The lattice energy of an ionic compound can be calculated using the Born-Lande equation:LE = -N * M * Z+ * Z- * e^2 / 4 * * 0 * r0 Where:LE = Lattice energyN = Avogadro's number 6.022 x 10^23 mol^-1 M = Madelung constant for MgO, M = 1.748 Z+ = Charge of the cation Mg2+ = +2 Z- = Charge of the anion O2- = -2 e = Elementary charge 1.602 x 10^-19 C 0 = Vacuum permittivity 8.854 x 10^-12 C^2 J^-1 m^-1 r0 = Distance between ions sum of ionic radii First, we need to find the distance between the ions r0 . The ionic radii for Mg2+ and O2- are given as 0.72 and 1.40 , respectively. To find r0, we need to convert the radii to meters and then add them together:r0 = 0.72 + 1.40 * 1 x 10^-10 m/ r0 = 2.12 * 1 x 10^-10 m/ r0 = 2.12 x 10^-10 mNow we can plug the values into the Born-Lande equation:LE = -N * M * Z+ * Z- * e^2 / 4 * * 0 * r0 LE = - 6.022 x 10^23 mol^-1 * 1.748 * 2 * -2 * 1.602 x 10^-19 C ^2 / 4 * * 8.854 x 10^-12 C^2 J^-1 m^-1 * 2.12 x 10^-10 m LE = -2.097 x 10^6 J/molTo convert the lattice energy from J/mol to kJ/mol, we divide by 1000:LE = -2.097 x 10^6 J/mol * 1 kJ / 1000 J LE = -2097 kJ/molThe calculated lattice energy of magnesium oxide MgO is approximately -2097 kJ/mol. However, the given lattice energy of MgO is -3795 kJ/mol. This discrepancy may be due to the approximations used in the Born-Lande equation or the ionic radii values provided. In practice, experimental values are often used to refine these calculations.