When is a particles charge spread out?

In summary, the charge of an electron in quantum mechanics is not always spread out over the area where its position is uncertain. Its charge density at any given point is proportional to the probability of finding the electron in that vicinity, as described by the wave function. This can lead to stable systems, such as the H_{2}^{+} molecule, where the electron acts as a glue between two protons. However, according to Heisenberg's Uncertainty Principle, it is not possible to determine the velocity and position of an electron simultaneously.
  • #1
box
12
0
Correct me if I'm wrong but i think in quantum mechanics there are times when the charge of an electron is spread out in the area where its positon is uncertin, such has a ground state hydrogen atom. And there are times when even though the electrons position is unknown over a certin area the charge is not spread over the whole area but is modeled to be in a more certin spot. Such has when you have two protons and one electron that is equaly likely to be orbiting both of them, The protons don't repell each other because the electrons charge is only on one of them and not evenly spread betwen the two. So am I right in saying that sometimes an elecrons charge is spread out over the area were its position is uncertin and somtimes its not? If so what determines if its the former or the latter?
 
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  • #2
aS PER hEISENBERG'S uNCERTAINITY pRINCIPLE , YOU CANNOT POSSIBLE DTERMINE THE VELOCITY AND POSITION OF AN ELECTRON simultaneously..

Imagine this , suppose you witness a fast moving electron and wth great precision you pin it up against the wall with a pin, before pinning it up , the electron was so fast that you couldnot determine its position and now you pinned it up in hope to determine the position correctly, now when you see the pinned-electron , it spreads itself and looks more like a cloud rather than a particle , this is what happens as per Heisenberg's..

More at :
http://www.doxlab.co.nr/
 
  • #3
box said:
Correct me if I'm wrong but i think in quantum mechanics there are times when the charge of an electron is spread out in the area where its positon is uncertin, such has a ground state hydrogen atom. And there are times when even though the electrons position is unknown over a certin area the charge is not spread over the whole area but is modeled to be in a more certin spot. Such has when you have two protons and one electron that is equaly likely to be orbiting both of them, The protons don't repell each other because the electrons charge is only on one of them and not evenly spread betwen the two. So am I right in saying that sometimes an elecrons charge is spread out over the area were its position is uncertin and somtimes its not? If so what determines if its the former or the latter?

Ever heard of overlap integral,or charge exchange integral...?My guess is "no".

Daniel.
 
  • #4
For nonrelativistic QM, the square of the electron's wave function times the electric charge is the spatial charge density, which in turn is determined by the specific dynamics of the electron's system. For relativistic QM the same is true -- up to a few technical matters.

There are no stable two-proton one or two electron systems. Replace a proton by a neutron, and you are talking helium city, a stable place.

Regards,
Reilly Atkinson
 
  • #5
I think he meant a Hidrogen molecule.That's pretty stable.And it has no neutrons.


Daniel.
 
  • #6
reilly said:
For nonrelativistic QM, the square of the electron's wave function times the electric charge is the spatial charge density,

This is what I guessed but when reading the Feynman lectures on physics vol 3 chapter 10 he talks about a two state system made up of two separated protons with one electron that's orbiting a different proton in each state. Now when you have a superposition of both states I would guesse the electrons charge would be spread out over both protons (it seemes to me your statement above says this) but then I would think the protons would repel each other. However Feynman says the protons don't repel because one proton is nutrual because of the electron orbiting it. (well they did repel or atract but not because both protons were positive)
Sorry if what I wrote dosn't make a lot of sense.
 
  • #7
Since you're talkig about the H_{2} molecule,words won't do.Mathematics should come first.So how about you do some reading & caculations...?The proton may be screened,but not neutral.

Daniel.
 
  • #8
Hello box,

it seems strange that a [itex]H_{2}^{+}[/itex] molecule exists, because as you mentioned one would think that the protons repel each other. However QM calculations indeed show that it is stable only because of that one electron.

Why is this so? You can think of the electron acting as glue between the protons (or as dextercioby said the proton's charge is screened by the electron's negative charge)
 
  • #9
Edgardo said:
Hello box,

it seems strange that a [itex]H_{2}^{+}[/itex] molecule exists, because as you mentioned one would think that the protons repel each other. However QM calculations indeed show that it is stable only because of that one electron.

Why is this so? You can think of the electron acting as glue between the protons (or as dextercioby said the proton's charge is screened by the electron's negative charge)

And this is a good opportunity to add that that single electron in between the two H nucleus is actually in a Schrodinger Cat-type state where it is "localized" at BOTH nucleus simultaneously! [See? All of physics/QM are really connected!] The electron is being spread out over both nucleus in such a way that the overlap of its location from both nucleus causes a bonding state and an antibonding state of the ground state. This is something chemists have seen way before QM, but it had to wait till QM for there to be an explanation for the existence of such a state.

Zz.
 
  • #10
To answer the original question :
box said:
So am I right in saying that sometimes an elecrons charge is spread out over the area were its position is uncertin and somtimes its not?
No, that's not right. As explained previously, the charge density at some point [itex]\vec{r}[/itex] scales with the probability of finding the electron in the vicinity of [itex]\vec{r}[/itex].

[tex]\rho(\vec{r}) = e|\psi({\vec{r})|^2 [/tex]
 

1. What is meant by a particle's charge being "spread out"?

When a particle has a charge, it means that it has an electric field around it due to the presence of electrically charged particles. When we say that a particle's charge is "spread out", it means that the distribution of this electric field is not concentrated at a single point, but rather spread out over a larger area.

2. How can a particle's charge be spread out?

A particle's charge can be spread out in two main ways. The first is through the presence of multiple charged particles within the particle itself, resulting in a net charge that is distributed throughout the particle. The second is through the influence of external electric fields, which can cause the particle's charge to spread out in response to the field's strength and direction.

3. What are the implications of a particle's charge being spread out?

A particle's charge being spread out can have various implications depending on the context. In some cases, it may result in a weaker overall electric field compared to a concentrated charge, as the field is distributed over a larger area. It can also affect the interactions between particles, as the distribution of charge can impact the strength and direction of electric forces between them.

4. Can a particle's charge be both spread out and concentrated at the same time?

Yes, a particle's charge can be both spread out and concentrated at the same time. This is because the concept of a "spread out" charge refers to the distribution of the electric field, while the concept of a "concentrated" charge refers to the net charge of the particle. So, a particle can have a concentrated net charge while also having a spread out distribution of this charge.

5. How is a particle's charge spread out or concentrated measured?

The distribution of a particle's charge can be measured through various techniques such as electric field mapping and charge density measurements. These methods involve measuring the strength and direction of the electric field at different points around the particle or determining the amount of charge per unit area of the particle. The net charge of a particle can be measured using a variety of instruments, such as an electroscope or a charge detector.

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