For these expressions, energies are expressed in electron volts per Na+–Cl– pair, and r is the distance in nanometers. The net energy EN is just the sum of the preceding two expressions. (a) Superimpose on a single plot EN, ER, and EA versus r up to 1.0 nm. (b) On the basis of this plot, determine (i) the equilibrium spacing r0 between the Na+ and Cl– ions, and (ii) the magnitude of the bonding energy E0 between the two ions. (c) Mathematically determine the r0 and E0 values the solutions to Problem 2.18, and compare these with the graphical results from part (b). Solution (a) Curves of and are on the plot below. EA, ER, EN (b) From this plot: r0 = 0.24 nm E0 = 5.3 eV (c) From Equation 2.17 for EN A = 1.436 B = 7.32 106 n = 8 Thus, and = 5.32 eV – 2.20 Consider a hypothetical X+–Y– ion pair for which the equilibrium interionic spacing and bonding energy values are 0.38 nm and eV, respectively. If it is known that n in Equation 2.17 has a value of 8, using –5.37 the results of Problem 2.18, determine explicit expressions for attractive and repulsive energies EA and ER of Equations 2.9 and 2.11.
For these expressions, energies are expressed in electron volts per Na+–Cl– pair, and r is the distance in nanometers. The net energy EN is just the sum of the preceding two expressions. (a) Superimpose on a single plot EN, ER, and EA versus r up to 1.0 nm. (b) On the basis of this plot, determine (i) the equilibrium spacing r0 between the Na+ and Cl– ions, and (ii) the magnitude of the bonding energy E0 between the two ions. (c) Mathematically determine the r0 and E0 values the solutions to Problem 2.18, and compare these with the graphical results from part (b). Solution (a) Curves of EA, ER, and EN are on the plot below. (b) From this plot: r0 = 0.24 nm E0 = 5.3 eV (c) From Equation 2.17 for EN A = 1.436 B = 7.32 106 n = 8 Thus, and = – 5.32 eV 2.20 Consider a hypothetical X+–Y– ion pair for which the equilibrium interionic spacing and bonding energy values are 0.38 nm and –5.37 eV, respectively. If it is known that n in Equation 2.17 has a value of 8, using the results of Problem 2.18, determine explicit expressions for attractive and repulsive energies EA and ER of Equations 2.9 and 2.11.
Solution%20Manual%20for%20Materials%20Science%20and%20Engineering%20An%20Introduction%209th%20Edition%20Callister,%20Rethwisch.docx