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Homework Statement
An electron initially at rest is scattered by a photon.
a) Which scattering angle corresponds to the largest Compton shift and why?
b) At what minimum photon energy can half of the photon energy be transferred onto the electron?
Homework Equations
[tex]\Delta \lambda = \lambda_2 - \lambda_1 = \frac {h}{m_e c} (1 -cos\theta)[/tex]
where [tex]\Delta \lambda[/tex] is the compton shift, [tex]\lambda_2[/tex] and [tex]\lambda_1 [/tex] are the final and initial photon wavelengths, m is the mass of the electron, c the speed of light, and [tex]\theta [/tex] the scattering angle.
The Attempt at a Solution
a) Pretty straightforward, for a maximum shift [tex]\delta \lamba[/tex] the [tex](1 -cos\theta)[/tex] must be a maximum, ie. [tex]cos\theta) = 0[/tex] which happens at 90 degrees.
b) I might be confused in understanding the question. Way I figured, is that the the initial photon kinetic energy is shared equally between the reflected photon and electron. So conservation of mechanical energy (without potential energy, electron initially at rest, K = hf for photon and K= 0.4mv² for electron)
[tex]h \frac {c}{\lambda_1} = h \frac {c}{\lambda_2} + 0.5 m v^2[/tex]
So since the final energy of the photon is half the initial, that means the reflected photon and electron have equal resultant kinetic energies.
[tex]h \frac {c}{\lambda_1} = 2 h \frac {c}{\lambda_2} = m v^2[/tex]
I'm still not getting what "minimum" is