Ionizing a sphere till it explodes?

[BrianConlee]

This is a double question.

Can I ionize an object by attaching one end of a high voltage source to it? (assume it is not grounded, perhaps suspended by a insulator). I'm thinking a greatly oversized capacitor situation.

Ok, now the real question. I have a metal sphere. Just say 10 cm radius for the sake of argument. Anyways, I begin to remove the electrons from the atoms in the sphere. We'll say it's a lead sphere. (82 protons, 82 electrons per atom). I continue this process, and I'm preventing any electron leakage back into the sphere from an outside source.

Is there a point where the positive repulsion of the atoms with each other would cause the sphere to explode? Is there a way to calculate what point this would happen?

Ok, three questions:
I know the outermost electrons can peel off relatively easily, but how much energy am I going to need to get all 82?

Thanks so much.

(I love thought experiments)

 

[Brin]

I am just going to try to answer everything at the end.

This is a double question.
Can I ionize an object by attaching one end of a high voltage source to it? (assume it is not grounded, perhaps suspended by a insulator). I'm thinking a greatly oversized capacitor situation.

Ok, now the real question. I have a metal sphere. Just say 10 cm radius for the sake of argument. Anyways, I begin to remove the electrons from the atoms in the sphere. We'll say it's a lead sphere. (82 protons, 82 electrons per atom). I continue this process, and I'm preventing any electron leakage back into the sphere from an outside source.

Is there a point where the positive repulsion of the atoms with each other would cause the sphere to explode? Is there a way to calculate what point this would happen?

Ok, three questions:
I know the outermost electrons can peel off relatively easily, but how much energy am I going to need to get all 82?

Thanks so much.

(I love thought experiments)

What you're talking about is ionizing the individual atoms in lead. Ionization occurs when the electrons are removed from the atoms, it's equal to the energy of the electron around the nucleus. So for Hydrogen its like -13.6 eV.

Uh, to completely ionize lead? I... don't know. I think the first level is easier to ionize than hydrogen, but it gets progressively harder with each of their binding energies. I mean, think about the potential between 82 protons and 1 electron, phew.

Just for fun I used Bohr like arguments to calculate the total energy of an electron in the very first energy level with all other electrons stripped. I found it had a total energy of
-183981 electron volts. It also had a relativistic velocity, which I ignored. I guess in theory you could gather up the proper equations and run it through Mathematica and get a total sum. I won't bother doing this, as I think that's already a pretty unreasonable amount of energy.

If you really want to ionize a big ball of some sort, why not just add electrons like a van-de-graaf machine?

The total potential on one of those is limited by the dielectric of air. You could in theory surround it with a super dielectric, however, I don't think this will ever cause it to explode :(

Note that the most amount of potential you can get on a big van-de-graaf is V=R*E where R is the radius of your ball, E is the max e-field before you start ionizing whatever your dielectric is.

The pressure on the outside of a conductor is given by Griffiths on page 103 as
P=(E^2)*epsilon/2
where epsilon is the permittivity of free space.


If you can accurately define what kind of pressure would cause an explosion for you, I would think that you could plug that into there, figure out what the E field is. Then take that, figure out what kind of charge collection you would need, then figure out what kind of dielectric would give that kind of thing to you.

After all that, calculate your electric bill. It's about 0.14 dollars per kWh where I'm at. You'll probably be in Tier 3 region though, so 0.25 per kWh :P

 

[BrianConlee]

Thanks so much for taking the time to answer my question.

You're correct, I do want to ionize the atoms. You're absolutely right about the increased binding energy, and it is quite amazing. The low fruit of this process is certainly the electrons in the outermost shell.

Would the atoms begin ionizing if I attached a voltage to the sphere? Not putting the sphere in a circuit. I realize this would just run current through the sphere, but rather just one end of a voltage source.

Maybe not to completely ionize lead, but say pic off maybe an average of 40 electrons? I could probably do some optimization to calculate the lowest energy cost to produce the strongest possible positive charge.

I do want to ionize a big ball, but not with a negative charge. I want it to have a positive charge. But with the van-de-graaf, I was considering some method of applying static electricity.

To add to the thought experiment, we could say the sphere is isolated in a vacuum, and the distance to the walls of the vacuum chamber could be large enough to withstand considerable voltage.

What I was wondering also was it even possible that enough electrons could be removed from the ball, so that the positive charges on the nuclei would push each other apart?

Thanks again so much for taking the time to answer.

 

[Buzzworks]

It may be possible if you can forcefully and rapidly 'inject' ions inside a sphere made up of an insulating material. Like those high energy ions coming from a particle accelerator.

But a conducting sphere such as lead? Maybe never, as the voltage gets higher, the ions will just migrate to the outside surface of the sphere as the ions won't have a hard time doing such because of abundance of free electrons in any conducting material.

 

[Brin]

Thanks so much for taking the time to answer my question.

You're correct, I do want to ionize the atoms. You're absolutely right about the increased binding energy, and it is quite amazing. The low fruit of this process is certainly the electrons in the outermost shell.

Would the atoms begin ionizing if I attached a voltage to the sphere? Not putting the sphere in a circuit. I realize this would just run current through the sphere, but rather just one end of a voltage source.

I'm not entirely certain, but I would assume that any source you were to use to create the high potential would need to be higher potential and paradoxically small enough to supply the potential without discharging prematurely.

Also, this is just a bad way to essentially "ground" your sphere. It wouldn't ionize anything though.

Maybe not to completely ionize lead, but say pic off maybe an average of 40 electrons? I could probably do some optimization to calculate the lowest energy cost to produce the strongest possible positive charge.

Still a ridiculously costly thing. I also doubt, highly, that it has ever been done. You'd probably need to create some sort of lead gas, ionize the hell out of it, and watch as it basically never undergoes a state change to a solid ever again.

I do want to ionize a big ball, but not with a negative charge. I want it to have a positive charge. But with the van-de-graaf, I was considering some method of applying static electricity.

Why positive?

To add to the thought experiment, we could say the sphere is isolated in a vacuum, and the distance to the walls of the vacuum chamber could be large enough to withstand considerable voltage.

This still doesn't solve your discharge problem. The field will still discharge, and even sooner than when it is in air. I think the electrostatic pressure equation above is actually just the result of electrons pushing up against each other, squeezing each other out. There comes a time when the surface is saturated with free electrons, and they pop off.

What I was wondering also was it even possible that enough electrons could be removed from the ball, so that the positive charges on the nuclei would push each other apart?

Thanks again so much for taking the time to answer.

See, here I would assume that after stripping of enough electrons (say 40) the effective charge of each atom goes from zero (neutral atom) to +42, in which case, the repulsion is way greater than say 2 protons pushing away from each other. You'd probably just have an energetic fermi gas, right?


One other thought, I'm really tired and probably haven't been entirely thorough in my above explanations, but if you could maybe figure out the mechanism for delivering electrons to the van-de-graaf, consider a supply of positrons. This is only meant to be a theoretical circumstance, in reality though I have a feeling that positively ionizing a big ball would be very difficult. To really give you a definitive and calculated answer though, I'd need to think a little longer about what electrons in conductors are (i.e. they are free electrons flyin' about over atoms at the very surface of the material) and we're talking not only removing those free electrons, but also ionizing the atoms that make up the very structure of the conductor. I can't help but think this so-called structure would very quickly fall apart. But that's just all according to the cartoon version of physics I have in my mind when it comes to solid-state stuff.

 

[BrianConlee]

FASCINATING. My imagination is going in circles here.

But a conducting sphere such as lead? Maybe never, as the voltage gets higher, the ions will just migrate to the outside surface of the sphere as the ions won't have a hard time doing such because of abundance of free electrons in any conducting material.

When you say the ions will migrate, are you saying the actual atoms will move to the outside, or will the electron holes migrate?

I'm not entirely certain, but I would assume that any source you were to use to create the high potential would need to be higher potential and paradoxically small enough to supply the potential without discharging prematurely.

Also, this is just a bad way to essentially "ground" your sphere. It wouldn't ionize anything though.

Still a ridiculously costly thing. I also doubt, highly, that it has ever been done. You'd probably need to create some sort of lead gas, ionize the hell out of it, and watch as it basically never undergoes a state change to a solid ever again.
Why positive?

I want positive because charging it negatively is more about adding electrons to the sphere, and I guess that's a relatively simpler concept.

What if we look at it this way. A large plated capacitor, fully charged. We pull it apart and curl one of the plates into a sphere. (you could have the plates the shape of a sphere sliced up and put flat, the curved triangles)

Do you then have a sphere positively charged?

Brin, I think in a very similar cartoonish manor! i know EXACTLY what you mean lol.

Is there some electrical method to ionize the sphere besides trying to rely on the photolectric effect, heating it, or accelerating individual atoms?


If you want, you could hollow the sphere, put an overall negative charge on the outter surface and the corresponding positive charge on the inner surface? Or Vise Versa.

Could something like that be more feasible maybe? Instead of charging the entire sphere, you move the balance of charge and direct it to one part of the sphere.

Another consideration I had was Two spheres, one encompassing the other, And treat them like two capacitor plates, with a good dielectric in between. Then you could make the inner sphere negatively charged and the outside sphere positively charged? (vise versa?)

Thoughts?

 

[MagnetDave]

Brian,

What's your motive here, out of curiosity?

As far as the "exploding" sphere, that won't happen. Catastrophic things like that usually don't. What you need to do is envision the process. As you build up charge, you eventually get to a point where there repulsion forces START to become too much. Then, an atom flies off, then another, and your sphere slowly turns to vapor.

BUT- that's assuming you're in a vacuum. If you're in an atmosphere, the buildup of charge will cause the gas the area to ionize and give up electrons, neutralizing your process. OR, if you're really fast, it will strike an arc and give you a lightning bolt. The point is - a lot of other process kick in before the explosion. This is not to say it can't happen. Quite the opposite...

I HAVE seen conductors explode. In our industry we rely heavily on dumping large, fully charged capacitors into dead shorts, and eventually aging copper under massive pulse loads does explode, blowing copper dust everywhere in a very unpleasant-to-be-near process.

 

[BrianConlee]

You could say my motive is curiosity. I really enjoy thought experiments to help bolster my understanding of physics to the extreme. That's where all the fun is.

Ok, let's take the same sphere, how much charge separation can we accomplish?

You're making the inside of a hollow sphere positively charged, and migrating the electrons to the surface.

I was kinda imagining the ions becoming so positive they got ejected. But I can definitely see what you're saying with the dumping... the real sudden accumulation of charge. Instead of the gradual.

I'm really just trying to understand the limits of reality... and then how to surpass them, at least "in theory" as Mr. Data would say.

 

[sophiecentaur]

I'm interested that no one has introduced the words Coulomb Force and Plasma into this argument.
The force to separate just 1C of + charge from 1C of - charge by 1m is pretty big (easy to work out). The easiest way to keep a mass of ions and electrons in equilibrium would be to get it hot enough and turn it into a plasma (again, not difficult to establish the required temperature, which could tell you the energy needed).

 

[BrianConlee]

sophiecentaur you're absolutely right... only you're neglecting one detail I pointed out earlier.

:)

I wanted to have a solid lead ball ionized.

Although, this does raise an interesting question:

Could you heat the lead, ionize it, and the cool it somehow back to a solid while retaining it's ionized state? Although I don't think this would be practical.

I believe it was pointed out though that the positive charges between the lead atoms would "throw" them out from the solid. This was why I was considering moving the positive charge to one part of the sphere and the negative charge to the other... like a giant capacitor.

 

[Buzzworks]

I believe it was pointed out though that the positive charges between the lead atoms would "throw" them out from the solid. This was why I was considering moving the positive charge to one part of the sphere and the negative charge to the other... like a giant capacitor.

You can simply induce static electricity to make that happen - at the point of voltage break down.

But since you want an extreme one, you'll need to put them in a high pressure gas chamber with 100% pure (densest known gas in existence) inside it. One such gas is sulfur hexaflouride and the other one is even denser but *dangerously* radioactive - forgot what it is.

I assume the setup would involve an insulated lead ball placed between charged electrodes with just high voltage enough and/or close enough to be at or near voltage break down of high pressure sulfur hexaflouride gas.

I think you can also do it away with very powerful magnetic fields to try to induce high electrostatic gradient in combination with techniques used above.

 

[BrianConlee]

how would you induce the static electricity? in a method similar to a van de graff?

Is it possible, (hopefully not too much to ask) for a brief diagram of what you're proposing?

I don't want to invite scrutiny, but at least perhaps assure my imagination of what you're describing is accurate. (doesn't have to be the mona lisa, lol)Thanks so much!