8

Can somebody explain what would happen if an electron & a proton, very close to each other are left to "fall" to each other in a straight line?

tryst with freedom
  • 7,940
rim
  • 175

5 Answers5

27

They would form a hydrogen atom.

They would not merge, because merging would result in a neutron, which is heavier than a proton and an electron combined. However, if they are sufficiently forcibly "slammed" into each other, they might form a neutron (and an electron neutrino, which has an negligible mass). The neutron would later decay into proton, electron and electron anti-neutrino (it has a half-life of about 10 minutes).

Danijel
  • 2,856
  • 1
  • 15
  • 23
  • 3
    I would add something like "yes, they are attracted to each other via electric charge, but when they get very close, the nuclear forces become significant (and repulsive). – Carl Witthoft Jul 14 '21 at 14:50
  • 1
    Can you elaborate a little on your statement about "repulsive nuclear force", what are the criterion for a repulsive nuclear force & that too of which kind, strong or weak? As generaly what is said about strong nuclear force is that they are attractive & short ranged – rim Jul 14 '21 at 15:57
  • Why they need to be "slammed" to make a neutron. Which repulsive force is responsible for acting against the attractive electric force between proton & electron – rim Jul 14 '21 at 16:17
  • 10
    @rim it is because neutron is heavier than proton and electron combined, so they need some extra energy to form a neutron. This has not about repulsive and attractive forces, it is about masses. If neutrons were less massive, then that extra energy would not be needed, but then hydrogen atoms would not be stable - they would decay into neutrons. – Danijel Jul 14 '21 at 20:33
  • 1
    In most cases, proton and electron will just bounce off each other (scatter). Forming a hydrogen atom has some probability (neither 0 nor 1), the process requires radiating a photon(s) as well. – fraxinus Jul 15 '21 at 07:18
  • @fraxinus they would certainly form a hydrogen atom if they lack sufficient kinetic energy to escape each other, which seemed to implied by the question. However, in that case, they already are a hydrogen atom from the start, which may be a highly excited Rydberg atom but it will eventually decay to the ground state. – Danijel Jul 15 '21 at 08:33
  • 2
    Which nuclear force, strong or weak, will act as a repulsive force in the said electron-proton interaction? Can someone describe or point towards the expression for such a force? – rim Jul 15 '21 at 10:41
  • 5
    @rim there is no relevant repulsive force. Electron and proton interact gravitationally, electromagnetically and with weak nuclear interaction (electrons do not interact with the strong one). Weak nuclear interaction may turn them into a neutron (if there is enough energy) and later causes that neutron to decay. But its repulsive/attractive behavior is irrelevant here. The only relevant thing it does in this story is "transmuting" particles (with some nonzero probability when allowed by conservation laws). – Danijel Jul 15 '21 at 11:27
  • 'They would form a hydrogen atom.' Not necessarily. – my2cts Jul 15 '21 at 15:02
  • 'They would not merge' This cannot be excluded. – my2cts Jul 15 '21 at 15:02
  • 'if they are sufficiently forcibly "slammed" into each other' There is nothing that keeps electron and proton separate. In fact in atoms there is always substantial s electron density at the nucleus. – my2cts Jul 15 '21 at 15:08
  • @my2cts nothing keeps them separate, but the fact that a neutron is more massive keeps them from becoming a neutron (they need extra energy to do it and kinetic energy could do the trick). Being on the same place is not the same as being another particle. – Danijel Jul 15 '21 at 17:36
  • @Danijel Read my answer, though. They can become neutron plus neutrino. – my2cts Jul 15 '21 at 22:28
  • @my2cts given enough energy, yes. But not without it. And yes, a sufficient localization can also work, which also falls under sufficient kinetic energy. – Danijel Jul 16 '21 at 06:49
  • From the post above you cannot conclude that there is not rnough energy. Hence a neutron can form. – my2cts Jul 18 '21 at 21:22
14

Can somebody explain what would happen if an electron & a proton, very close to each other are left to "fall" to each other in a straight line?

One of the three solid evidences that classical electrodynamics and mechanics could not describe electrons, protons and atoms was exactly the fact that in classical electrodynamics the electron attracted by the proton charge would by acceleration fall on the proton neutralizing it, with a continuous electromagnetic radiation.

Instead there existed discrete frequencies , the atomic spectra. Quantum mechanics was invented, leading to fitting the hydrogen spectra with quantized energy solutions.

The other two experimental no-goes of classical physics that quantum mechanics explained mathematically at the time were the photoelectric effect and black body radiation.

anna v
  • 233,453
3

I wish to point out that electrons are LEPTONS, and protons are HADRONS (forgive the SCREAMING). All protons are made up of 3 quarks (u u d). Neutrons have (u d d) quarks. Leptons have 0 quarks and do not participate in strong force interactions which are mediated by gluon exchanges between the hadron's component quarks. A lepton can only contribute energy (from its kinetic motion). While Coulomb attraction exists between the proton and incoming electron, you need a lot of energy to get a proton u quark to transition to d (a naive probability of ⅔, assuming you approach to within $10^{-17}$ meters), but to balance out all the quantum book-keeping, you also need an electron anti-neutrino! A Feynman diagram would show this (see http://hst-archive.web.cern.ch/archiv/HST2002/feynman/examples.htm). As such, the electron would more probably lose its energy as Bremsstralung emissions.

Quantum Mechanic
  • 4,921
user8150805
  • 39
2

If they are simply falling directly towards each other, they can't combine. To combine, they would need to form a neutron, but a neutron has slightly more mass. The extra mass would have to come from another particle, or source of energy - for example smashing them together forcefully enough.

So as they can't combine, they would remain as a proton and electron. They would be attracted to each other because of having an opposite charge, but when they got "too close", the nuclear interactions would become dominant (more powerful) and cause them to repel each other.

Another way of looking at the energy needed to merge, is its the energy needed to overcome that repulsion when they get very close.

So they would end up close but not too close. Attracted electrically, but unable to get very much closer or merge.

So it would remain as a hydrogen atom - a proton with a single bound electron.

Stilez
  • 4,233
  • 3
    Electron is not repelled from the proton by any nuclear interactions. It just remains around the proton with a finite mean distance (Bohr radius) due to Heisenberg uncertainty. – Ruslan Jul 15 '21 at 14:48
  • 'If they are simply falling directly towards each other' They are not. The electron wave function will quickly spread. – my2cts Jul 15 '21 at 14:49
  • 2
    I'm using simple.nontechnical terms here, because clearly the question is phrased in a way that suggests a slightly less technical but more intuitive description may be of use. – Stilez Jul 15 '21 at 17:19
1

There is a probability that they will form a neutron, a hydrogen atom in some s state or an unbound electron proton system. Each of these possibilities can occur with a relative probability depending on the initial state. So it is not correct to say that a hydrogen atom must result, even without specifying in which state.

Quantum mechanics tells us that a very localised electron centered at a proton corresponds to a superposition of hydrogen bound and ionised states. A very localised electron has very high kinetic energy which may exceed the potential energy. The quickest way to see this is to use Heisenberg's uncertainty principle for position and momentum. HUP tells you that a strongly localised electron wave function requires a superposition of very high momentum waves. Very high momentum means very high kinetic energy as well.

Note that if components with high enough kinetic energy are present to overcome the mass difference of neutron and proton and to create an electron neutrino of sufficient energy and momentum, also a neutron plus neutrino may be formed.

my2cts
  • 24,097
  • 1
    Can you please elaborate how a localised electron will have high kinetic energy required for overcoming the overwhelming attractive electric force. – rim Jul 14 '21 at 16:12
  • I added a paragraph on Heisenberg uncertainty. – my2cts Jul 14 '21 at 21:52
  • @rim Electrons are not little balls of stuff. They are quanta - waves with some very specific properties. Just like a sound wave isn't localized, electrons aren't either. Electrons bound to atoms fill something called an orbital - essentially, a complicated standing wave. That ultimately means that electrons have discrete states they can occupy, with discrete energy levels. The thing is, the more localized a quantum is (the less uncertainty there is in its position), the higher momentum (and speed) it must have - if you think about sound again, high frequency sound waves are "smaller". – Luaan Jul 15 '21 at 14:38