Consider a one-dimensional chain of alternating singlyionized positive and negative ions. Show that the potential energy associated with one of the ions and its interactions with the rest of this hypothetical crystal is U(r) = -ake(e2)/(r)where the Madelung constant is a = 2 ln 2 and r is the distance between ions. Suggestion: Use the series expansion for ln (1 + x).

Consider a one-dimensional chain of alternating singlyionized positive and negative ions. Show that the potential energy associated with one of the ions and its interactions with the rest of this hypothetical crystal is U(r) = -ake(e2)/(r)where the Madelung constant is a = 2 ln 2 and r is the distance between ions. Suggestion: Use the series expansion for ln (1 + x).

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Question

Consider a one-dimensional chain of alternating singlyionized positive and negative ions. Show that the potential energy associated with one of the ions and its interactions with the rest of this hypothetical crystal is
U(r) = -ak_e(e²)/(r)
where the Madelung constant is a = 2 ln 2 and r is the distance between ions. Suggestion: Use the series expansion for ln (1 + x).

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