The equilibrium bond length of a diatomic molecule is set by the electron cloud

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

The equilibrium bond length of a diatomic molecule is set by the electron cloud, so it hardly changes when a nucleus is replaced by a heavier isotope. Take

R_e = 127.46\,\mathrm{pm}

, the equilibrium separation of

\mathrm{H^{35}Cl}

, as also the equilibrium separation of

\mathrm{D^{35}Cl}

. Using atomic masses

m_{\mathrm D} = 2.0141\,\mathrm u

and

m_{\mathrm{^{35}Cl}} = 34.9689\,\mathrm u

(with

1\,\mathrm u = 1.66054\times10^{-27}\,\mathrm{kg}

), treat

\mathrm{D^{35}Cl}

as a rigid rotor and calculate its rotational constant

B_e

\mathrm{cm^{-1}}

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