Calculating the frequency of the fundamental vibrational mode

In summary, the frequency at which a bond vibrates can be calculated by knowing the frequencies of EM radiation it absorbs. For example, carbon monoxide has a stretching frequency of around 2100 cm-1, which corresponds to an energy of approximately 0.3 eV. This is the energy required for the bond to jump from n=0 to n=1. The equation to calculate vibrational energy is E_n=hf(n+1/2). This means that the energy of the n=0 mode is equal to 0.3 eV/2. The classical interpretation is that this frequency represents the fundamental vibration between the two atoms.
  • #1
mycotheology
89
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]?
 
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  • #2
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.
 

FAQ: Calculating the frequency of the fundamental vibrational mode

1. What is the fundamental vibrational mode?

The fundamental vibrational mode refers to the lowest possible frequency at which a molecule can vibrate in a specific direction. This frequency is associated with the stretching and bending of chemical bonds within the molecule.

2. Why is calculating the frequency of the fundamental vibrational mode important?

Calculating the frequency of the fundamental vibrational mode is important because it provides valuable information about the structure and properties of a molecule. It can also help in identifying and characterizing different chemical bonds within the molecule.

3. How is the frequency of the fundamental vibrational mode calculated?

The frequency of the fundamental vibrational mode can be calculated using the equation: v = 1/2π √(k/m), where v is the frequency, k is the force constant, and m is the reduced mass of the molecule.

4. What factors affect the frequency of the fundamental vibrational mode?

The frequency of the fundamental vibrational mode is affected by the strength of the chemical bonds, the mass of the atoms involved, and the shape and symmetry of the molecule. Other factors such as temperature and pressure can also have an impact on the frequency.

5. Can the frequency of the fundamental vibrational mode be measured experimentally?

Yes, the frequency of the fundamental vibrational mode can be measured experimentally using techniques such as infrared spectroscopy or Raman spectroscopy. These methods involve shining a beam of light on the molecule and analyzing the resulting vibrations to determine the frequency.

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