Rotational absorption lines of the rare isotopologue are measured in the far infrared…

PHYSICS · Subjective · Fermi University Physics · Atomic, Molecular & Optical Physics · Molecular structure and spectra · Molecular structure and spectra

Reading the Spectrum, Ch Two nuclei on one curve: rotation, vibration and the spectrum of a diatomic molecule

Problem

Rotational absorption lines of the rare isotopologue

\mathrm{^{13}C^{16}O}

are measured in the far infrared and found to be very nearly evenly spaced by

3.680\,\mathrm{cm^{-1}}

. Treating the molecule as a rigid rotor, with atomic masses

m(\mathrm{^{13}C}) = 13.0034\,\mathrm u

and

m(\mathrm{^{16}O}) = 15.9949\,\mathrm u

, find the bond length

R_0

\mathrm{^{13}CO}

implied by this spacing.

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