Force between two atoms

[Little Bang]

Suppose we had a universe that contained only two atoms of hydrogen, separated by a few meters. Would there be a force between them that would cause them to come together and form diatomic hydrogen?

[Jay-qu]

Gravity would bring them together, but I dont think it would provide enough energy for the bonding to occur.

 

Gravitational potential energy [math]=\int\frac{2M_HG}{{r^2}}dr[/math]

[math]= -\frac{2M_HG}{r}[/math]

 

sorry just wanted to use some latex :hihi:

 

subbing in for G, mass of Hydrogen and r = 2;

 

[math]= -\frac{2(1.67*10^{-24})(6.67*10^{-11})}{2} - (-\frac{2(1.67*10^{-24})(6.67*10^{-11})}{5.29*10^{-11}})[/math]

[math]= -1.12*10^{-34} + 4.21*10^{-24)[/math]

[math]= 4.21*10^{-24}[/math] Jules

 

I beleive this is that max energy of the system, further analysis is been taken :)

[Little Bang]

Old Albert thought that there might be a relationship between electromagnetism and gravity and I wonder if his obsession with disproving the findings of quantum mechanics might have interfered with him actually seeing that relationship. If you look at the universe that I imagined, the proton of one atom would be attracted to the electron of the other atom and vice versa. The two protons would repel each other and the two electrons would do the same. I’ll call the two protons A and B. When the wave function of electron A is on the near side of B and the wave function of electron B is on the far side of B there is a force of attraction between them. There might be a specific distance of separation where the forces of repulsion and attraction exactly balance. It sure would simplify things if someone could find a relationship between gravity and electromagnetism.

[Jay-qu]

well, at distances of around 2m the difference between the repulsion force between the two protons, two electons and the attraction between opposite protons and electrons will be approximatly balanced, only when they get closer will the slight difference in these forces become noticeable. What I am trying to work out is the distance at which this will occur. I am having trouble thinking out where you must consider the electon to be.. do you smear it out because its moving so fast around the nucleus?

[Qfwfq]

do you smear it out because its moving so fast around the nucleus?

Definitely yes.

 

Calculations based on the charge distribution according to probability density, for a known state, give excellent results.

 

[math]\rho(\vec x, t)=e |\Psi(\vec x, t)|^2[/math]

[Jay-qu]

cool, does this equate to having a -e charge at the center of the atom?

[Qfwfq]

If the distribution is spherically symmetric, yes for the field outside it. This isn't usually the case and the net force between two overall neutral atoms is typically repulsive at short distances and slightly attractive at those a little more than a certain value, after which it drops rapidly toward zero. Details can be found in books on the structure of materials.

 

-e

:doh:

I forgot the - sign! I was talkin' about an anti-atom!

[hallenrm]

Suppose we had a universe that contained only two atoms of hydrogen, separated by a few meters. Would there be a force between them that would cause them to come together and form diatomic hydrogen?

 

I think that the possibility of the two atoms coming together to for a molecule will depend pn the energy with which they come close to one another. Once they are in rather close proximity, of the order of a few atomic radii, the probability of their forming a molecule will depend on the probability of the electrons to be on the opposite sides of the two atoms so that the coulombic attraction between the positive charge (on the protons) and the negative charge on the electron is the dominant force.:doh:

[Little Bang]

Hall, whether or not the two hydroen atoms unit is really incidental, I don't know why I even put that in the thread. I just think that there will always be an electromagnetic force between atoms and that force might be related in some way to what we describe as gravity. We can explain the workings of gravity extremely accurately but we have not been able to show how it works.

[hallenrm]

Dear Little Bang, I was reading this article in the New Scientist magazine, it appears that the author of this article is saying somewhat similar thoughts.

 

http://www.newscientist.com/channel/fundamentals/mg19225771.800?DCMP=NLC-ezine&nsref=mg19225771.800

[Little Bang]

Thanks Hall, I had to subscribe so that I could read the entire article. It was interesting and could be interpreted in the fashion I suggest. I don't like their idea of an extremely large graviton particle to explain their results. I've never been a big fan of some particle mediating the force of gravity.

[Jay-qu]

Thanks Q, I might do some calculations on that later today :hihi:

 

LB I am not sure what you mean by an EM force between atoms that might be related to how we describe gravity, could you try and re-iterate that for me so I can understand better :shrug:

[cwes99_03]

If the universe only contains these things, what causes the electron to travel around the proton?

Would the em forces of one atom cause a difference in the interaction between the proton and electron of the other atom?

 

We could think about this for a long time.

 

I would say that you are looking at a general set of possible distances which vary on the order of a few angstroms in distance from each other.

 

Set up the equations that define the forces for a certain set of arrangements of the atoms and their sub parts, then weight those equations with a rough percentage of how often the atoms would be in that configuration and you will have a rough approximation.

 

I think what you'll eventually be looking at is a wave law of attraction saying that on average the attractive force between the two atoms is 0 to whatever magnitude you want to calculate to (realizing that to calculate to the nano Newton you'd have to have a bunch more geometric arrangements for how the protons and electrons are respectively arranged with more accurate weighting of how often they might occur in that arrangement, and probably a supercomputer to help you calculate those values.

 

This is a good one for the philosophy truly sucks thread, as I don't see much value in thinking about this. But that might only be how little I can think about its applications.

[Little Bang]

Jay

The atoms A and B that I referred to in post #3. The proton of atom A will be attracted to the electron of atom B and the proton of B to the electron of A. Unlike charges attract, That attraction will decrease over distance and I suspect that the decrease wil be exactly like the decrease of gravity over distance.

[Jay-qu]

Well yeah that is true, its the inverse square law, the force between them decreases as a function of [math]\frac{1}{r^2}[/math] that applies for both gravity and electomagnetic forces.

[Qfwfq]

But the overall force doesn't go inverse square. That between the opposite charges is orders of magnitude larger than the gravitational attraction between them but is offset by the repulsion.

 

Thanks Q, I might do some calculations on that later today

Not an easy undertaking, it implies estimating how the orbitals are affected when the distance is not too many times the Bohr radius, which is where the force can be appreciable. Complicated.

 

My memories are vague but I think I only read that such computations had been done but without such a detailed description of the method; I'm really not sure even if you would succeed with estimates based on first order terms, with more elaborate perturbative methods or with iterative number crunching. Don't be disappointed if you just find yourself utterly lost.

[Jay-qu]

dont worry Im not dissapointed, the fun is in trying :shrug: