The potential energy between two atoms in a molecule is given by `U(x)= (a)/(x^(12))-(b)/(x^(6))`, where a and b are positive constants and x is the distance between the atoms. The atom is in stable equilibrium when

Options

A. `x = 6sqrt((11a)/(5b))`
B. `x = 6sqrt((a)/(2b))`
C. `x =0`
D. `x = 6sqrt((2a)/(b))`

Answer

D

Explanation

The potential …………
Condition for stable equilibrium `F = (dU)/(dx) = 0`
`implies -(d)/(dx)[(a)/(x^(12))-(b)/(x^(6))]= 0 implies -12ax^(-13)+6bx^(-7)=0`
`implies (12a)/(x^(13))=(6b)/(x^(7)) implies (2a)/(b) = x^(6) implies x = 6sqrt((2a)/(b))`