

I just realized that angle is 180degrees. *slaps forehead*

 

[kyle8921]

I would approach this problem by first understanding the principles of the Compton effect and its underlying conservation laws. The Compton effect is a phenomenon where a photon interacts with a free electron, resulting in a change in the wavelength of the photon and the kinetic energy of the electron. This interaction can be described by the conservation of energy and momentum.

In this case, we have a head-on collision between a photon with a wavelength of 0.100nm and a free electron. We can use the conservation of energy equation, which states that the initial energy of the system (photon and electron) must be equal to the final energy. In this case, the initial energy is the energy of the photon, which is given by 1.986*10^-15 J. After the collision, the photon recoils directly backward, so its final energy will be the same as its initial energy.

Next, we can use the conservation of momentum equation, which states that the initial momentum of the system must be equal to the final momentum. The initial momentum of the system is the momentum of the photon, which is given by 6.626*10^-24 N.s. After the collision, the electron is knocked into the forward direction, so its momentum will be equal to the final momentum of the system.

Using these two equations, we can solve for the final kinetic energy of the electron and the wavelength of the recoiling photon. The final kinetic energy of the electron can be calculated using the non-relativistic formula, which is given by KE = (1/2)mv^2. We can use the final momentum of the system to calculate the velocity of the electron, and then use that velocity to calculate its kinetic energy.

The wavelength of the recoiling photon can be calculated using the Compton equation, which states that the change in wavelength (Δλ) is equal to the Compton wavelength (h/mc) multiplied by (1-cosθ), where θ is the angle between the initial and final direction of the photon. In this case, since the photon recoils directly backward, the angle θ is 180 degrees and cosθ is equal to -1. We can then use the final energy of the photon, which we calculated earlier, to solve for its final wavelength.

In conclusion, by using the principles of conservation of energy and momentum, we can determine the kinetic energy of the electron and the wavelength of the recoiling photon