What is the maximum energy an electron can have after scattering a 40keV photon?

[bmb2009]

Homework Statement

A photon carrying energy of 40keV scatters from an electron initially at rest. what is the maximum energy the electron can have?

Homework Equations

The Attempt at a Solution

I tried using conservation of energy

Initial: 40keV (energy of photon) + mc^2 (rest energy of electron)
Final: To have the most energy all the energy of the photon should be transfer to kinetic energy of the electron correct?

so wouldn't the final energy just be the rest energy of the electron + the kinetic energy of the electron? Not sure where I am missing an idea..thanks for the help

 

[TSny]

There's something else that needs to be conserved besides energy.

 

[bmb2009]

There's something else that needs to be conserved besides energy.

I know momentumn does too but how do i combine these two to get the total final energy?

 

[TSny]

If you're allowed to use the well-known http://hyperphysics.phy-astr.gsu.edu/%E2%80%8Chbase/quantum/comptint.html then you will not need to go through the algebra of combining the energy and momentum equations.

If you are required to derive the result starting from conservation of energy and momentum, then what would each conservation equation look like?

Note that "scattering" implies that there will be a photon present after the "collision" as well as before.

 

[bmb2009]

Yes i derived that equation but i still don't see the connection to the energy of the electron... I assume that to maximize the energy of the electron the change in wavelength should be largest at an angle of pi correct? that would yield 2h/mc=delta lambda but now how do i find the energy of the electron??

 

[bmb2009]

ahhh nevermind i figured it out.. thanks for the guidance..it's appreciated!

 

[TSny]

ok, good!