The potential energy function for the force between two atoms in a diatomic molecule is approximate given by `U(r) = (a)/(r^(12)) - (b)/(r^(6))`, where `a` and `b` are constants and `r` is the distance between the atoms. If the dissociation energy of the molecule is `D = [U (r = oo)- U_("at equilibrium")],D` is

Options

A. `b^(2)/6a`
B. `b^(2)/2a`
C. `b^(2)/12a`
D. `b^(2)/4a`

Answer

`(4)`

Explanation

`F = -(dU)/(dx) = - [a(-12)x^(-13) - b(-6)x^(-7)]=0`
`x = ((2a)/b)^(1/6)`
` At x = infty, U (infty) = 0`
`U_(eq) = (ab)^(2)/(4a) - (b^(2))/(2a) = (b^(2))/(4a) - (b^(2))/(2a) = - (b^(2))/(4a)`
`U_(infty) - U_(eq) = (b^(2))/(4a)`