# How close does an electron get to a proton to be attracted

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## Main Question or Discussion Point

I couldn't fit the whole question, it should say
"How close does an electron have to get to a proton to be attracted to it"

And I know it can depend on the speed and direction they are traveling. Can we just pretend they are stationary for this answer please.

By attracted I mean the electron will change its course to move towards the proton

## Answers and Replies

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Nugatory
Mentor
By attracted I mean the electron will change its course to move towards the proton
Look at the equation that describes the force between two stationary charged objects. Is there any distance at which there is not an attractive force between them?

Look at the equation that describes the force between two stationary charged objects. Is there any distance at which there is not an attractive force between them?
You're talking about Coulombs law. All that does us sum up the net attraction or repulsion. It is impossible to determine if the force is enough to actually move a particle.

So if that is my best reply then is it safe to assume that the answer to my question is not known?

Any one know of any other forums where I can try to find an answer?

PeroK
Homework Helper
Gold Member
You're talking about Coulombs law. All that does us sum up the net attraction or repulsion. It is impossible to determine if the force is enough to actually move a particle.

So if that is my best reply then is it safe to assume that the answer to my question is not known?

Any one know of any other forums where I can try to find an answer?
Any force, however small, will move a particle. So, in theory, it doesn't matter how far apart the two particles are, they will move towards each other. In practice, however, you cannot set a proton and an electron one light-year apart, say, and see whether they start to move towards each other. On a large scale, e.g. the Solar system, objects tend to be electrically neutral and electrical attraction or repulsion over large distances is not relevant to the behaviour of the Solar system.

The issue is more important for gravity. Again, in theory, gravity works over any large distance, but it's important to know whether this is actually the case. And, in the universe there are large masses a very long distance away from each other. The evidence we have is that gravity works as expected over the largest distances that we have been able to measure.

Mister T
Gold Member
You're talking about Coulombs law. All that does us sum up the net attraction or repulsion. It is impossible to determine if the force is enough to actually move a particle.
Force is not required for motion. Force is required to change motion, but there is no minimum amount required. The smaller the force the smaller the change in motion.

So if that is my best reply then is it safe to assume that the answer to my question is not known?
As distance between the particles increases the force decreases. There is no separation distance for which the force is zero.

Any one know of any other forums where I can try to find an answer?
Several people have given you the correct answer. You can look elsewhere for other answers, but unless you can tell us what you find unsatisfactory about the ones you've been given you will just be doing random searches with no way to tell which answers are valid.

RPinPA
Homework Helper
I think part of the problem here is semantics. You said this:
By attracted I mean the electron will change its course to move towards the proton
If by that you mean that the electron will move directly toward the proton, rather than on some path that misses it, the answer is that this will only happen if the electron started out stationary or already on the line directly toward the proton (or directly away from the proton if it's going slow enough). And in that case, there is no maximum distance (even in the case of moving directly away, at any distance if the electron is moving slowly enough it will eventually turn around). The Coulomb force goes to infinity, and F = ma says that as long as there's a nonzero force, there's a nonzero acceleration.

If the electron has some initial motion which is not directly toward or away from the proton, then the behavior is the same as for planets under Newton's Law of Gravitation: the path is going to be either a closed ellipse, a parabola, or a hyperbola, all of which will miss the central attracting object.

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CWatters
Homework Helper
Gold Member
I couldn't fit the whole question, it should say
"How close does an electron have to get to a proton to be attracted to it"
I'm wondering if there is something behind the question. Are you assuming that electrons in an atom aren't close enough to be attracted to the nucleus or they would have "fallen in"?

You're talking about Coulombs law. All that does us sum up the net attraction or repulsion. It is impossible to determine if the force is enough to actually move a particle.
This is criptic. What do you mean with "net attraction or repulsion"?

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lightarrow

I couldn't fit the whole question, it should say
"How close does an electron have to get to a proton to be attracted to it"

And I know it can depend on the speed and direction they are traveling. Can we just pretend they are stationary for this answer please.

By attracted I mean the electron will change its course to move towards the proton
Largest hydrogen atoms (ever detected in interstellar space) are about 0.5mm large. In liquid or solid electrolyte the noticeable (for purposes of chemistry) attraction starts from ~0.1mm too. For ion engine, recombination between separately emitted electrons and ions happens even if emitters are separated by several tens of cm.

Theoretically, the attraction force works up to infinity - the maximal recombination radius is mostly defined by electrical noise levels of background space, rather than by intrinsic properties of electron and proton.

gneill
Mentor
Just as with the gravitational force and orbits there will be an escape velocity for an electron being electrically attracted by a proton. If the electron's kinetic energy exceeds the potential energy of electron-proton system, the electron will escape.

sophiecentaur
Gold Member
Largest hydrogen atoms (ever detected in interstellar space) are about 0.5mm large.
How would they be detected? Absorption lines at low Radio frequencies? Do you have a reference about this - experimental details could be interesting.

As distance between the particles increases the force decreases. There is no separation distance for which the force is zero.
Thanks, that will get me to the next step

The Coulomb force goes to infinity, and F = ma says that as long as there's a nonzero force, there's a nonzero acceleration.
Thanks, mentioning infinity was helpful

Largest hydrogen atoms (ever detected in interstellar space) are about 0.5mm large. In liquid or solid electrolyte the noticeable (for purposes of chemistry) attraction starts from ~0.1mm too. For ion engine, recombination between separately emitted electrons and ions happens even if emitters are separated by several tens of cm.

Theoretically, the attraction force works up to infinity - the maximal recombination radius is mostly defined by electrical noise levels of background space, rather than by intrinsic properties of electron and proton.
Thanks a lot, that was most helpful

This is criptic. What do you mean with "net attraction or repulsion"?

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lightarrow
I was never top of the class in English. I'm just trying to learn some stuff some of which is not often discussed

How would they be detected? Absorption lines at low Radio frequencies? Do you have a reference about this - experimental details could be interesting.
Yes, it is radio lines argument which trace to
"Very large hydrogen atoms in interstellar space"
published back in 1991. I checked recently and found the following correction dated 2013 though:
https://pubs.acs.org/doi/abs/10.1021/ed400399y?src=recsys

It states the maximal atom size was over-calculated 100 times, and therefore correct answer for maximal hydrogen atom size in ISM is 5um, not 500um.