Rotation energy in a ball symmertical molecule, why only two axis?

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Discussion Overview

The discussion revolves around the rotational energy of a symmetrical diatomic molecule and the reasons for the limitation to two rotational axes. Participants explore the implications of molecular symmetry, moment of inertia, and quantum mechanics on rotational energy and its quantization.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions why there are only two axes of rotation for a symmetrical diatomic molecule, suggesting that rotation could occur around three axes, including the axis binding the atoms.
  • Another participant agrees that rotation is possible but notes that the moment of inertia in the third direction is very small, requiring a significant amount of energy for rotation.
  • A further elaboration indicates that quantum mechanics requires a minimum angular momentum (h-bar) for rotation, and the relationship between angular momentum and energy suggests that the energy needed for rotation increases with a smaller moment of inertia, effectively "freezing out" the last rotational mode.
  • One participant raises a point about the concept of rotating a single atom, discussing the quantization of energy levels at the atomic level and how this relates to molecular rotation.
  • Another participant acknowledges the responses, indicating that their understanding has improved as a result of the discussion.

Areas of Agreement / Disagreement

Participants generally agree that while rotation can occur, the energy requirements and quantum mechanical constraints limit the effective rotational modes of symmetrical diatomic molecules. However, the exact implications of these constraints and the nature of rotation around the binding axis remain points of discussion.

Contextual Notes

The discussion touches on the limitations imposed by molecular symmetry, the dependence on moment of inertia, and the effects of quantum mechanics on rotational energy levels, but these aspects are not fully resolved.

DemoniWaari
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I was just wondering that when we have a molecule, and you introduce heat, the molecule starts to get translation, rotation and vibration energy. I'm considering just a molecule with two atoms and one axis which binds them together.

Now the real question is that why is there only two axis in rotation energy? Can't you have three axis there? I mean that you can rotate in the x, y and z direction. And yes, I do know that the third one is parallel with the axis which binds the atoms together, but can't you still make it rotate?

I do realize that if the molecule is NOT symmetrical in that axis THEN it sure is considered a third axis on which the molecule can rotate. But even when it is symmetrical can't you pump energy in it?

On a macroscopic level I do see that when you make something like that rotate around it's own axis it doens't "change" when you look at it, but it STILL can have energy on that rotational axis, which rose this question in my mind.

I hope my explanation makes any sense, thanks for your answers!

Thanks.
 
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I think you can rotate the molecules. However, the moment of inertia is really small in that direction, which makes the energy required for the rotation really large.
 
To elaborate on that, quantum mechanics says that to get a rotation, you need at least h-bar worth of angular momentum (action is quantized in h-bar bundles). The connection between angular momentum and energy is that the rotational energy is the square of the angular momentum divided by twice the moment of inertia, so even if you use the minimum angular momentum, the energy you need will scale like the inverse of the momentum of inertia. So as mfb said, this requires more energy than is easily obtainable when the moment of inertia is very small, and the last rotational mode is "frozen out." The same thing happens to the other two rotational modes at very low temperature-- they don't get excited, and don't show up in the specific heat of the molecules at very low T.
 
Consider rotating just a single atom. What does that even mean? You have a cloud of electrons surrounding a nucleus, which may or may not have some angular momentum around the center of mass. The energy levels of the atom are already quantized with respect to angular momentum. In a sense, the rotation degree of freedom is already taken into account at the atomic level.

And as mfb and Ken were getting at, the energy splitting due to angular momentum is large compared with the molecular rotation levels.
 
Last edited:
Oh thank you all for your answers! This cleared up my thoughts :)
 

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