The potential energy function for the force between two atoms in a diatomic molecule is approximately given by `U(x) =a/x^(12)-b/x^(6)` where a and b are constant and x is the distance between the atoms. Find the dissoociation energy of the molecule which is given as `D=[U(x- infty)-U_(at equilibrium)]`

Options

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

Explanation

[4]
Condition for stable equilibrim
`rArr F=-(dU)/(dx)=0`
`rArr-(d)/(dx)[(a)/(x^(12))-(b)/(x^(6))]=0`
`rArr -12ax^(-13)+6bx^(-7)=0`
`rArr (12a)/(x^(13))=(6b)/(x^(7))rArrx^(6)rArrx=6sqrt((2a)/(b))`