Q4. The potential energy of diatomic molecule is given in terms of the interatomic distance r by the relation U(r) = -a/r^2 + b/r^10 Calculate the equilibrium spacing of the two atoms and the lattice when a=1.44x10-39 J/m^2 and b=2.19x10-115 J/m^10.
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Adi S.
The potential energy (V(r)) between a pair of neutral atoms or molecules is very well-approximated by the Lennard-Jones Potential, given by the expression: V(r) = 4ε[(σ/r)^12 - (σ/r)^6] where ε and σ are constants and r is the distance between the molecules. The potential energy is plotted in the figure below: The vertical axis is in units of ε, while the horizontal axis is in units of σ. (a) At what separation distance, in terms of σ and ε, is the potential energy zero? (b) Why does the potential energy approach zero as the distance gets bigger? (c) What is the equilibrium distance? What is the potential energy at the equilibrium distance? (Express your answers in terms of σ and ε.)
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