Calculating the frequency of the fundamental vibrational mode

Click For Summary
SUMMARY

The discussion centers on calculating the frequency of the fundamental vibrational mode of carbon monoxide (CO) based on its absorption of electromagnetic (EM) radiation. The stretching frequency of CO is approximately 2100 cm-1, which corresponds to an energy of about 0.3 eV. The energy levels for vibrational modes are described by the equation En = hf(n + 1/2), leading to the conclusion that the energy of the n=0 mode is 0.15 eV. This establishes a clear relationship between vibrational frequency and energy absorption in molecular bonds.

PREREQUISITES
  • Understanding of vibrational spectroscopy
  • Familiarity with the concepts of energy quantization in quantum mechanics
  • Knowledge of the relationship between frequency and energy (E = hf)
  • Basic principles of molecular bonding and stretching frequencies
NEXT STEPS
  • Research the application of vibrational spectroscopy in identifying molecular structures
  • Study the quantum mechanical model of molecular vibrations
  • Explore the implications of vibrational frequencies in chemical reactions
  • Learn about the use of Fourier Transform Infrared (FTIR) spectroscopy for analyzing molecular vibrations
USEFUL FOR

Chemists, physicists, and students studying molecular spectroscopy, particularly those interested in the vibrational characteristics of diatomic molecules like carbon monoxide.

mycotheology
Messages
86
Reaction score
0
Can you calculate the frequency at which a bond vibrates when you know what frequencies of EM radiation it absorbs? Using carbon monoxide as an example. It has a stretching frequency at around 2100 cm-1. In electron volts, that would be around 0.3 eV. If I'm not mistaken, this is the energy it absorbs to jump from n=0 to n=1 (or is it n=1 to n=2?). Anyhow, if its the former then ΔE = [itex]\frac{3}{2} - \frac{1}{2}hf[/itex] = hf.

I know that the equation to calculate the energy of vibrational normal modes is [itex]E_n=hf(n + \frac{1}{2})[/itex] so wouldn't that mean that the energy of the n=0 mode is equal to [itex]\frac{0.3 eV}{2}[/itex]?
 
Physics news on Phys.org
That's certainly what it means.
The classical picture is that this is the frequency of the fundamental at which the two atoms vibrate towards each other.
 

Similar threads

Graduate Number of thermal photons in a real (finite Q) cavity
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Method of calculating the vacuum energy divergence
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Deriving the time-dependent wave equation from Energy eigenfunctions
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Photon Emitted without Changing Energy Levels
  • · Replies 8 ·
Replies
8
Views
1K
Graduate A question about the mode expansion of a free scalar field
  • · Replies 2 ·
Replies
2
Views
3K
Analysing the Normal Modes and Dynamics of a Cluster of Atoms
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Does there exist a proof for these conjectures?
  • · Replies 2 ·
Replies
2
Views
2K
Understanding solution to equations of motion of n coupled oscillators
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Can anyone give me the details of creating a cat state in Circuit QED?
  • · Replies 16 ·
Replies
16
Views
4K
Raman Spectroscopy: Understanding Stokes and Anti-Stokes Lines
  • · Replies 7 ·
Replies
7
Views
3K