JEE Main Physics question
The potential energy as a function of the force between two atoms in a diatomic molecule is given by U(x) = a/x¹² − b/x⁶, where a and b are positive constants and x is the distance between the atoms. The position of stable equilibrium for the system of the two atoms is given by
Answer: (D)
Solution
F = −dU/dx = 0 ⟹ 12a/x¹³ = 6b/x⁷ ⟹ x⁶ = 2a/b ⟹ x = (2a/b)^(1/6).