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Exercise 2.9: The Madelung constant In condensed matter physics the Madelung constant gives the total felt by an atom in a solid. It depends on the charges on the other their locations. Consider for instance solid sodium chloridetable chloride crystal has atoms arranged on a cubic lattice, but with alternati chlorine atoms, the sodium ones having a single positive charge +e and ones a single negative charge -e, where e is the charge on the electron. If position on the lattice by three integer coordinates (i, j, k), then the sodi at positions where i + i + k is even, and the chlorine atoms at positions when is odd. Consider a sodium atom at the origin, i = j = k = 0, and let us calcula Madelung constant. If the spacing of atoms on the lattice is a, then the distan the origin to the atom at position (i,j,k) is total electric poen other atoms nearby able salt. The sodium berating sodium and the chlorine on li we label each be sodium atoms fall ons where i+j+k s calculate the the distance from Via)2 + (ja)2 + (ka)2 = av 12 +2 + k3, and the potential at the origin created by such an atom is V(ij,k) = 47100212 + 12+k?' with eo being the permittivity of the vacuum and the sign of the expression depending! on whether i++k is even or odd. The total potential felt by the sodium atom is then the sum of this quantity over all other atoms. Let us assume a cubic box around the sodium at the origin, with L atoms in all directions. Then Votal = M, > Vi,j,k) = ilk -L not i=;=k=0 47760a", where M is the Madelung constant, at least approximately-technically the Madelung! constant is the value of M when L +00, but one can get a good approximation just by using a large value of L. L.U I USER-DE e and print the Madelung constant for sodium chloride. alue of L as you can, while still having your program run in reasonable Write a program to calculate and print the Madelung ce Use as large a value of L as you can, while time--say in a minute or less