Compton Scattering Problem

[Prologue]

Homework Statement

Show that, regardless of its initial energy, a photon cannot undergo compton scattering through an angle of more than 60 degrees and still be able to produce an electron positron pair. (Hint: Start by expressing the Compton wavelength of the electron in terms of the maximum photon wavelength needed for pair production.)

Electron/Positron rest energy: 0.511 MeV

Homework Equations

Compton equation: $$\lambda' - \lambda = \lambda_{c}(1 - cos(\phi))$$

The Attempt at a Solution

$$\lambda_{c} = \frac{h}{mc} = 2.426*10^{-12}$$

$$\frac{Mass of e^{-}*Mass of e^{+}}{h} = \frac{2(0.511)*10^{6}eV}{3.97*10^{-15}eV*s} = 2.57 * 10^{20}Hz$$


Umm yeah, that is about it. In other words I have no idea how to express it in terms of the maximum wavelength needed for pair production. I'll keep working on it though.

 

[Dick]

The units of lambda_c are meters. Don't leave off units. For the second calculation you mean sum of the rest energies, not product of the rest masses (at least that's what you actually calculated). Now turn that Hz into a wavelength. That's the maximum value of lambda'. Now put theta=60 degrees in. What do you notice?

 

[Prologue]

I did notice what was happening, but I didn't know how to show it. You are correct about the multiplying of the masses, I was really just trying to illustrate what I was doing in the next step, you are correct that it should be a sum. I ended up going with the 'explanation in english' approach rather than a more mathematical way. Thanks for the reply.