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In the vibrational spectrum of CO2, the number of fundamental vibrational modes common in both infrared and Raman are:
  • a)
    Three
  • b)
    Two
  • c)
    One 
  • d)
    Zero
Correct answer is option 'D'. Can you explain this answer?
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In the vibrational spectrum of CO2, the number of fundamental vibratio...
Vibrational Spectrum of CO2

The vibrational spectrum of CO2 can be studied using two types of spectroscopy techniques - Infrared (IR) and Raman spectroscopy.

Infrared Spectroscopy

Infrared spectroscopy uses infrared radiation to study the vibrational modes of a molecule. When IR radiation is absorbed by a molecule, it causes the molecule to vibrate in a particular way, and the energy required for this vibration corresponds to a specific frequency of IR radiation.

Raman Spectroscopy

Raman spectroscopy, on the other hand, uses laser light to study the vibrational modes of a molecule. When laser light is scattered by a molecule, some of the scattered light has a different frequency than the incident laser light. This frequency difference corresponds to the vibrational energy of the molecule.

Fundamental Vibrational Modes

The fundamental vibrational modes of a molecule are the modes in which the molecule can vibrate without breaking any bonds. These vibrations correspond to the lowest energy levels of the molecule.

CO2 has three atoms - one carbon and two oxygen atoms. Each of these atoms can vibrate in three different ways (in three different directions), giving a total of nine possible vibrational modes.

However, some of these modes are not allowed due to symmetry constraints. In particular, two of the vibrational modes involve the carbon atom moving in the same direction as the two oxygen atoms, which would result in a change in the molecular dipole moment. Since CO2 is a linear molecule, it has a zero dipole moment, and these modes are not allowed.

Common Fundamental Vibrational Modes

When we consider the fundamental vibrational modes of CO2 that are allowed in both IR and Raman spectroscopy, we find that there are no such modes. This is because the vibrational modes that are allowed in IR spectroscopy involve a change in the dipole moment of the molecule, while the modes that are allowed in Raman spectroscopy involve a change in the polarizability of the molecule.

Since CO2 is a linear molecule with a zero dipole moment, it does not have any allowed vibrational modes that involve a change in the dipole moment or polarizability. Therefore, there are no fundamental vibrational modes of CO2 that are common to both IR and Raman spectroscopy.
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In the vibrational spectrum of CO2, the number of fundamental vibrational modes common in both infrared and Raman are:a)Threeb)Twoc)Oned)ZeroCorrect answer is option 'D'. Can you explain this answer?
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