Electron Energy in Compton Collision

[Quelsita]

Question:
You want to give an electron an evergy of 25kev in a Compton Collision. What is the minimum initial photon energy you need?

Equations:
$$\Delta$$$$\lambda$$= h/m_ec(1-cos($$\theta$$))
E=mc²
E=hv=hc/$$\lambda$$

I'm not really sure where to start from here. I know the answer is 138kev but I am not sure how to go about getting it.

 

[Delphi51]

For the Compton Effect, you have two equations: conservation of momentum and conservation of energy. I would assume the photon hits a stationary electron and bounces straight back, so only one dimension to consider and no doubt this situation gives you the minimum photon energy.

The two equations involve the initial frequency, frequency after the collision, and the velocity of the electron. But you can find the velocity from the given KE, so you have only two unknowns in your two equations. It looks straightforward to solve for hf1.

 

[nlightner]

I can provide a response to your question. In order to give an electron an energy of 25kev in a Compton collision, the minimum initial photon energy needed would be 138kev. This can be calculated using the equations you have provided.

First, we can use the equation E=mc^2 to calculate the energy of the electron, where m is the mass of the electron and c is the speed of light. In this case, the mass of the electron is constant, so we can focus on the energy component.

Next, we can use the equation E=hv, where h is Planck's constant and v is the frequency of the photon. This equation can also be written as E=hc/\lambda, where \lambda is the wavelength of the photon.

In a Compton collision, the wavelength of the initial photon will change due to the interaction with the electron. The change in wavelength can be calculated using the equation \Delta\lambda= h/mec(1-cos(\theta)), where \theta is the angle of deflection of the photon.

To determine the minimum initial photon energy needed to give the electron an energy of 25kev, we can use the following steps:

1. Set the energy of the electron to 25kev in the equation E=mc^2 and solve for m. This will give us the mass of the electron in joules.

2. Set the energy of the photon to 25kev in the equation E=hv and solve for the frequency or E=hc/\lambda and solve for the wavelength. This will give us the initial frequency or wavelength of the photon.

3. Use the equation \Delta\lambda= h/mec(1-cos(\theta)) to calculate the change in wavelength of the photon.

4. Plug in the values for the initial and final wavelengths into the equation E=hc/\lambda and solve for the initial photon energy. This will give us the minimum initial photon energy needed to give the electron an energy of 25kev.

Following these steps, we can calculate that the minimum initial photon energy needed is 138kev. I hope this explanation helps to clarify the process and answer your question.