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why 3N-5 vibrational mode for linear whereas 3N-6 for linear?

why 3N-5 vibrational mode for linear whereas 3N-6 for linear?

Grade:Upto college level

1 Answers

kiran kumar
34 Points
7 years ago

A molecule can vibrate in many ways, and each way is called a vibrational mode. For molecules with N atoms in them, linear molecules have 3N – 5 degrees of vibrational modes, whereas nonlinear molecules have 3N – 6 degrees of vibrational modes (also called vibrational degrees of freedom). As an example H2O, a non-linear molecule, will have 3 × 3 – 6 = 3 degrees of vibrational freedom, or modes.

Simple diatomic molecules have only one bond and only one vibrational band. If the molecule is symmetrical, e.g. N2, the band is not observed in the IR spectrum, but only in the Raman spectrum. Asymmetrical diatomic molecules, e.g. CO, absorb in the IR spectrum. More complex molecules have many bonds, and their vibrational spectra are correspondingly more complex, i.e. big molecules have many peaks in their IR spectra.

The atoms in a CH2X2 group, commonly found in organic compounds and where X can represent any other atom, can vibrate in nine different ways. Six of these involve only the CH2 portion: symmetric and antisymmetric stretching, scissoring, rocking, wagging and twisting, as shown below. (Note, that because CH2 is attached to X2 it has 6 modes, unlike H2O, which only has 3 modes. The rocking, wagging, and twisting modes do not exist for H2O, since they are rigid body translations and no relative displacements exist.

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