# How exactly do protons and electrons interact with each other?

How do these particles exchange information about charge and position between themselves, even though there's mostly empty space between them?

Also what happens if a free electron passes closer to a nucleus of a hydrogen atom than its own electron?

My random guesses so far:

1. Proton won't react because it's somehow locked with its existing electron
2. Proton will catch it and release the previous one
3. Proton will catch it and keep both of them with half the force
4. Existing electron will simply repel incoming one
5. Something else?

## 2 Answers

The proton and electron exchange information via a gauge boson, in this case, a virtual photon. This is how the electromagnetic interaction is mediated.

As for your other question, the electron will get decelerated and deflected and emit a photon, releasing some of its energy in a process called Bremsstrahlung

• It might also be caught into a hydrogen anion en.wikipedia.org/wiki/Hydrogen_anion , if it has the appropriate energy as it scatters. – anna v Mar 31 '14 at 18:53
• @annav Does it mean that the proton attracts both of these electrons with half the force or does it do so with full force but only for 1/2 time each one? Isn't charge quantized and therefore unable to be divided? – Ardath Mar 31 '14 at 19:03
• look at the energy levels of the hydrogen atom hyperphysics.phy-astr.gsu.edu/hbase/hyde.html#c2 . If an electron with the appropriate energy is caught at the lowest n=1 level has two spin states so two electrons can be there. the atom is neutral with one,but the other energy level exists and can catch a second electron if it has the correct energy or if it releases part of its energy in a photon. The electron(s) are in orbitals around the nucleus, i.e. probability distributions in space hyperphysics.phy-astr.gsu.edu/hbase/chemical/eleorb.html – anna v Mar 31 '14 at 19:24
• In quantum mechanics one no longer talks of "attraction" since the possible positions and energy levels are quantized, not continuous as in classical attractive force physics. The potential is the 1/r potential of electricity but the solutions are the energy levels and two electrons with different spins can be at the same level, and also electrons can be caught at higher energy levels. – anna v Mar 31 '14 at 19:30

C: See "Quantum Mechanics". More specifically you're wanting solutions to the Schrodinger Equations that represent your system. In this case that is an electron represented by a probability density function $$\psi (\vec{x},t )$$ under a potential $$V(\vec{x})$$ which is the potential energy function of the system. This contains information regarding the relative distances and charges of the particles in the system.

Once we find solution $\psi(\vec{x},t),$ for both space and time variables for $$i\hbar\frac{\partial }{\partial t}\psi=\hat{H}\psi$$ where $\hat{H}$ contains information regarding the energy of the system from the aforementioned potential $V(\vec{x})$, we have a time evolutionary model of the system!

This allows us to create a 3 Dimensional moving picture of the probability density of the electron in this system. In other words, we can see the various locations this electron can be with respect to the hydrogen atom. The plot would not be of $\psi(\vec{x},t)$, but of $|\psi(\vec{x},t)|^{2}$ per the rules of the underlying mathematics. Knowing the energy equations of motion we can calculate the Euler-Lagrange Equations of motion for the system. These turn out to be the equations of motion that would answer your questions as to how your system would interact.

From there we can calculate the corresponding momentum equations of the system and arrive at the same functions for motion aforementioned. For a more rigorous introduction to the course I recommend Mathematics for Quantum Mechanics: An Introductory Survey of Operators, Eigenvalues, and Linear Vector Spaces (Dover Books on Mathematics) by John David Jackson or Lectures on Quantum Mechanics by Paul Dirac.

For a more conceptual introduction I recommend The Quantum World: Quantum Physics for Everyone by Kenneth W. Ford and Diane Goldstein or The Quantum Universe: (And Why Anything That Can Happen, Does) by Brian Cox.

Happy reading, scholar!

• Also just read the other answer, and if you look at the plot you see on the wiki page for the exact picture of the scenario, you see position-momentum trajectories labeled by their energies C: – Doryan Miller Mar 31 '14 at 19:15