Linear ionic crystal Consider a line of 2N ions of alternating charge q with a repulsive potential energy A R n between nearest neighbors (a) Show that at the equilibrium separation (CGS) U (R 0 ) 2Nq 2 In2 R 0 (1 1 n) (b) Let the crystal be compressed so that R 0 R 0 (l ) Show that the work done in compressing a unit length of the crystal has the leading term 1 2C 2 , where (CGS) C (n 1) q 2 In2 R 0 To obtain the results in SI, replace q 2 by q 2 4 0 Note We should not expect to obtain this result from the expression for U (R 0 ), but we must use the complete expression for U(R)

Question: Linear ionic crystal Consider a line of 2N ions of alternating charge q with a repulsive potential energy A/R n between nearest neighbors. (a)

Linear ionic crystal Consider a line of 2N ions of alternating charge ± q with a repulsive potential energy A/Rⁿ between nearest neighbors.

(a) Show that at the equilibrium separation (CGS) U (R₀) = – 2Nq²In2/R₀(1 – 1/n).

(b) Let the crystal be compressed so that R₀ → R₀(l – δ). Show that the work done in compressing a unit length of the crystal has the leading term 1/2Cδ², where (CGS) C = (n – 1) q² In2/R_0.To obtain the results in SI, replace q² by q²/4πε₀. Note: We should not expect to obtain this result from the expression for U (R₀), but we must use the complete expression for U(R).

Step by Step Solution

★★★★★

3.49 Rating (179 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a In equilibrium and UR N au OR A R N aq R nA a 2 log 2 Madel... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

14-P-S-S-G-P (15).docx

120 KBs Word File

Students Have Also Explored These Related Solid State Questions!

Show that at the position where the magnitude of the voltage on the Line is a maximum the input impedance is purely real.

Consider a line of positive charge with line charge density ? as measured in a frame S at rest with respect to the charges.(a) Show that the electric field a distance r from this charged line has...

Diatomic line, consider a line of atoms ABAB. . . AB, with an AB bond length of 1/2a, the form factors are fA, fB for atoms A, B, respectively. The incident beam of x-rays is perpendicular to the...

Consider a line of 2 N ions of alternating charge q with a repulsivepotential energy A / R between nearest neighbors.A ) Show that at the equilibrium separation U ( R , ) = - 2 Ng ` ( 1 - 1 / n ) h 2...

In an ionic crystal lattice each cation will be attracted by anions next to it and repulsed by cations near it. Consequently the coulomb potential leading to the lattice energy depends on the type of...

1. Consider two charges as shown in figure below: P r = 2m r = 2m 60 60 +q -q Which of the following is correct for the net electric field Enet and total electric potential Vtotal at point P? A. Enet...

For my condensed matter physics class, please add explanation to solution! Thank-you 02 (10 points) Consider a one-dimensional crystal chain of alternating charged ions of charge iq. Assume that the...

Among 900 people in a state 90 are found to be chapatti eaters. Find the confidence interval for p at 99% level of significance.

The repulsive core-core energy between neighboring ions separated by r in a binary ionic crystal of 2N ions of alternating positive and negative charges of e is A/r^n ,where n=9 and A=2.23 x 10^-105...

Detail and illustrate the properties of each element of a RFID capture system

Edgewater Enterprises manufactures two products. Information follows: Sales price Variable cost per unit Product mix Product A $ 18.50 $ 6.85 Weighted average CM 40% per unit Product B $ 21.75...

Given the information on page 90 for Pamplin Inc.: a. How much is the firms net working capital and what is the debt ratio? b. Complete a common- sized income statement, a common- sized balance...

11.17 Calculate the value of Z L in the circuit of Fig. 11.48 in order for Z L to receive maximum average power. What is the maximum average power received by Z L ? -/10 2 ZL 30 40 5/90 A 20

what is the Procedure for designing and operating a management accounting system for a university?

Q19 ) (Input / Output) A RAID can fail only if the data is not recoverable after a crash. Suppose that the probability of one drive crashing in a given hour is p . Also suppose that the RAID has 4...

Define facility location. What is the need of new facility location?

Consider a lattice of fixed hydrogen atoms; suppose that each atom can exist in four states: Find the condition that the average number of electrons per atom be unity. The condition will involve ?,...

In carbon monoxide poisoning the CO replaces the O2 absorbed on hemoglobin (Nb) molecules in the blood. To show the effect, consider a model for which each adsorption site on a heme may be vacant or...

Suppose that at most one O2 can be bound to a heme group (see problem 8), and that when (O2) = 10-5 we have 90 percent of ht hemes occupied by O2. Consider O2 as having a spin of 1 and a magnetic...

The chemical potential was defined by (5) as (F/N) a,V . an equivalent expression listed in table 5.1 is = (U/N) a,V Prove that this relation, which was used by Gibbs to define , is equivalent to...

Find the maximum height to which water may rise in a tree the assumption that the roots stand in a pool of water and the uppermost leaves are in air containing water vapor at a relative humidity r =...

P9-6 Defining and Analyzing Changes in Current Liabilities LO9-1 International Business Machines (IBM) is a leading provider of computer products and services. The company is known for its hardware...