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
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)
- At what temperature, in terms of Tc, is the critical field of a superconductor one-half its value at T = 0 K?arrow_forwardd) Show that the resistivity canbe expressed (via the familiar notation) as, m p= net here m is the electronmass; † is the period of time that elapses between two subsequent collisions, the electron undergoes with copper nuclei throughout its chaotic motion in the body of copper (supposing that the current carrying cable is made of copper). Hint: Write F=eE, i.e. the electric force reigning on the electron. Write also the acceleration a=F/m, an electron is subject to, based on the Newton's law ofmotion.arrow_forwardGraph below shows the electron occupancy probability P(E) as a function of energy for Bismuth (mBi = 3.47 × 10-25 kg) at the temperature T = 0 K. What is the number of conduction electrons per unit volume for Bismuth? 1 1 2 3 4 5 6 7 8 E (ev) P(E)arrow_forward
- The potential energy of a system of two atoms is given by the relation U =-A/r + B/r10 A stable molecule is formed with the release of 8 eV energy when the interatomic distance is 2.8 Å. Find A and B and the force needed to dissociate this molecule into atoms and the interatomic distance at which the dissociation occurs.arrow_forwardA brittle material has the properties Sut=30 kpsi and Suc=90 kpsi. Using the brittle Coulomb- Mohr and modified-Mohr theories, determine the factor of safety for the following states of plane stress. Ox=-15 kpsi, o,=10 kpsi, txy=-15 kpsiarrow_forwardIn solid KCI the smallest distance between the centers of a. potassium ion and a chloride ion is 314 pm. Calculate the length of the edge of the unit cell and the density of KCI, assuming it has the same structure as sodium chloride.arrow_forward
- One model for the potential energy of a two-atom molecule, where the atoms are separated by a distance r, is U(r) = Uo[(¹) ¹2 – ( )²] where ro = 0.8 nm and U₁ = 6.1 eV. Note: 1 eV = 1.6 × 10-19 J. Some helpful units: [Force] = eV/nm [Energy] = eV [distance] = nm Equilibrium Distance What is the distance between the atoms when the molecule is in stable equilibrium? Click here for a hint T'eq Hint: Hint: Hint: Hint: Hint: Hint: Force If the distance between the atoms increases from equilibrium by r₁ = 0.35 nm, then what is the force from one atom on the other associated with this potential energy? (Enter your answer as postive if they repel each other, and negative if they attract.) Fr(req+r₁) Hint: Hint: 0.89105934nm Kinetic Energy Hint: The atoms are oscillating back and forth. The maximum separation of the atoms is r₂ = 2 nm. What is the kinetic energy of the atoms when they are separated by the equilibrium distance? Click here for a hint K(req) Hint: Hint: = -1.288eV/nm 3.99eVarrow_forwardX- Hall Effect demonstrates that it is the electrons that are free to move. Y- Germanium and Selenium are materials that are intermediate between insulators and conductors. O X is true and Y is false O X is false and Y is true O X and Y are both true O X and Y are both falsearrow_forward15.8 V 3.20 40 0.8 0 9.5 V "loop 1.5 0 20 0.7 0 3.8 n 28 V 17 V 0.50 Which of the following coefficient matrices represent the KCL and the KVL equations? -1 -1 -8 -3.5 -5 -1 -1 1 -8 3.5 0. -3.5 -5 -1 -1 -1 8. -3.5 3.5 -5 1 -1 -1 -8 3,5 -6.8 3.5 -5arrow_forward
- Construct the electron density along the x-axis of a crystal given the following structure factors:h 0 1 2 3 4 5 6 7 8 9Fh +30.0 +8.2 +6.5 +4.1 +5.5 -2.4 +5.4 +3.2 -1.0 + 1.1h 10 11 12 13 14 15Fh +6.5 +5.2 -4.3 -1.2 +0.1 +2.1arrow_forwardThe number of silicon atoms per m3 is 5 × 1028. This is doped simultaneously with 5 × 1022 atoms per m3 of Arsenic and 5 × 1020 per m3 atoms of Indium. Calculate the number of electrons and holes.arrow_forwardK:54)arrow_forward
- Modern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage LearningUniversity Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStax