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Multi-Electron Configurations and Orbital Diagrams

The potential...

Question

The potential energy of a diatomic molecule is given by|
U=A/r^12 - B/r^6
where r is the distance between the atoms that make up the molecule and A and B are positive constants.Find the equilibrium seperation between the atoms

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Solution

$U = \frac{A}{r^{12}} - \frac{B}{r^{6}} I n c a s e o f e q u i l i b r i u m, F = - \frac{d U}{d r} = 0 S o, \frac{d U}{d r} = - 12 \frac{A}{r^{13}} + \frac{6 B}{r^{7}} = 0 \frac{6 B}{r^{7}} = \frac{12 A}{r^{13}} r^{6} = \frac{2 A}{B} r = {(\frac{2 A}{B})}^{1 / 6}$

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