Find the error in the following working for carbon monoxide: "The potential curve of…

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

Find the error in the following working for carbon monoxide: "The potential curve

V(R)

of a diatomic molecule is just the electrostatic repulsion of its two bare nuclei. For CO the carbon nucleus has charge

+6e

and the oxygen nucleus

+8e

; at the measured equilibrium separation

R_e = 112.8\,\mathrm{pm}

their repulsion is

V(R_e) = \frac{(6e)(8e)}{4\pi\epsilon_0 R_e} = \frac{48 \times 1.440\,\mathrm{eV\,nm}}{0.1128\,\mathrm{nm}}

so the well depth of the CO curve should be about this value." (Here

e^2/4\pi\epsilon_0 = 1.440\,\mathrm{eV\,nm}

, the same combination used for Coulomb energies between point charges.) The measured dissociation energy of CO is

D_e = 11.2\,\mathrm{eV}

. ((a)) Evaluate the expression above for

V(R_e)

and compare it, in size and in sign, with

D_e

. ((b)) Identify the error in this reasoning and state in one or two sentences what

V(R)

actually represents, and why it is so much smaller than, and of opposite character to, the bare nuclear repulsion.

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