Consider the infinite series for the Madelung constant of the NaCl-type struc- ture. Its convergence depends on how the successive terms are chosen. The expression, as given below, is written such that the terms are sequential attrac- tive and repulsive interactions coming from sequential shells that purely contain cations or anions. Z₁ Z2e² 4Tend Uc 12 8 √2 √√3 √4 √5 6 24 + 24 √6 (1) a, Calculate the sum of this series for two, three, four, five, and six terms. For each successive shell, determine the total number of cations and anions sur- rounding the central anion. b, What can you say about the convergence of this series after 6 terms? c, Which of these successive sums is closest to the Madelung constant for the rocksalt structure of +1.7476? For which series is the total charge enclosed

Consider the infinite series for the Madelung constant of the NaCl-type struc- ture. Its convergence depends on how the successive terms are chosen. The expression, as given below, is written such that the terms are sequential attrac- tive and repulsive interactions coming from sequential shells that purely contain cations or anions. Z₁ Z2e² 4Tend Uc 12 8 √2 √√3 √4 √5 6 24 + 24 √6 (1) a, Calculate the sum of this series for two, three, four, five, and six terms. For each successive shell, determine the total number of cations and anions sur- rounding the central anion. b, What can you say about the convergence of this series after 6 terms? c, Which of these successive sums is closest to the Madelung constant for the rocksalt structure of +1.7476? For which series is the total charge enclosed