An alive electron was observing a photon with frequency f1 while it was coming to hit him!The photon has hit the electron and reflected in the opposite direction relative to the alive electron. The electron has seen the new reflected photon with a frequency f2. Assuming the the collision was elastic if observed from an inertial frame of reference.
The relation between f2 and f1 is:
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The photon before hitting the electron has an energy E = h ⋅ f 1 where h is Planck's constant. When the photon hits the electron a part of this energy is transfered to the electron and this would implies that the photon would lose some energy, I mean f2 would be less than f1, but the collision is elastic so the lost energy is recovered giving f2 = f1, due to f2 can't be greater than f1 (extra energy can't be created)