Exploring the Vibrational Degrees of Freedom for Diatomic Molecules

In summary, the vibrational degree of freedom of a diatomic molecule is not independent, and can only be 2.
  • #1
td21
Gold Member
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8
For diatomic molecule, why is the vibrational degree of freedom equal to two at high temperature?
Why not just one?
Thank you very much.
 
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  • #2
The energy of the vibration is the sum of the potential energy and the kinetic energy. The first is determined by the change of the distance between the atoms, the other is determined by their speeds. Speed and distance are the two degrees of freedom.

ehild
 
  • #3
td21 said:
For diatomic molecule, why is the vibrational degree of freedom equal to two at high temperature?

You are mistaken. Diatomic molecules have exactly one vibrational degree of freedom, regardless of temperature.

You may have mean something else, which is related to degrees of freedom and temperature, but but you will have to formulate your question correctly.
 
  • #4
Are you referring to rotational and vibrational degrees of freedom?
 
  • #5
Khashishi said:
Are you referring to rotational and vibrational degrees of freedom?
If you asked me, the answer is NO.

The diatomic molecule can perform only one kind of vibration: the interatomic distance change sinusoidally in time.

But the general SHM motion of angular frequency ω is of the form x=Asin(ωt+θ). Two data are needed to know the energy of the vibrating body : for example, the position and the velocity at the same time.
In Kinetic Theory, the Equipartition Principle assigns two (1/2 kT) average energy to a single vibration.ehild
 
  • #6
ehild said:
the Equipartition Principle assigns two (1/2 kT) average energy to a single vibration.

But not two degrees of freedom, as stated in the original message.
 
  • #7
td21 said:
For diatomic molecule, why is the vibrational degree of freedom equal to two at high temperature?
Why not just one?
Thank you very much.

A number of sources refer to "libration" as a separate degree of freedom. This is described as a flexing or bending of the inter-atomic axis. Other sources do not mention libration.
 
  • #8
klimatos said:
A number of sources refer to "libration" as a separate degree of freedom. This is described as a flexing or bending of the inter-atomic axis. Other sources do not mention libration.
Libration is restricted rotation. It does not exist for free diatomic molecules. Libration can happen in some external force field, or a diatomic part of a molecule can librate with respect to the other part.
http://en.wikipedia.org/wiki/Libration_(molecule)
ehild
 
  • #9
klimatos said:
A number of sources refer to "libration" as a separate degree of freedom.

The total number of degrees of freedom in a system of particles cannot be greater than the sum of the degrees of freedom of all the particles assumed unconstrained. The latter is 6 for a diatomic molecule. The nomenclature of the degrees of freedom commonly used in this case - 3 for the motion of CoM, two rotational and one vibrational - is thus maximal and any other degree freedom will not be independent.
 

1. What are vibrational degrees of freedom for diatomic molecules?

Vibrational degrees of freedom refer to the ways in which a molecule can vibrate. In diatomic molecules, these vibrations occur along the bond between the two atoms, causing the atoms to move closer together and farther apart.

2. How are vibrational degrees of freedom related to a molecule's energy levels?

The vibrational degrees of freedom are directly related to a molecule's energy levels. As a molecule vibrates, it gains or loses energy, resulting in different energy levels. The more vibrational degrees of freedom a molecule has, the more energy levels it can have.

3. Why is exploring vibrational degrees of freedom important in chemistry?

Exploring vibrational degrees of freedom is important in chemistry because it allows us to understand the behavior and properties of molecules. It also helps us to predict how molecules will interact with each other and their surroundings, which is crucial in fields such as materials science and drug design.

4. How can we measure the vibrational degrees of freedom in a diatomic molecule?

There are several techniques for measuring the vibrational degrees of freedom in a diatomic molecule, including infrared spectroscopy, Raman spectroscopy, and neutron scattering. These methods involve shining light or particles on the molecule and analyzing the resulting vibrations.

5. Can the vibrational degrees of freedom be changed in a molecule?

Yes, the vibrational degrees of freedom in a molecule can be changed through various means, such as changing the temperature or applying external forces. These changes can affect the molecule's energy levels and overall behavior, making it a valuable tool in chemical reactions and material properties.

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