Let us consider a free electron in space, which is initially at rest. Now let us consider a photon of frequency f, which collides with our free electron giving all its energy to it. This energy will manifest itself as the K.E. of the electron after the collision. Therefore, we can write hf=(1/2)mv^2 where, h: Planck's Constant m: Mass of the electron v: velocity of the electron after the collision Also, whole of the momentum of the photon will also be transfered to the electron hf/c=mv Solving the two equations, we get v=0 or v=2c(which defies special relativity). Now, v=0 cannot be the solution, as the energy in the electron has to manifest itself in some or the other form, and the only form is K.E. (if I'm not mistaken). The solution v=2c is not compatible with the fact that c is the ultimate speed. So, what's the problem?