InterviewSolution
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InterviewSolution
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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` isA. `(b^2)/(6a)`B. `(b^2)/(2a)`C. `(b^2)/(12a)`D. `(b^2)/(4a)` |
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Answer» Correct Answer - D `U=(a)/(x^(12))-(b)/(x^(6))=ax^(-12)-bx^(-6)` `F=-(dU)/(dx)=-[a(-12)x^(-13)-b(-6)x^-7]=0` (for equilibrium) `x=((2a)/(b))^((1)/(6))` At `xinfty`,`U(infty)=0` `x=((2a)/(b))^((1)/(6))` `U_(at eq)=(axxb^2)/(4a^2)-(bxxb)/(2a)=(b^2)/(4a)-(b^2)/(2a)=-(b^2)/(4a)` `U_(infty)-U_(at eq)=(b^2)/(4a)` |
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