The potential energy function for the force between two atoms in a diatomic molecule is approximately given by U(x)=a/(x¹²)-b/(x⁶), where a and b are constants and x is the distance between the atoms. If the dissociation energy of the molecule is D=[U(x=∞)-U_at equilibrium], D is

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(4) (b²)/(4a). Equilibrium: (dU)/(dx)=-(12a)/(x¹³)+(6b)/(x⁷)=0⇒ x⁶=(2a)/b. U_eq=a/((2a/b)²)-b/(2a/b)=(b²)/(4a)-(b²)/(2a)=-(b²)/(4a). D=0-(-(b²)/(4a))=(b²)/(4a).

The potential energy function for the force between two atoms in a diatomic molecule is approximately given by U(x)=a/(x¹²)-b/(x⁶), where a and b are constants and x is the distance between the atoms. If the dissociation energy of the molecule is D=[U(x=∞)-U_at equilibrium], D is

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