Concept explainers
The Madelung constant (Section 37.3) is notoriously difficult to calculate because it’s the sum of an alternating series of nearly equal terms. But it can be calculated for a hypothetical one-dimensional crystal consisting of an evenly spaced line of alternating positive and negative ions (Fig. 37.25). Show that the potential energy of an ion in this “crystal” can be written as
where the Madelung constant α has the value 2 ln2.
FIGURE 37.25 Problem 61
Want to see the full answer?
Check out a sample textbook solutionChapter 37 Solutions
Mastering Physics with Pearson eText -- Standalone Access Card -- for Essential University Physics (3rd Edition)
Additional Science Textbook Solutions
Introduction to Electrodynamics
The Cosmic Perspective Fundamentals (2nd Edition)
Mathematical Methods in the Physical Sciences
Fundamentals of Physics Extended
Fundamentals Of Physics - Volume 1 Only
The Cosmic Perspective (8th Edition)
- 1)A Si crystal in the form of a cube of side 1.0 nm is at equilibrium at 300 K.The edge of the conduction band is Ec = -1.0 eVa) What is the energy of a conduction electron in the ground state (in eV) ?b) What is the energy of the conduction electron in the first excited state (in eV)?arrow_forwardA three-level laser emits a light of wavelength of 5500 Å. What will be the ratio of population of upper level (E2) to the lower level (E1) if the optical pumping mechanism is shut off (Assume T = 300 K)? At what temperature for the above condition the ratio of population will be half? [kB = 1.38 × 10-23 JK-1]arrow_forwardMass of electron m₀ : 9.1 × 10⁻³¹kg Avogadro number N₂ : 6.02 × 10²³ Charge of electron ℯ : 1.6 × 10⁻¹⁹ C 1 ℯV = 1.6 × 10⁻¹⁹ J Boltzman costant k₃ : 1.38 × 10⁻²³ J/K = 8.6 × 10⁻⁵ ℯV/K R = 8.314 J/K·mol Q. The equilibrium interatomic spacing and melting point of sodium halide are as follows. Explain the reasons for the observed trend. NaF NaCI NaBr NaI interval(nm) 0.23 0.28 0.29 0.32 meltingpoint(℃) 988 801 740 660arrow_forward
- A diatomic F2 molecule is in the l = 1 state, (a) What is the energy of the molecule? (b) How much energy is radiated in a transition from a l =2 to a l = l state?arrow_forwardb) If the effective mass of electron is 0.4m0 having momentum 2.416×10−16 ????.?????then calculate energy of free electron in “electron volt” at the bottom of conduction bandarrow_forwardTin (Sn) has a superconductive critical temperature Tc = 3.7 K and critical magnetic field at T = 0 K equal to Bc = 31 mT. What is the maximum magnetic field Sn can sustain at the critical temperature without losing its superconducting state? What is the minimum radius required for an infinite linear wire of Sn if it is to carry a current of 200 A at T = 3.0 K whilst still in its superconducting state?arrow_forward
- The molar polarization of fluorobenzene vapour varies linearly with T−1, and is 70.62 cm3 mol−1 at 351.0 K and 62.47 cm3 mol−1 at 423.2 K. Calculate the polarizability and dipole moment of the molecule.arrow_forward(a) Suppose a piece of very pure germanium is to be used as a light detector by observing, through the absorption of photons, the increase in conductivity resulting from generation of electron–hole pairs. If each pair requires 0.67 eV of energy, what is the maximum wavelength that can be detected? In what portion of the spectrum does it lie? (b) What are the answers to part (a) if the material is silicon, with an energy requirement of 1.12 eV per pair, corresponding to the gap between valence and conduction bands in that element?arrow_forward
- Physics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningModern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- University Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStax