The covalent and ionic potential curves of an alkali halide cross at a distance R_c=…

PHYSICS · Multi-part · Fermi University Physics · Atomic, Molecular & Optical Physics · Molecular structure and spectra · Molecular structure and spectra

Deriving the Spectrum, Ch The Born-Oppenheimer separation and the chemical bond

Problem

The covalent and ionic potential curves of an alkali halide

\mathrm{AB}

cross at a distance

R_c=\frac{e^2/4\pi\epsilon_0}{I_A-A_B},

where

I_A

is the ionisation energy of the alkali atom,

A_B

is the electron affinity of the halogen atom, and

e^2/4\pi\epsilon_0=14.40\,\mathrm{eV\,\mathring{A}}

. For potassium and fluorine,

I_{\rm K}=4.34\,\mathrm{eV}

and

A_{\rm F}=3.40\,\mathrm{eV}

. ((a)) Find the covalent-ionic crossing distance

R_c

for

\mathrm{KF}

. ((b)) The measured bond length of

\mathrm{KF}

R_e=2.17\,\mathrm{\mathring{A}}

. Compare

R_c

with

R_e

and comment on what this says about the character of the bond near equilibrium.

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