# 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 D2h 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]

(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 D6h 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, Ih, 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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