Overtone absorption bands of carbon monoxide (CO) give the following vibrational…

PHYSICS · Multi-part · 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

Overtone absorption bands of carbon monoxide (CO) give the following vibrational level spacings

\Delta G(v) = G(v+1)-G(v)

\Delta G(0) = 2143.3\,\mathrm{cm^{-1}}

\Delta G(1) = 2116.7\,\mathrm{cm^{-1}}

\Delta G(2) = 2090.1\,\mathrm{cm^{-1}}

\Delta G(3) = 2063.5\,\mathrm{cm^{-1}}

. ((a)) Show that the spacings fall by a constant amount from one to the next, and use this to find

\omega_e

and

\omega_ex_e

. ((b)) Extrapolate the spacings to zero (a Birge-Sponer estimate) using

D_e \approx \omega_e^2/4\omega_ex_e

, and give the result in eV. ((c)) The tabulated dissociation energy of CO is

D_e = 11.16\,\mathrm{eV}

. Compare your estimate with this value, and say in one sentence why a two-constant fit taken from the lowest levels need not give the true well depth exactly.

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