Monatomic gases degrees of freedom

[Danijel Gorupec]

in monatomic gases, why isn't atom rotation taken as one possible degree of freedom - that is, why energy cannot  be stored in atom rotation? Is this degree of freedom non-existent or just frozen?

Google finds many answers, but they seem to differ. Some say that rotation is simply not physical (whatever it means), some say that a single quantum of rotational energy is much larger than available energy at normal temperatures...

[swansont]

Atoms are symmetric. How would you know they are rotating? What would that “look” like?

From another perspective, how would you give the atom the angular momentum it would have to have, and how would it manifest itself?

[Danijel Gorupec]

12 hours ago, swansont said:

Atoms are symmetric. How would you know they are rotating? What would that “look” like?

From another perspective, how would you give the atom the angular momentum it would have to have, and how would it manifest itself?

Hmm... I guess, one way to know that they are rotating is by measuring heat capacity of the gas (and from this we know that they are NOT rotating). But this is a proof of neither, imo.

Because atoms are not solid bodies, I guess that their rotation would mean a net non-zero rotation of all the parts. So, when thinking about your last sentence, I guess that my question should actually be: why in monatomic gases, thermal excitation do not cause change in orbital momentum of atom's external electrons? Is this a better way to ask?

(I really am not sure what I am talking about - I am just learning the new stuff here).

[swansont]

3 hours ago, Danijel Gorupec said:

Hmm... I guess, one way to know that they are rotating is by measuring heat capacity of the gas (and from this we know that they are NOT rotating). But this is a proof of neither, imo.

Because atoms are not solid bodies, I guess that their rotation would mean a net non-zero rotation of all the parts. So, when thinking about your last sentence, I guess that my question should actually be: why in monatomic gases, thermal excitation do not cause change in orbital momentum of atom's external electrons? Is this a better way to ask?

Changes in their angular momentum can be measured, but in QM this is not physical spinning.  In e.g. hydrogen, you could flip the hyperfine state, which is the 1420 MHz transition. The only way to give the electron orbital angular momentum would be to have it jump from the 1S to the 2P level, which requires a 10.2 eV photon or from a collision (which is not something you see very much in a thermal system). But that doesn't involve any physical spinning of the atom. That notion is inconsistent with QM.

[John Cuthber]

39 minutes ago, swansont said:

.  In e.g. hydrogen, you could flip the hyperfine state, which is the 1420 MHz transition.

You can get that transition, but the classical interpretation (i.e. the one involving an actual rotation) is that it is only the electron which spins, not the whole atom.

 

[swansont]

21 minutes ago, John Cuthber said:

You can get that transition, but the classical interpretation (i.e. the one involving an actual rotation) is that it is only the electron which spins, not the whole atom.

 

Yes, precisely. The electron spin flips, but that's it. No atomic motion. There is no other interaction available to the ground-state atom until you get to 10.2 eV.

 

[Danijel Gorupec]

Ok, I see that the 'rotating atom' is a problematic idea.

Some back of the envelope calculations, if I did it correctly: Average kinetic energy of a gas particle at 300K is about 0.04eV; The 1420MHz photon has about 6 micro-eV.

Therefore, the thermal motion cannot excite an electron in a hydrogen atom from 1S to 2S, but it should be able to flip-flop its spin easily. Is this happening in a real gas? (I guess it might be happening in monatomic hydrogen, but not sure about H2 - probably spin cannot be flipped in H2?)

Next, if we are dealing with heavier atoms (say argon) then I expect external electrons have smaller difference between energy levels - possibly comparable to 0.04eV. Should I then expect that those electrons in argon contribute to the heat capacity of argon gas?

 

4 hours ago, swansont said:

... or from a collision (which is not something you see very much in a thermal system).

I guess you are referring to the very high (10.2eV) temperature needed - not that there is some other limitation why collisions are unable to excite quantum states?

[John Cuthber]

At 100,000 K a transition needing 10.2 eV would be perfectly acceptable, but it still wouldn't be a rotation

[Danijel Gorupec]

3 minutes ago, John Cuthber said:

At 100,000 K a transition needing 10.2 eV would be perfectly acceptable, but it still wouldn't be a rotation

I understand... I abandoned the idea that rotation of atoms can be used as energy storage (to aid heat capacity). I can accept that atom rotation is not a thing.

I am investigating now if electron energy transitions in some heavier atoms are small enough to count as 'unfrozen' degrees of freedom for heat storage.

 

[Carrock]

1 hour ago, Danijel Gorupec said:

Therefore, the thermal motion cannot excite an electron in a hydrogen atom from 1S to 2S, but it should be able to flip-flop its spin easily. Is this happening in a real gas? (I guess it might be happening in monatomic hydrogen, but not sure about H2 - probably spin cannot be flipped in H2?)

H spins can normally be easily flipped:

Isospin monatomic hydrogen is interesting and unique in that two atoms cannot combine into H2 since with isospin electrons that combination is energetically unfavourable due to Pauli exclusion.

Let it warm up a little and some spins will be thermally flipped; heterospin H atoms will combine into H2 with enormous energy release...

H2 atoms have no net spin so spin can't be flipped.

Offtopic, liquid isospin monatomic hydrogen is so chemically unreactive that it is supposed (unlike helium) to be impossible to freeze.

Multielectron atoms which would normally be diatomic can't be made stable in this way. e.g. isospin fluorine atoms would have plenty of opposite spin electrons for interatomic interactions.

 

I read (most of) that in Scientific American years ago and haven't been able to find a good reference since, but it all seems very plausible.....

An earlier Eagle comic had a more limited discussion, with Dan Dare accidentally blowing up a few spaceships, which inspired my interest.

[Danijel Gorupec]

On 10/31/2019 at 12:32 AM, Carrock said:

I read (most of) that in Scientific American years ago and haven't been able to find a good reference since, but it all seems very plausible.....

Yes, it makes sense to me too... In fact, I guess that the spin-flipping due to the thermal agitation is the reason why paramagnetic materials stop being paramagnetic when removed from an external field.

In the meantime I tried to find more argon data to check if argon energy levels are spaced close enough to be excited by room-temperature collisions... unsuccessfully... But I guess not.

Anyway, it is my 500th post, and I am giving +1 to everybody... you lucky devils!