Modern Physics
3rd Edition
ISBN: 9781111794378
Author: Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher: Cengage Learning
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Chapter 12, Problem 8P
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 α = 2.13. (b) Does this infinite series converge rapidly? Calculate the fourth term as a check.
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1.2 Below 24.5 K, Ne is a crystalline solid with an FCC structure. The interatomic interaction energy
per atom can be written as:
(1)
6
E(r) = -28
2E 14.45*
(ii)
(iii)
–
12
13¹] (ev/atom)
Where, & and o are constants that depend on the polarizability, the mean dipole moment, and the
extent of overlap of core electrons. For crystalline Ne, & = 3.121 x 10-3 eV and a = 0.274 nm.
12.13
Show that the equilibrium separation between the atoms in an inert gas crystal is given
by ro= (1.090) o.
What is the equilibrium interatomic separation in the Ne crystal?
Find the bonding energy per atom in solid Ne.
Estimate kBT at room temperature, and convert
this energy into electronvolts (eV). Using this result, answer the following:
(a) Would you expect hydrogen atoms to be ionized
at room temperature? (The binding energy of an
electron in a hydrogen atom is 13.6 eV.)
(b) Would you expect the rotational energy levels
of diatomic molecules to be excited at room temperature? (It costs about 10−4 eV to promote such
a system to an excited rotational energy level.)
Estimate kBT at room temperature, and convert this energy into electronvolts (eV). Using this result, answer the following:
(a) Would you expect hydrogen atoms to be ionized at room temperature? (The binding energy of an electron in a hydrogen atom is 13.6 eV.)
(b) Would you expect the rotational energy levels of diatomic molecules to be excited at room temperature? (It costs about 10-4 eV to promote such a system to an excited rotational energy level.)
Chapter 12 Solutions
Modern Physics
Ch. 12 - Prob. 1QCh. 12 - Prob. 2QCh. 12 - Prob. 3QCh. 12 - Prob. 4QCh. 12 - Prob. 5QCh. 12 - Prob. 6QCh. 12 - Prob. 7QCh. 12 - Prob. 8QCh. 12 - Prob. 9QCh. 12 - Prob. 11Q
Ch. 12 - Discuss the differences between crystalline...Ch. 12 - Prob. 13QCh. 12 - Prob. 15QCh. 12 - Prob. 16QCh. 12 - Prob. 17QCh. 12 - Prob. 19QCh. 12 - Prob. 21QCh. 12 - Prob. 22QCh. 12 - Prob. 1PCh. 12 - Prob. 2PCh. 12 - Prob. 3PCh. 12 - Prob. 4PCh. 12 - Prob. 5PCh. 12 - Prob. 6PCh. 12 - Prob. 7PCh. 12 - The Madelung constant for the NaCl structure may...Ch. 12 - Prob. 9PCh. 12 - Prob. 10PCh. 12 - Prob. 11PCh. 12 - Prob. 12PCh. 12 - Prob. 13PCh. 12 - Prob. 15PCh. 12 - Prob. 16PCh. 12 - Prob. 18PCh. 12 - Prob. 19PCh. 12 - Prob. 20PCh. 12 - Prob. 21PCh. 12 - Determine the current generated in a...Ch. 12 - Prob. 23PCh. 12 - Under pressure, liquid helium can solidify as each...Ch. 12 - Prob. 25P
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