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Problem with Theory of Resistance

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1. The problem statement

The explanation of resistance in my textbook and given by my teacher (when I actually took the class) doesn't make much sense upon analysis to me.

From the model that I was taught, resistance is explained as such:

The charge carriers are flowing in current, and will periodically run into 'atoms.' This causes them to pause for a moment and slow down due to the collision, and then pick up speed again due to the electric field pressing them on.

The atoms then vibrate from the collision, and thus the kinetic energy imparted into the atoms is released as thermal energy. Which is why resistors heat up and whatnot.

Analysis and problem with model

Now this doesn't make much sense when I think about what atoms are.

In a metallic conductor the electrons are what are flowing in a 'sea' of them. So the electrons are what would bump into atoms.

Atoms are mostly empty space. There are electrons kind of orbitting about and at the very center the nucleus composed of protons and neutrons. So for an electron to hit an atom, what we are saying is that the electrons are hitting either other electrons or the nucleus.

It is impossible for them to hit other electrons (or so I think) because they would repel each other with immense force.

If an electron manages to hit the nucleus, the attractive force between the two should be so strong that it should no longer continue to move. Seeing as how the attractive force varies inversely proportional to distance squared, when the electron comes within such close range of the protons, and actually strikes them, the attractive force should be huge and should easily overcome whatever is producing the field/voltage that made the electron start to move in the first place.

So what gives?
 
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If an electron manages to hit the nucleus, the attractive force between the two should be so strong that it should no longer continue to move. Seeing as how the attractive force varies inversely proportional to distance squared, when the electron comes within such close range of the protons, and actually strikes them, the attractive force should be huge and should easily overcome whatever is producing the field/voltage that made the electron start to move in the first place.

So what gives?
So what you're saying is that in a stable atom electrons don't orbit nuclei, they simply stick to the protons?

There's more than meets the eye! *hums Transformers theme*

Another way to think about it would be through mechanical energy.
 
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Haha...you're right. That's always bothered me too.

So are these two phenomenon related?

Are the electrons actually bumping into the nucleus?

Optimus Prime in the nucleus.
 

Hurkyl

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(Disclaimer: I am far from an expert -- so take my words with a grain of salt)


I would imagine that an electron that managed to actually strike the nucleus would do so with far too much momentum to actually stay there. In fact, it could get no more stuck getting caught in the unoccupied orbital of the lowest energy!

But I imagine that "running into an atom" isn't analogous to a picture like one billiard ball striking another. I would expect it to be more like an electron getting too close and slingshotting around the atom (with some exchange of kinetic energy likely), or that it's just not physically meaningful to speak in any more detail than "an electron came in with some velocity, interacted with the atom, and left with a different velocity".
 
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I would imagine that an electron that managed to actually strike the nucleus would do so with far too much momentum to actually stay there. In fact, it could get no more stuck getting caught in the unoccupied orbital of the lowest energy!

But I imagine that "running into an atom" isn't analogous to a picture like one billiard ball striking another. I would expect it to be more like an electron getting too close and slingshotting around the atom (with some exchange of kinetic energy likely), or that it's just not physically meaningful to speak in any more detail than "an electron came in with some velocity, interacted with the atom, and left with a different velocity".
Yar! The electron's got all this energy to conserve. It would have to lose some if it wanted to stick around.

I'm not sure what it means to talk about collisions between the constituents of an atom, either. Hmm. In any case, here are a couple of interesting links that talk a bit about the subject:

https://www.physicsforums.com/archive/index.php/t-40541.html
http://www.mathpages.com/home/kmath538/kmath538.htm
 
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Thanks for the responses guys.

That does make sense Hurkyl...but why the slingshotting around it?

Here's another website that states the familiar theory:

http://micro.magnet.fsu.edu/electromag/electricity/resistance.html

Looks like a cool website but here is the same part that I don't understand:

As electrons move through the conductor, some collide with atoms, other electrons, or impurities in the metal.

I can understand electrons colliding with the fieldof another electron, not the electron itself. But if it collided with the rest of the atom, which should be positively charged, then the momentum would be too large for it to stick?

Or does it slingshot around it like Hurkly suggested? Does this have a relation to the same reason why electrons don't just cave into the nucleus in atoms?

So many questions lol.
 

Gokul43201

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As electrons move through the conductor, some collide with atoms, other electrons, or impurities in the metal.

I can understand electrons colliding with the fieldof another electron, not the electron itself.
The term "colliding with the atoms" is used loosely to imply that the mobile electrons are scattered by the potential (or the field, if you like that better) due to the lattice of ions that make up the conductor.

Electrons don't actually collide with each other like balls - they only scatter of each others' fields.

...or that it's just not physically meaningful to speak in any more detail than "an electron came in with some velocity, interacted with the atom, and left with a different velocity".
This is pretty close (to the typical propagator approach used by field-theorists), but a better description would note that, in a solid, each "free electron" actually interacts with the entire lattice of ions (not with individual atoms).
 
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Thanks for the response Goku.

By lattice of ions I assume you mean the kind of framework that exists between the atoms themselves. So the electrons are interacting with this entire lattice of ions.

What prevents them from attracting themselves to the ions (which I imagine to be positively charged since their electron has gone off conducting somewhere)?

And a natural followup to that question would be...how exactly do they interact?
 
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Things dont have to come in contact when undergoing a collision. For example, the gravitational slingshot technique used by satellites/spaceships is a nearly perfect elastic collision even though the ship never comes in contact with the planet. Energy is still transferred and the ship speeds up
 

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