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The spectra shown below is due to :

An absorption band against wavenumber in cm-1 made of two broad humps of similar height on either side of a sharp, intense central spike

  • A.Perpendicular vibrations in a linear polyatomic molecule
  • B.Vibrational-rotational transitions in a diatomic molecule
  • C.Effect of nuclear spin homonuclear diatomic molecule
  • D.Breakdown of Born-Oppenheimer approximation

Answer: A

The band is due to perpendicular vibrations in a linear polyatomic molecule.

A vibration-rotation band normally has a P branch (ΔJ = -1) and an R branch (ΔJ = +1), the two broad humps. A sharp, intense central Q branch (ΔJ = 0) appears only when the vibration carries angular momentum about the molecular axis, which is the case for a perpendicular vibration of a linear polyatomic molecule, such as the bending mode of CO2 or HCN.

A diatomic molecule's vibration-rotation band (and a parallel band of a linear molecule) has only P and R branches with a gap at the centre, not a spike. Nuclear spin statistics alter the intensities of alternate lines, and breakdown of the Born-Oppenheimer approximation does not produce a Q branch.

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