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To calculate the cohesive energy, let us consider the general situation of two identical atoms. As the atoms approach, the attractive forces increases and potential energy decreases. At the equilibrium position the potential energy of either two atom is given by

U= decrease in potential energy due to attraction + increase in potential energy due to repulsion.

work done in moving through a small distance dr is given by

du(r) + F(r)dr

Hence the potential energy if the atom

U(r)=int du(r) = int F(r)dr

= int(A/rM - B/rN)dr

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