How to Calculate Scattered Photon's Wavelength and Electron's Kinetic Energy?

[cutecarebear]

Hello everyone! I've got a problem I've been working on for the past two days and can't seem to figure out. The problem is as follows:

Homework Statement

Two different experiments use two different wave lengths for the Comptom Shift. The scattered photons wavelengths and scatter angles (Φ) and the scattered electrons' kinetic energy and scatter angled are measured. The following measurements were obtained:

λ₁: 20 nm Φ₁= 60°
λ₂: 500 nm Φ₂= 60°

1.What is the scattered photon's wavelength for the two experiments?
2.What is the scattered electron's kinetic energy?

The Attempt at a Solution

So far, I've managed the first part (I think).

Δλ= h/mc (1-cos Φ)
Δλ= ((6.63 *10^-34)/ ((9.11*10^-31)*(3*10⁸)) * (1-1/2)
Δλ= ((6.63 *10^-34)/(2.27*10^-23))
Δλ≈1.2*10^-12

So there's the wavelength, I think. Next up is the Kinetic energy:

Kin=mc²(ɣ-1)
ɣ= (1/√(1-(v/c)²)) (Lorentz factor)

I end up with
Kin= (9.11*10^-31 * 9*10¹⁶) (ɣ-1) when I substitute in the mass of an electron and the speed of light.

I cannot for the life of me get ɣ. Or, rather, I can't get "v" within ɣ. Since it is relative, I am pretty sure I can't use DeBroglie's stuff (λ=h/p and then P=mv), though I tried. It didn't work out well. Any ideas? Thanks so much for the help!

 

[anathema]

Hello,

Thank you for sharing your problem with us. It seems like you are on the right track with your calculations for the scattered photon's wavelength. However, I would recommend double checking your units and conversions to ensure you get the correct result.

As for the scattered electron's kinetic energy, you are correct in using the Lorentz factor, but there are a few steps missing in your calculation. First, you need to find the velocity of the electron using the Compton shift formula you already calculated for the scattered photon's wavelength. Then, you can plug that velocity into the Lorentz factor equation to find the value of ɣ. Finally, you can use the mass and speed of the electron to calculate the kinetic energy.

I hope this helps and good luck with your calculations! Don't hesitate to reach out if you have any further questions.