Correct Answer - B
`U_((x)) =(a)/(x^(12)) - (b)/(x^(6))`
`F=-(U(x))/(dx)=+(12 a)/(x^(13)) - (6b)/(x^(7))`
At normal distance between the molecules, F=0
`:. +(12a)/(x^(13)) - (6b)/(x^(7))=0` or `x((2a)/(b))^(1//6)`
`U_((oo))=(a)/(oo^(12)) - (b)/(oo^(6))=0`
Dissociation energy of molecule,
`D=U_((x=oo)) - U_("at equilibrium")`
`=0-((a)/(x^(12))-(b)/(x^(6)))` where, `x=((2a)/(b))^(1//6)`
`D=(-a)/(x^(12))+(b)/(x^(6))=-(a)/((2a//b)^(12//6))+(b)/((2a//b)^(6//6))`
`=-(b^(2))/(4a)+(b^(2))/(2a) = (b^(2))/(4a)`