Compton scattering on massless electron

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Hello! I found this problem where we are asked what happens to the energy of the outgoing photon in a Compton interaction, if the mass of the electron goes to zero and what is the physical intuition of it. So the formula is this: $$\lambda - \lambda_0 = \frac{h}{m_0 c}(1-cos \theta)$$ So when the electron gets massless its compton wavelength gets higher (infinite in the limit) and hence it spreads out and plugging in there you get that the final wavelength of the photon is infinite, which means that it has zero energy. But I am not sure what is the logic behind. Beside the obvious math, what is the explanation for the fact that the electron gets all the energy of the photon? Thank you!
 

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PeterDonis
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I found this problem
Where? Is this a homework problem?
 

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