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

The Correct Option is C

For equilibrium

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

⇒ \(r^5 = \frac{2A}{B}\)

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