Why does an electron lose kinetic energy if it passes a nucleus? (Bremsstrahlung Radiation Q) When learning about X-rays we are told that they are created through braking radiation. When we are learning about braking radiation we are told that this occurs when an electron passes close to a nucleus and slows down causing a reduction in kinetic energy, which is then emitted as an X-ray.
The problem that I have is why it slows down. The electron would be accelerated towards the nucleus as it approaches and then I would expect it to be negatively accelerated by the same amount as it travels away from the nucleus. Thus, I would expect to see the kinetic energy conserved over the whole event and no braking radiation. What am I missing here?
 A: The explanation you've given is a bit mangled, and it's not surprising that (under the assumptions you state) you've come to the conclusion that there should be no effect.
The key piece that you're missing is that according to classical electrodynamics, accelerating charges emit electromagnetic waves.  These waves carry energy away to infinity, and so (by conservation of energy) the total energy of the accelerating charge must decrease.  The intensity of the emitted waves is proportional to the square of the acceleration of the charge, and so there's no cancellation between the "ingoing" and "outgoing" travel of the electron;  both legs of the trip emit a positive amount of energy.  These emitted waves are what we observe as bremsstrahlung.  (The details get more complicated when we add in quantum mechanics, but that's not really necessary to get a picture of why the electron's energy decreases.)
In the limit of "small" acceleration, the radiated energy goes to zero, and so we can often neglect the effects of this energy loss.  In this limit, your logic would be correct:  the particle would have a certain amount of KE when it was far away from the scattering atom, would accelerate and change its KE as it approached the atom, and then would return to its original amount of KE as it flew away from the atom.  It's only because the acceleration of the electron is sufficiently large that this "energy loss to radiation" effect becomes important.
