Question

Assume that the binding energy curve of two ions as a function of their distance d has the shape V(d) = −A/d + B/d8 , consisting of an attractive and a repulsive term. Sketch this binding energy curve schematically. b) The distance between Mg2+ ions and O2- ions in a MgO crystal is d0=2.106 Å (that is, 0.2106 nm). Calculate the Coulomb energy (in eV=1.602·10-19 J) that attracts these ions to one another. (ε0=8.85·10−12 J/(V2 ·m)) c) Assuming that the minimum of the binding energy curve is at d0, calculate the magnitude of the constant B (in eV·Å)

Answer 1

(b) To find the coulomb energy, the expresion for coulomd energy U ;is

U= -4q²/4r since the charge on both cation and anion is +2 and -2 so overall charge is -4

now q=1.6 *10^-19 , pie= 3.14, = 8.85 *10^-12 , r= 0.2106 nm

so U= -4 * 1.6 * 10^-19 *1.6 * 10^-19 / 4 * 3.14 *8.85 * 10^-12 * 0.2106 * 10^-9

= 43.7 * 10-19 J

Now since we want answer in eV so if 1eV = 1.602 * 10^-19 J

so 1 J= 1/ 1.602 * 10^-19 eV

so 43.7 * 10^-19 J = 43.7 * 10-19 * 1/ 1.602 * 10^-19 eV

U= 27.27 eV