Solving the Mystery of Hydrogen Atom Ionization

[dreamspy]

Here comes a pretty hard question, which not even my QM teacher has been able to answer.

When we think about one hydrogen atom, and put it in an electric field along the z-axis $$\bar E = \bar e_z E$$. Then the potential for a hydrogen atom will look like this:

$$U = -\frac{e^2}{4\pi \epsilon_0 \sqrt{x^2+y^2+z^2}} - eEz$$

This looks approximately like this:

Here the blue line is the potential. Now let's say that the energy of the electron is the red line. If we let enough time go by, the electron should tunnel out of the atom and drift of into infinity in the z-direction, due to the applied electric field.

According to this then if one takes a gas of hydrogen atoms, and encloses them in a container. Then applies the electric field E, the gas should ionize and form a plasma, given enough time...

But in the lab this doesn't happen.

Why?



Regards
Dreamspy

 

[Mapes]

Then applies the electric field E, the gas should ionize and form a plasma, given enough time...

Why would the gas necessarily form a plasma? Why wouldn't the ionized proton accelerate to the cathode, pick up an electron, and desorb back into the chamber as an uncharged atom?

Under certain circumstances a plasma might form, but it's not inevitable just because one is applying an electric field.

 

[dreamspy]

You are right. If the atoms ionize, they should go towards the -z direction, and probably meet a free electron from another ionized atom, and combine back to a uncharged atom. But when the atoms at the edges of our container ionize, the resulting electrons can't meet a proton to desorb into (if they are on the right side of the container). The same goes for the protons, but just if they are on the other side of the container. Given enough time, shouldn't we have a cloud of electrons on one side and a cloud of ionized protons on the other side?

Could the reason why this doesn't happen be because of thermal movement of the particles?

 

[Mapes]

Why would they collect into a cloud? Why wouldn't they contact the solid, conducting cathode and anode?

 

[willem2]

According to this then if one takes a gas of hydrogen atoms, and encloses them in a container. Then applies the electric field E, the gas should ionize and form a plasma, given enough time...

But in the lab this doesn't happen.

Why?

The electric field is much too weak compared to the forces holding an atom together, and the tunneling rate will be essentially 0. That graph is rather misleading, and the asympotes should be nearly horizontal.

 

[dreamspy]

But if the electric field would be strong enough, we should get plasma?

 

[Dadface]

If ionisation occured,for example by the passage of a radioactive particle,then this could give rise to an ion avalanche and a plasma in the vincinity of this avalanche.This is observed with sparking in the air such as lightning where the electric field needed is the order of 3.6 million volts per metre.Many such sparks are momentary,the light from the spark being produced when the ionised/excited atoms recover and the sound from the spark being due to the air getting heated and setting up a pressure wave.To maintain sparking and any plasma the field needs to be maintained.Overall I think that with high intensity fields some quite complicated mechanisms go on with atom excitation ionisation and recovery plus field emission,secondary emission(and possibly even photoelectric emission)from the electrodes.

 

[dreamspy]

Why would they collect into a cloud? Why wouldn't they contact the solid, conducting cathode and anode?

I'm not sure why you are talking about anodes and cathodes? The container could be a complete dielectric, and the source of the electric field shouldn't matter.

 

[dreamspy]

The electric field is much too weak compared to the forces holding an atom together, and the tunneling rate will be essentially 0. That graph is rather misleading, and the asympotes should be nearly horizontal.

Yes you are right, the graph is highly exaggerated. But still, does the slope of the asympotes matter? That should only affect the time needed for the electrons to tunnel, right?

 

[dreamspy]

If ionisation occured,for example by the passage of a radioactive particle,then this could give rise to an ion avalanche and a plasma in the vincinity of this avalanche.This is observed with sparking in the air such as lightning where the electric field needed is the order of 3.6 million volts per metre.Many such sparks are momentary,the light from the spark being produced when the ionised/excited atoms recover and the sound from the spark being due to the air getting heated and setting up a pressure wave.To maintain sparking and any plasma the field needs to be maintained.Overall I think that with high intensity fields some quite complicated mechanisms go on with atom excitation ionisation and recovery plus field emission,secondary emission(and possibly even photoelectric emission)from the electrodes.

Given a strong enough field, then stating that a simple plasma should form is maybe a little to much of a simplification? If we get a soup of electrons and ionized hydrogen atoms we will have attraction and negative attraction between particles, and this state can hardly be stable.

 

[Dadface]

Given a strong enough field, then stating that a simple plasma should form is maybe a little to much of a simplification? If we get a soup of electrons and ionized hydrogen atoms we will have attraction and negative attraction between particles, and this state can hardly be stable.

What do you mean by "simple plasma"?Electrostatic interactions play a part in the dynamics of plasmas so what do you mean when you write that "this state can hardly be stable"?

(Are you referring to a non neutral plasma eg a beam of protons?)