Chapter 9, Problem 3P

The Madelung constant for the NaCl structure may be found by summing an infinite alternating series of terms giving the electrostatic potential energy between an Na+ ion and its 6 nearest Cl neighbors, its 12 next-nearest N+ neighbors, and so on (see Fig. 12.1a). (a) From this expression, show that the first three terms of the infinite series for the Madelung constant for the NaCl structure yield = 2.13. (b) Does this infinite series converge rapidly? Calculate the fourth term as a check.

Under pressure, liquid helium can solidify as each atom bonds with four others, and each bond has an average energy of 1.74 × 10–23 J. Find the latent heat of fusion for helium in joules per gram. (The molar mass of He is 4.00 g/mol.)

To improve the semiconducting characteristics of GaAs, 1.31 x 10^15 atoms of Be are incorporated into the material. Be has an ionization energy of 0.6eV. What is the concentration/s of the majority and minority charge carrier?