Can two objects with the same center of mass oscillate about that center?

In summary, there is no optical phonon in the dispersion curve for a one-dimensional monatomic chain of atoms because all of the atoms are the same and cannot produce the necessary electromagnetic activity. Additionally, two atoms of the same mass cannot oscillate about their center of mass due to the lack of a restoring force.
  • #1
WolfOfTheSteps
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Homework Statement



Explain why there is no optical phonon in the dispersion curve for the one-dimensional monatomic chain of atoms.

The Attempt at a Solution



I am completely confused. I know that optical phonons get their name because when an array of 2 atoms of different charge oscillate they are eloctramagnetically active and can absorbe or emit infrared radiation.

So I could say optical phonons are impossible for monatomic chains because you would need two atoms of different charge to get phonons.

But, I think that is wrong. Because elsewhere I read that optical phonons are described by oscillations about a center of mass, while acoustic phonons are described by a translation of the center of mass. This must imply that monatomic chains cannot have oscillations about the atom pair's centers of mass. So now I'm thinking there must be some reason why two atoms of the same mass cannot oscillate about their center of mass...

But I have no idea what that reason would be! Just imagining two balls connected by a spring, it seems that they can oscillate about this center.

Any help would be greatly appreciated!
 
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  • #2




Thank you for your question. I can tell you that there is indeed no optical phonon in the dispersion curve for a one-dimensional monatomic chain of atoms. This is because, as you correctly stated, optical phonons require atoms of different charge to create the necessary electromagnetic activity. In a monatomic chain, all of the atoms are the same and therefore cannot produce this effect.

Additionally, the reason why two atoms of the same mass cannot oscillate about their center of mass is due to the laws of physics. In order for two objects to oscillate, they must have a restoring force acting between them. This restoring force is provided by the spring in your example, but in the case of a monatomic chain, there is no spring or any other force acting between the atoms. Therefore, they cannot oscillate about their center of mass.

I hope this helps clarify the concept of optical phonons in a monatomic chain. Let me know if you have any further questions.
 
  • #3




You are correct in your understanding of optical phonons being described by oscillations about a center of mass. In a one-dimensional monatomic chain, all of the atoms have the same mass and are equally spaced apart. Therefore, there is no possibility for oscillations about a center of mass, as the atoms are all identical and equally spaced. This results in a lack of optical phonons in the dispersion curve. In order for optical phonons to exist, there needs to be a difference in mass or spacing between the atoms, which allows for the necessary oscillations to occur.
 

1. What does it mean for two objects to have the same center of mass?

Having the same center of mass means that the distribution of mass in both objects is balanced and located at the same point. This point is known as the center of mass, or the point where the entire mass of the object can be considered to be concentrated.

2. Can two objects with different masses have the same center of mass?

Yes, it is possible for two objects with different masses to have the same center of mass. This occurs when the distribution of mass in each object is such that the overall center of mass is in the same location.

3. What is oscillation and how does it relate to the center of mass?

Oscillation refers to the repetitive back-and-forth movement of an object around a central point. In the case of two objects with the same center of mass, they can oscillate around that center point as a result of the balance of forces acting on them.

4. Are there any real-world examples of two objects with the same center of mass oscillating?

Yes, one example is a simple pendulum, where the object at the end of the string and the pivot point have the same center of mass and can oscillate around that point. Another example is a see-saw, where two people of different masses can balance and oscillate around the center of the see-saw.

5. How is the behavior of two objects with the same center of mass different from those with different centers of mass?

Objects with the same center of mass will have symmetrical and balanced movements, while those with different centers of mass may experience uneven or chaotic movements. Additionally, objects with different centers of mass may require external forces to maintain their balance, while those with the same center of mass can naturally oscillate without external influence.

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