Question

If the potential energy of two molecules is given by, $U=\frac{A}{r^{12}}-\frac{B}{r^6}$ then at equilibrium position, its potential energy is equal to:

• A. $\frac{A^2}{4B}$
• B. $-\frac{B^2}{4A}$
• C. $\frac{2B}{A}$
• D. $3A$

Answer 1

The correct option is B $-\frac{B^2}{4A}$

• At equilibrium net force is zero and force is given as $-\frac{dU}{dr}=\frac{12A}{r^{13}}-\frac{6B}{r^7}$ making it @@zero@@ lead us following relation $r^6=\frac{2A}{B}$
• just put the above value in expression of $U$ ,we get $U=-\frac{B^2}{4A}$.
• Option B is correct.