What is the wavelength of the incident photon?

[roeb]

Homework Statement

If the maximum energy imparted to an electron in Compton scattering is 45 keV. What is the wavelength of the incident photon?

Homework Equations

The Attempt at a Solution

$$\lambda_2 - \lambda_1 = h/mc (1 - cos \theta )$$
My first initial thought was to apply conservation of energy.

initial = final

hf + $$m_0 c^2$$ = $$m_0 c^2$$ + Ke + hf'
Where Ke = 45 keV (the kinetic energy of the scattered electron).
Since the problem states maximum energy, I thought that this would mean that theta = 90.

I then proceeded to get f - f' = 1.08 x 10^(19) Hz.

Then I was thinking well, since this is a maximum energy, why not say that f' = 0 (all of the photon's energy is absorbed, but then again that isn't really scattering is it?)

Unfortunately, using c = f $$\lambda$$ I still get the incorrect answer.

Does anyone know what I did incorrectly?

$$test$$

 

[alphysicist]

Hi roeb,

Homework Statement

If the maximum energy imparted to an electron in Compton scattering is 45 keV. What is the wavelength of the incident photon?

Homework Equations

The Attempt at a Solution

$$\lambda_2 - \lambda_1 = h/mc (1 - cos \theta )$$
My first initial thought was to apply conservation of energy.

initial = final

hf + $$m_0 c^2$$ = $$m_0 c^2$$ + Ke + hf'
Where Ke = 45 keV (the kinetic energy of the scattered electron).
Since the problem states maximum energy, I thought that this would mean that theta = 90.

I believe this is an error. The maximum of the energy transferred to the electron does not occur when theta=90 degrees. Do you see what angle it needs to be instead?