The potential energy U of two atoms, a distance r apart , is U = -A/(r^m)+ B/(r^

Question

The potential energy U of two atoms, a distance r apart , is

U = -A/(r^m)+ B/(r^n) , m=2, n = 10

Given that the atoms form a stable molecule at a separation of 0.3 nm with an

energy of -4 eV, Calculate A and B. Also, find the critical separation at which the

molecule breaks.

Sketch an energy/distance curve for the atoms, and sketch beneath this curve

the appropriate force/distance curve.

Also, what is an energy of eV ? the units i guess is what im asking.

Explanation / Answer

Let r0 be the equilibrium distance The equilibrium potential is U0 = -A/r0³ + B/r0? At an equilibrium position the potential energy attains a minimum. That means dU/dr = 0 at r=r0 3·A/r04 - 9·B/r0¹° = 0 A = 3·B/r06 Substitute back to equilibrium potential equation U0 = -3·B/r0? + B/r0? = 2·B/r0? => B = -(1/2)·U0·r0? => A = 3·B/r06 = -(3/2)·U0·r0³ Hence, A = -(3/2) · (-5.0eV) · (0.4nm)³ = 0.48 eV·nm³ B = -(1/2) · (-5.0eV) · (0.4nm)? = 6.5536×10?4 eV·nm?

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