Posted: March 8th, 2015

Determine the symmetry representation for the 3N coordinates of all the atoms in (A) and hence identify the irreducible representation for the normal modes of vibration involving both the stretching and bending of bonds.

Molecular Spectroscopy assessment

• The lifetime of the ²P excited-electronic state of Na is 16ns. What is the minimum width of the

²S (2s)       ²P (3p) transition that could be observed in an emission spectrum of Na. [2]

• A resonant wavelength of 589 nm for the ²S (2s)  ²P (3p) transition in Na has been measured in a laboratory instrument. However, a measurement using a space telescope directed towards a nearby galaxy has identified that the same transition at 595 nm. How fast is the galaxy moving relative to us? Justify the answer by clearly explaining the calculation required. [3]

• The structure of diborane, B₂H₆ (A), with D_2h symmetry, is shown below:

• Determine the symmetry representation for the 3N coordinates of all the atoms in (A) and hence identify the irreducible representation for the normal modes of vibration involving both the stretching and bending of bonds. [6]
• State the number of bands that should appear in the IR and Raman spectra of (A) in the gas phase. [2]

• Prismane (B) is a cage-shaped molecule with D_3h

(B)

• Determine the symmetry representation for the 3N coordinates of all the atoms in B and hence identify the irreducible representation for the normal modes of vibration involving both the stretching and bending of bonds. [6]
• Prismane and benzene are structural isomers with formula C₆H₆. The irreducible representation for the normal modes of vibration of benzene in the D_6h point group is

2A1g+A2g+2B2g+E1g+4E2g+A2u+2B1u+2B2u+3E1u+2E2u.

Describe how the molecules prismane and benzene could be distinguished experimentally. [3]

(5) The structure of the cage-shaped molecule dodecahedrane, C₂₀H₂₀, is shown below. This molecule possess icosahedral, I_h, symmetry, and the point group contains the following symmetry transformations: C₅,C₅²,C₃,C₂, i, S₁₀, S₁₀³, S₆, . Illustrate these symmetry transformations on the structure diagram provided on the separate answer sheet. You need to show only one example of each symmetry transformation (i.e. ONLY ONE of the axes of the C₅ rotation axes, ONLY ONE of the C₅² rotation axes, …., and ONLY ONE of the  planes). [3]

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