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When atoms are formed, first nucleus is formed and then, nucleus attracts electrons(we can call them free electrons) and we get an atom.

but in terms of Bremsstrahlung, what happens is:

In the case of an electron passing close to a positively charged atomic nucleus, the electric field of the nucleus would exert an attractive force on the electron due to their opposite charges. This attractive force can cause the electron to be deflected from its original path and change direction.

So why in Bremsstrahlung's case, attractive force causes electron's direction change + deacceleration and why in atom formation, this force actually attracts and makes the electron stay at its orbit. I looked at other answers, but still not fully able to grasp it since i'm a beginner. So would appreciate easy and correct explanation.

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  • $\begingroup$ Maybe one of the answers to this will be helpful? - Why doesn't an electron ever hit (and stick on) a proton? $\endgroup$
    – mmesser314
    Commented Apr 24, 2023 at 14:50
  • $\begingroup$ Bremsstrahlung happens at high energy, typically (many) thousands of times the ionization energy of the atom. It's the difference between keV-MeV of electron energy for a Bremsstrahlung process vs. 10eV for electron capture in an atom. $\endgroup$ Commented Apr 24, 2023 at 15:45
  • $\begingroup$ maybe my answer here will help in how quantum mechanics is involved physics.stackexchange.com/questions/550316/… $\endgroup$
    – anna v
    Commented Apr 24, 2023 at 16:59

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In layman's terms, during Bremsstrahlung the nucleus is attempting to decelerate the electron to capture it into orbit. However, the incoming electron is too energetic, too fast, and the slowed down electron is still moving fast enough to escape, or that the nucleus is already surrounded by electrons. In the case it is fast enough to escape, then there is obviously no way to form an atom, unless it stops being fast enough to escape.

But there is also the latter case, where the atom is already formed, and there is no more space to form more bound electrons. This is purely a quantum behaviour, due to Pauli's Exclusion Principle. There is no way to explain this classically.

Really these things are much more intricate and you should not be looking for easy beginner explanations. I feel dirty typing this up.

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  • $\begingroup$ Thank you ! much appreciated. question if you don't mind: nucleus tries to decelerate electron, because of attractive force between them right ? but due to how energetic electron is, attractive force can't win over it, and all it does is change its speed/direction, right ? $\endgroup$
    – Matt
    Commented Apr 24, 2023 at 18:24
  • $\begingroup$ see pdg.lbl.gov/2021/reviews/… $\endgroup$
    – JEB
    Commented Apr 24, 2023 at 18:28
  • $\begingroup$ At such a layman level, yes. $\endgroup$ Commented Apr 24, 2023 at 18:34
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Thinking about bremsstrahlung in terms of slowing down or changing direction is not really helpful. At the electron energies at which brem is significant, the atomic electrons don't really matter, other than: they present an electric field, and there are $Z$ times more of them than nuclei. However, the effect goes as the electric field strength squared, so nucleus has $Z$ times the cross section of $Z$ atomic electrons.

Note: the sign of the charge is irrelevant. The nucleus is not trying to capture the electron; rather, the electron is passing through a strong field near the nucleus, and it interacts.

Regarding the direction change of the electron, that is not considered (as multiple scattering via ionization will totally dominated it). What is of concern is the opening angle of the photons, which is strongly forward peaked. There is a formula for it.

As mentioned: the effect has a lot of nuances, and has been calculated and measured in depth by theorist and experimentalist.

The full Bethe-Heitler formula can be found in Wikipedia, and it is far to detailed to describe here:

enter image description here

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