For two atoms separated by x, potential energy is U(x)=a/x¹²-b/x⁶, with a, b>0. Find their stable equilibrium separation.
Options

Question

For two atoms separated by x, potential energy is U(x)=a/x¹²−b/x⁶, with a,b>0. Find their stable equilibrium separation.

G1 Physics · Accepted Answer

Step 1 — Principle: Equilibrium occurs where dU/dx = 0; stable equilibrium also requires a local minimum of U. Step 2 — Working: Differentiate: dU/dx=−12a/x¹³+6b/x⁷=0. Step 3 — Working: Then 6b x⁶=12a, giving x=(2a/b)¹ᐟ⁶. Step 4 — Working: At this separation U is minimum. Correct answer: A — (2a/b)¹ᐟ⁶.