Find minimum energy of a photon to produce 25keV electron in compton scatter?

[j2dabizo]

Homework Statement

What is the minimum energy that photons must have to produce 25 keV electrons in a Compton scattering? (answer in keV)

Homework Equations

Not too sure here, We know E_incident= E_final + K.E._electron

We know that the work function (binding energy) is also taken into account but most of the time it is in eV, so we can (i think) omit that here.

The Attempt at a Solution

Not sure once again. How can we find the minimum incident energy of a photon without any other info but the 25 K.E. of the electron.

My logic tells me that, why can't it be 26 keV, E_final = 1kev and KE of electron = 25 kev.

Help please Thanks

 

[ideasrule]

To start off, take a look at the Compton scattering formula: http://en.wikipedia.org/wiki/Compton_scattering#Description_of_the_phenomenon

To give electron as much energy as possible, you want the photon to lose as much energy as possible. What's the maximum possible change in the photon's wavelength?

Once you get that, use the conservation of energy to relate the electron's final energy (25 keV) to the photon's initial and final wavelengths. You now have 2 equations with 2 unknowns, and can solve for the photon's initial energy.