Question

The vibrational modes in \[C{{O}_{2}}\] is:

Answer 1

Hint: We know that the carbon dioxide is a triatomic molecule, it is not arranged in a triangular fashion. It is a linear molecule with all the three atoms arranged in the same line. Hence, we would use the relation between the number of linkages of the atoms of the molecule to determine the vibrational degrees of freedom.

Complete answer:
As we know that the symmetric carbon dioxide molecule as shown above, the two oxygen molecules vibrate about the carbon molecule. Each vibrational motion has both kinetic and potential energies. So, one degree of freedom of vibrational motion is taken as two. Since the above molecule vibrates along two linkages, we can directly conclude it has four degrees of freedom.
$O\underset{1}{\mathop{-}}\,C\underset{2}{\mathop{-}}\,O$
There are molecules which contain only two atoms of different elements namely carbon monoxide \[\left( CO \right)\] and hydrogen chloride \[\left( HCl \right).\] They do absorb infrared radiation, but try to have short life in the atmosphere owing to their reactivity or solubility. Therefore, they are not responsible much for the greenhouse effect and so they are not considered when discussing greenhouse gases. Carbon-dioxide is a greenhouse gas and it is responsible for Global-Warming. A layer of carbon dioxide which is present in the atmosphere traps the infrared radiation coming from earth's surface and then it eventually heats the earth's atmosphere which results in global warming.
Vibrational modes of carbon dioxide \[\left( C{{O}_{2}} \right)\] a linear molecule has \[3\times 3-5=4~\] vibrations. These modes are responsible for the green home effect in which heat radiated from the earth is obtained (trapped) by \[C{{O}_{2}}\] molecules in the atmosphere.

Note:
Remember that of the two twisting modes, the atom is just carefully straight when the measure of bowing is zero. It has been demonstrated both by theory and by Coulomb blast imaging experiments. That this is never, in reality, valid for the two modes without a moment's delay. In a gas stage test of carbon dioxide, none of the atoms are straight because of the vibrational movements.