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If the potential energy between two molecules is given by U = -A/r⁶ + B/r¹², then at equilibrium, separation between molecules, and the potential energy are:
- (2B/A)^(1/6), -A²/2B
- (2B/A)^(1/6), -A²/4B
- (B/A)^(1/6), 0
- (B/2A)^(1/6), -A²/2B
Correct answer: (2B/A)^(1/6), -A²/4B
Solution
At equilibrium, the potential energy is minimized, which occurs when the derivative of U with respect to r equals zero. Solving this condition leads to the separation distance of (2B/A)^(1/6) and the corresponding potential energy of -A²/4B.
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