Question

Consider a hypothetical X+-Y' ion pair for which t

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Answer #1

From the equilibrium separation equation,

\:

r_{o}=\left ( \frac{A}{nB} \right )^{1/(1-n)}

\:

for n=10,

\:

r_{o}=\left ( \frac{A}{10B} \right )^{-1/9}

\:

rearranging for A,

\:

A=10Br_{o}^{-9} \: \: \: \: \: \: \: \: \: \: \: (1)

\:

From the equation for bonding energy,

\:

E_{o}=-\frac{A}{\left ( \frac{A}{10B} \right )^{-1/9}}+\frac{B}{\left ( \frac{A}{10B} \right )^{-10/9}}=-\frac{A}{r_{o}}+\frac{B}{r_{o}^{10}} \: \: \: \: \: \: \: \: \: \: \: \: (2)

\:

inserting eq. (1) in (2),

\:

E_{o}=-\frac{10Br_{o}^{-9}}{r_{o}}+\frac{B}{r_{o}^{10}}

\:

isolating the constant B,

\:

B=-\frac{E_{o}r_{o}^{10}}{9}

\:

inserting data given,

\:

B=-\frac{(-6.13eV)(0.35nm)^{10}}{9}

\:

or

\:

{\color{Blue} B=0.000018789\, eV\cdot nm^{10}\approx 1.88\times 10^{-5}\, eV\cdot nm^{10}}

\:

from eq. (2), we can calculate the constant A,

\:

E_{o}=-\frac{A}{r_{o}}+\frac{B}{r_{o}^{10}}

\:

thus,

\:

A=\left ( \frac{B}{r_{o}^{10}} -E_{o} \right )r_{o}

\:

inserting data given,

\:

A=\left [ \frac{ 1.88\times 10^{-5}\, eV\cdot nm^{10}}{(0.35nm)^{10}} -(-6.13eV) \right ](0.35nm)

\:

or

\:

{\color{Blue} A=2.384031341\, eV\cdot nm \approx 2.38\, eV\cdot nm}

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