Degrees of freedom in a molecule

Click For Summary

Homework Help Overview

The discussion revolves around the degrees of freedom in molecules, particularly focusing on linear molecules and their vibrational modes. Participants are exploring the relationship between translational, rotational, and vibrational motions, as well as the associated energies.

Discussion Character

  • Conceptual clarification, Assumption checking, Mixed

Approaches and Questions Raised

  • Participants are attempting to understand the calculation of vibrational degrees of freedom (x) in the context of the equation Cv = NfK/2. Questions are raised about the nature of energies associated with vibrational modes and how many modes exist for N-atomic molecules.

Discussion Status

There is active engagement with various interpretations of vibrational modes and degrees of freedom. Some participants are clarifying the distinction between vibrational modes and degrees of freedom, while others are questioning the assumptions made about the energy contributions from these modes. The discussion is ongoing, with no explicit consensus reached.

Contextual Notes

Participants are navigating the complexities of molecular motion, including the implications of linear versus non-linear molecules and the definitions of vibrational modes. There is a focus on understanding the foundational concepts without resolving all uncertainties.

LCSphysicist
Messages
644
Reaction score
163
Homework Statement
.
Relevant Equations
.
1606475247798.png

I am not understand the solution of the letter b and c given by the author.
1606475311576.png

Since Cv = NfK/2, we have Cv/N = fK/2. Now, the degree of freedom of a N linear molecule is 3(trans) + 2(rot) + x, where x is the degree of freedom due the vibrational motion. I am having trouble to calc x, could you help me?
 
Physics news on Phys.org
Herculi said:
Homework Statement:: .
Relevant Equations:: .

View attachment 273247
I am not understand the solution of the letter b and c given by the author.

Since Cv = NfK/2, we have Cv/N = fK/2. Now, the degree of freedom of a N linear molecule is 3(trans) + 2(rot) + x, where x is the degree of freedom due the vibrational motion. I am having trouble to calc x, could you help me?
What kind of energies belong to a single vibration?
 
ehild said:
What kind of energies belong to a single vibration?
The kinetic energy due to the vibration and the potential stored (as in kx²/2)
 
Herculi said:
The kinetic energy due to the vibration and the potential stored (as in kx²/2)
Good! A two-atomic molecle has a single vibrational mode. When performig that motion, the molecule has both kinetic and potential energy. If you want to specify thevibrational state of the molecule, you have to give both the velocity and the phase of the vibrationThese are two degrees of freedom for each vibrational mode.
How many vibration modes has an N-atomic molecule?
 
ehild said:
Good! A two-atomic molecle has a single vibrational mode. When performig that motion, the molecule has both kinetic and potential energy. If you want to specify thevibrational state of the molecule, you have to give both the velocity and the phase of the vibrationThese are two degrees of freedom for each vibrational mode.
How many vibration modes has an N-atomic molecule?
"A two-atomic molecle has a single vibrational mode. " That's what i don't understand, two particles connected by a spring, as a model for a molecule, do not have two degree of freedom? So two vibrational mode which gives us 4 types of energy? The kinect and energy stored in one mode and in another mode.
 
Herculi said:
"A two-atomic molecle has a single vibrational mode. " That's what i don't understand, two particles connected by a spring, as a model for a molecule, do not have two degree of freedom? So two vibrational mode which gives us 4 types of energy? The kinect and energy stored in one mode and in another mode.
Two particles conneted by a spring corresponds to a single oscillator, a single vibrational mode, but it has two degrees of vibrational freedom,.
A molecule of N atoms can perform 3N independent motions. From these , 3 are translations of the whole molecule: and 3 are rotations of the whole molecule. When the molecule is linear, it performs 2 indepemdent rotations. The other 3N-6 (3N-5) motions are vibrations. A translating or rotating molecule has only kinetic energy, 1/2 kT for each degree of freedom. Each of the 3N-6 (3N-5) vibrational modes have kT average energy.
Both atoms iof a two-wtomic molecule can move in the x, y, z directionsthat makes 6 different motions. From these, 3 motions are the same for both atoms,they are translations The moleculée can also rotate about two perpendicular axes . The translating or rotating molecule is rigid, it does not change shape. And there is a single motion, when the atoms move relative to each other: it is vibration.
 
Last edited:

Similar threads

  • · Replies 8 ·
Replies
8
Views
5K
Replies
11
Views
2K
  • · Replies 2 ·
Replies
2
Views
3K
Replies
3
Views
7K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 2 ·
Replies
2
Views
7K
  • · Replies 31 ·
2
Replies
31
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 2 ·
Replies
2
Views
3K