# Relation of ionisation voltage vs. pressure for hydrogen

• A
T C
TL;DR Summary
Suppose a specific amount of hydrogen is enclosed in a metallic chamber and that is connected to high voltage source. The voltage is positive and is so high that all molecules inside the chamber have lost their electrons. I want to know whether the voltage can alter if pressure/density of the hydrogen changes.
Suppose we have specific amount of hydrogen gas enclosed inside a metallic chamber and that is connected to a very high positive voltage source. As the voltage is positive and that's so high that all the molecules inside the chamber lost their electrons and there is nothing but a nuclei gas is left inside the chamber. Now, in another instance, the same amount of hydrogen is enclosed inside a chamber but at a higher pressure/density. Now, I want to know whether the voltage necessary to strip all the molecules of their electrons will vary as the pressure/density is high but the amount/mass is the same.
My common sense tells me that as the energy necessary to move the electron away from is the nucleus is only dependent on the amount of charge present at the nucleus, therefore the pressure doesn't matter in the process. Just posting this to cross check whether what I have thought is correct or not.

Gold Member
Summary:: Suppose a specific amount of hydrogen is enclosed in a metallic chamber and that is connected to high voltage source. The voltage is positive and is so high that all molecules inside the chamber have lost their electrons. I want to know whether the voltage can alter if pressure/density of the hydrogen changes.

Suppose we have specific amount of hydrogen gas enclosed inside a metallic chamber and that is connected to a very high positive voltage source.
This doesn't sound right to me. Even if the chamber carries a huge charge, there will be no potential difference within it (if that's what you are actually describing) so why would the H atoms ionise?
It is true, however, that the pressure on a gas will affect ionisation a car spark plug with insufficient EHT voltage supplied may strike when there's no compression but may not strike at maximum compression. But, of course, under those conditions, there is a Potential Difference between the electrodes.

T C
I have already mentioned that it's positively charged. And how can an atom be positively charged without losing its electron?

Gold Member
Starting with a box of ions? I wasn’t clear about that.

willem2
Summary:: Suppose a specific amount of hydrogen is enclosed in a metallic chamber and that is connected to high voltage source. The voltage is positive and is so high that all molecules inside the chamber have lost their electrons. I want to know whether the voltage can alter if pressure/density of the hydrogen changes.
whether you start with ions, or with neutral hydrogen, if you use the inside of a hollow conductor, you will end up with neutral hydrogen.
If you start with neutral hydrogen, there will be no electric field inside conductor, so there's no reason for the hydrogen to ever become ionized.
If there are ions inside the conductor, they will repel, and hit the conductor and become neutral by picking up electrons.. A positive charge on a hollow conductor will be on the outside.

If you tried hooking up a sphere in an a large vacuum to a Vandergraaf generator and give the sphere a large positive charge, you would get some positive ions. It will be very hard to ionize all of the contents, because the positive sphere will repel the ions, they will bump into the walls of the chamber, where they will become neutral again.

T C
If you tried hooking up a sphere in an a large vacuum to a Vandergraaf generator and give the sphere a large positive charge, you would get some positive ions. It will be very hard to ionize all of the contents, because the positive sphere will repel the ions, they will bump into the walls of the chamber, where they will become neutral again
The inner walls of the container will also be positively charged. How can they supply electron to neutralise the ions?

willem2
The inner walls of the container will also be positively charged. How can they supply electron to neutralise the ions?
That is simply not possible. Inside a hollow conductor filled by a neutral material there will be no electric field, and thus no surface charges on it. If the conductor is filled with positive ions there will be a negative surface charge on the inside on it.
Use Gauss law on a surface through the conductor, around the hollow space. Since there is no electric field inside the conductor, the electrix flux through this surface is 0. Gauss law tells us there is now no net charge on the inside of the surface. The positive charge of the ions must be canceled by a negative charge on the inside of the surface.

T C
Use Gauss law on a surface through the conductor, around the hollow space. Since there is no electric field inside the conductor,
How can you say that there is no electric field inside the conductor?

Mentor
Now, I want to know whether the voltage necessary to strip all the molecules of their electrons will vary as the pressure/density is high but the amount/mass is the same.

https://en.wikipedia.org/wiki/Paschen's_law T C
This is for producing an arc between two electrodes. In my described scenario, there is only one kind of charge.

Mentor
This is for producing an arc between two electrodes. In my described scenario, there is only one kind of charge.
Can you draw a sketch? I think we are having trouble picturing what you want to do (or else what you want to do will not work). Thanks.

T C That's a very simple representation of what I want. The metallic container is connected to a positive source charge. I just want to know whether the hydrogen inside will also be ionised or not. And if the volume of the container be varied while keeping the amount of hydrogen inside the same, the voltage needed will vary or not.

Gold Member
A situation where all H atoms are ionized would require all the free electrons in the walls to be ionized too or there would be electrons available on the wall to neutralize the H ions.
Do some calculations to estimate the potential to which the box has to be raised to make this work.
Just use Q=CV and the number of atoms in the box X electronic charge. Assume a Capacitance of say 100pF

What happens at the molecular level doesn’t scale to the sizes you suggest.

Homework Helper
Gold Member
That's a very simple representation of what I want. The metallic container is connected to a positive source charge. I just want to know whether the hydrogen inside will also be ionised or not. And if the volume of the container be varied while keeping the amount of hydrogen inside the same, the voltage needed will vary or not.
You might see "coulombic explosion."

• • berkeman and sophiecentaur
Gold Member
No electrons to keep the container together!

The OP should consider just how much equipment is needed to produce a beam of Hydrogen ions, separated from their passenger electrons. The beam doesn't last long, left on its own.

A box of protons would be very handy and commonly used today, if it were obtainable.

• Bystander
T C
Just use Q=CV and the number of atoms in the box X electronic charge. Assume a Capacitance of say 100pF
Then I have only C, but how to determine Q? V can only be determined after that?

Gold Member
Number of atoms in a litre of a gas can be found from Avogadro’s number. I mole of gas at STP takes up about 22l. The Q you are after is pretty big. Thing is that if you are making a proposal, you have to find out some figures and it’s all easy to find.
Electric forces are enormous.

T C
The Q you are after is pretty big.
Maybe, but how to determine it?

Gold Member
Number of atoms times electronic charge. Number of atoms: Avogadro tells us that a mole of a gas contains 6e23.
I mole of a gas takes up 22.4 litres (standard temp and pressure)
The charge on each of those +ions is 1.6e-19 Coulombs so you can work out the total + charge in whatever volume you choose.
Off you go . . . . .
Once you have an estimate of that charge the Q=CV works.
Alternativey, use Coulomb's law for the force between two charges. This link has it all. The force to separate all the electrons from all the atoms - choose, say 1m can be worked out. See @Bystander 's post above. for a spoiler.

T C
The ionisation energy for a single hydrogen atom is known and multiplying that with Avogadro number is also known. That mean the amount of energy is 2.18 x 10-18 x 6.023 X 1023 Joule of energy that means 13.13 x 100000 Joule. That has to be divided by 1.6 x 10-19 x 6.023 x 1023 Coulomb of charge. If voltage (V) = Q/C, then it's not that much as per that formula.
For a single hydrogen atom, the energy needed to ionise is 2.18 x 10-18 J and the charge of a single electron is 1.6 x 10-19 Coulomb. By using that formula, the voltage needed to ionise a single atom is just 13.6 Volt.

Gold Member
The ionisation energy for a single hydrogen atom is known and multiplying that with Avogadro number is also known.
Your are doing the wrong calculation. Adding up all the individual ionisation energies is not enough. The ionisation energy for one electron and one proton is not the only energy involved. There are all the other charges, in the vicinity. They are all the same sign and repelling each other, in your model so there is no 'masking' which is what you get in a solid, liquid or even a gas. That is by no means the same situation as a large number of ions in the sort of proximity that you would get in the sort of experiment you describe. Take a Nebula, extending over perhaps a number of light years and you have a situation that would apply to your scenario.

For interest, just calculate the force between two 1C charges, separated by 1m. Use Coulomb's formula and re-think how your experiment could possibly be carried out.

• Bystander
T C
For interest, just calculate the force between two 1C charges, separated by 1m. Use Coulomb's formula and re-think how your experiment could possibly be carried out.
The force can be calculated. But, after that? How is the force related to the voltage?
And, by the way, now it seems to me that not the voltage, but rather the amount of energy is the factor here. Question is, whether the volume containing the amount of hydrogen can retain that amount of energy or not. A 1 kg lithium-ion battery can contain 180 kJ of energy. And, in this case, if the hydrogen is kept at 1 barA pressure, the volume is 22.4 litre and that contains 1313 kJ of energy. Hope that's not sufficient to make a coulomb explosion.

Gold Member
Just do the calculation for the force. Argue after you have a value.

T C
It's 8.988×109 N. Then?

Gold Member
It's 8.988×109 N. Then?
OK you got a value - good. "Then" think what a force of nearly 1010 represents. Your jaw should be dropping to the floor at this stage; it's not just a number. It's the sort of force that would be present inside a star, keeping the protons from flying away from each other.

The force would be equivalent of the Weight on Earth of a mass of 109 kg or about a million tonnes (a nonsense s scenario. That's the sort of force that we would be needed to contain this 1C in a container of around 1m (arm waving but the idea is there). Could we make a box like that? Physicists or Engineers have to keep their feet on the ground and always be aware of the orders of magnitude they are dealing with. (Cosmologists can get away with far bigger numbers. )

• Bystander
T C
One major flaw in this analysis is there is now way known to accumulate 2 coulomb of charge to small points and then put them 1 m apart. Before ionisation, the gas were at STP and that means the mean free path is 68 nm. After ionisation, I will consider to be the standard average distance between two ions. Now, what is the Coulomb force between two ions each having 1.6 x 10-19 Coulomb of charge and 68 nm apart from each other? My calculation tells me that the force is approximately 5 x 10-23 N.
To get the before calculated Coulomb force, 2 Coulomb of charges need to accumulated to a very small point.

Gold Member
To get the before calculated Coulomb force, 2 Coulomb of charges need to accumulated to a very small point.
No. They could be on the surfaces of two spheres. But my point was to show the orders of magnitude of the forces / energies that you are trying to discuss. If you could introduce a correction factor in any argument against what I wrote, would it really make a difference to the fact that the whole thing is impracticable (unless you have a handy star as a laboratory - OR if you scale it all down to the sort of scale that is obtained with existing experiments?

I already made the point that, if it could be done then it would have been and the work would have been in a ground breaking publication. One of the main problems in Fusion Experiments is how to contain a significant number of charged particles for long enough to achieve a nuclear reaction. It's the holy grail.

T C
But my point was to show the orders of magnitude of the forces / energies that you are trying to discuss.
The energy has already been calculated. And the force you want to mention depends on accumulation of charges. If the ions are evenly distributed, then the force can't be that high.
I already made the point that, if it could be done then it would have been and the work would have been in a ground breaking publication
That's the cliche argument used almost for eternity from any new thought. So, your main point is if it's possible, then it would have been done already.

• Bystander
Gold Member
That's the cliche argument used almost for eternity from any new thought.
And that's the cliche argument from someone who hasn't done the sums and who doesn't understand what's actually going on. I'm afraid you're over reaching yourself when you dismiss the knowledge base as you do. Do you think your idea is really "new thought"?

Potential is between all charges. You are only calculating the potential between a proton and an electron. Usually, there is a very small imbalance of charges. When there is the amount of isolated charge that you are proposing, you're in a totally different world to the one we live in.

T C
As per your explanation, if a 1 meter long hollow conducting box has just 2 Coulomb of charge, the force created by the Coulomb force will rip it up. And, so far, what math you have done other than calculating the force between two Coulomb charges?