# I Thermal motion of an ionised gas molecule in an electric field

1. Mar 17, 2017

### pranj5

What I want to discuss here is what happens to the thermal velocity when an ionised gas molecule has been put into an electric field. Due to the charge (e) and potential difference (V), how much velocity has been gained by the ion can be calculated easily.

eV = ½mv2

Where e is the charge of the ion, V is the potential difference, m is the mass of the ion and v is the velocity gained due to the potential difference.

From the formula above, it can be easily calculated that

v = https://www.physicsforums.com/file:///C:/Users/Payel/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif [Broken]

Now, question is, the gas molecule already has its velocity due to the temperature of the gas that is the Root Mean Square velocity of molecules at that temperature. I want to know whether the velocity gained by the potential difference will be added to the velocity or not.

Last edited by a moderator: May 8, 2017
2. Mar 17, 2017

### John Park

In general, yes, a charged particle, whatever its velocity, will be accelerated by an electric field. But for an ionised molecule in a gas the situation is a bit more complicated, because after it has traveled one mean-free-path the ion is likely to collide with another molecule. At that point its velocity will be randomised. With gases at normal pressures, the potential difference corresponding to a physical distance of one mean-free-path may be quite low, and in those cases the field would produce a slight heating of the gas.

3. Mar 20, 2017

### Khashishi

It's analogous to a column of gas in a gravitational field. In thermal equilibrium, the bottom isn't any hotter than the top; it's just at higher pressure.
On the other hand, if the density is very low, such that collisions are infrequent, then the particles at the bottom are moving faster than the particles at the top, but you would not have a Maxwell-Boltzmann distribution so the term thermal velocity would not be appropriate.

4. Mar 26, 2017

### pranj5

How that can be I just simply can't understand.
Thermal velocity simply means that the random velocity of molecules of gases. When a gas molecule is ionised and put inside an electric field, how can the thermal velocity just disappear?

5. Mar 26, 2017

### ZapperZ

Staff Emeritus
Please look up the Drude Model.

What you are asking is identical to the motion of conduction electrons in a standard, simple metal. You need to know a bit of statistical mechanics and the Boltzmann distribution. Unfortunately, your posts do not say much on whether this is something you already know, or capable of comprehending.

Zz.

6. Mar 26, 2017

### pranj5

Being a student of physics, I know both. But ionised molecules are different from conduction electrons. Electrons are almost massless and their thermal momentum is negligible in comparison to motion due to electric field. That's not the case for an ion.

7. Mar 26, 2017

### ZapperZ

Staff Emeritus
I looked again at your first post, and nowhere in there did you indicate that gravitational field plays a role. All you said was "...I want to discuss here is what happens to the thermal velocity when an ionised gas molecule has been put into an electric field..." Did I miss it?

It is imperative that you state clearly the parameters of your question. Both your first post and the title made no indication that you are also considering the weight of these ions. Otherwise, I feel like I'm chasing a moving target.

Zz.

8. Mar 26, 2017

### pranj5

When discussing gas laws, it has been considered that the weight of molecules is so small in comparison to their velocity that gravity plays actually very little or no part here. That's as far as I know.

9. Mar 26, 2017

### ZapperZ

Staff Emeritus
So then, why is this any different than the conduction electrons if the weight is ignored? Do you want to care about the minuscule effect of gravity or not?

Zz.

10. Mar 26, 2017

### pranj5

You haven't noticed that in case of electrons, I have used momentum, not mass.

11. Mar 26, 2017

### ZapperZ

Staff Emeritus
How does this answer my question?

This is like pulling teeth.

Zz.

12. Mar 27, 2017

### pranj5

Gas molecules have little mass but their velocity is high. That means we can neglect gravity as the mass is small but not the momentum as the velocity is sufficiently high.