Question

Potential energy as a function of $r$ is given by $U =\frac{ A }{ r ^{10}}-\frac{ B }{ r ^{5}}$, where $r$ is the interatomic distance, $A$ and $B$ are positive constants. The equilibrium distance between the two atoms will be:

• A. $\left(\frac{ A }{ B }\right)^{\frac{1}{5}}$
• B. $\left(\frac{B}{A}\right)^{\frac{1}{5}}$
• C. $\left(\frac{2 A }{ B }\right)^{\frac{1}{5}}$
• D. $\left(\frac{ B }{2 A }\right)^{\frac{1}{5}}$

Answer 1

Answer: (C)

$\frac{-10 A }{ r ^{11}}+\frac{5 B }{ r ^{6}}=0$
$r ^{5}=\frac{10 A }{5 B }=\frac{2 A }{ B }$