Photon-Electron collision problem

[Rainbow]

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 transferred 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?

 

[George Jones]

Newtonian concepts don't work in this situation. Relativistic energy and momentum conservation must be used, and these concepts forbid your situation. On its own, a free electron cannot absorb a photon.

 

[Rainbow]

Thank you for the help.

 

[Dale]

This is also the reason why when an electron and a positron anihlate they always produce at least two photons. With just one the 4-momentum wouldn't be conserved.