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cartonn30gel

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We are in a laboratory and there is a photon and an ultra-relativistic proton moving. The energy of the photon in the frame of reference of the laboratory is 35eV. The energy of the same photon in the frame of reference of the proton is 5MeV. What is the energy of the proton in the frame of reference of the laboratory?

2. Homework Equations

energy = h*f

Relativistic doppler effect

Lorenz velocity transformations

relativistic energy

3. The Attempt at a Solution

using energy = h*f

first frequency (f1) is 8.48*10^(15) Hz

second frequency (f2) is 1.21*10^(21) Hz

change of frequency is I guess because of Doppler effect

because f2 > f1, the proton and the photon must be approaching each other. But no matter what, the proton will see the photon approaching with a speed of c. I am not sure if it is valid to use the Doppler formula here. If I use, I get,

B=v/c=0,99999 (the relative speed of the photon and the proton)

then using Lorenz velocity transformation in x direction I get the speed of the proton to be -c. I thought this could be an indication of the proton's actually to be moving away from the photon (that means both moving in the same direction)

But then I cannot use Energy= (gama)*m*c^(2) because (gama) will be infinite.

I'd appreciate any help.

thanks