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

Answer 1

Answer: (C)

$(\frac{2A}{B})^{\frac{1}{5}}$

Answer 2

For equilibrium

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

⇒ $r^5 = \frac{2A}{B}$

And
$r=(\frac{2A}{B})^{\frac{1}{5}}$