The potential energy funtions for the force between two along in a distance molecule is approximatily given by
`U(x) = (a)/(x^(12)) - b)/(x^(6)) ` where `a` and `b` are constant and `x` is the distance between the aloms , if the discision energy of the molecale is `D = [U(x = oo) - U` atequlibrium ] , D is

Options

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

Answer

C

Explanation

(c ) At equibrium : `(dU(x))/(dx) = 0`
`rArr (-12a)/(x^(11) = (-6b)/(x^(5) rArr x = ((2a)/(b)) ^(1/6)`
`:. U_(at equilibrium) = (a)/(((2a)/(b))^(2) - (b)/((2a)/(b)) = b^(2))/(4a) ` and `U_(x= 0) = 0`
:. D= 0 - (-(b^(2))/(4a)) = (b^(2))/(4a)) `