1.1 The conventional unit cell for an fcc lattice is a cube with side length a. (a) Assuming that each lattice point is associated with a sphere of radius r, show that a² = 8r². (Hint: consider a single face of the cube, and that certain atoms will be touching each other.) (b) What is the total volume per unit cell taken up by spheres? (c) Hence show that the packing fraction of this structure is 2π 3√8 ~ 74%.

1.1 The conventional unit cell for an fcc lattice is a cube with side length a. (a) Assuming that each lattice point is associated with a sphere of radius r, show that a² = 8r². (Hint: consider a single face of the cube, and that certain atoms will be touching each other.) (b) What is the total volume per unit cell taken up by spheres? (c) Hence show that the packing fraction of this structure is 2π 3√8 ~ 74%.

Modern Physics

3rd Edition

ISBN:9781111794378

Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Publisher:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Chapter12: The Solid State

Section: Chapter Questions

Problem 5P

See similar textbooks

Similar questions

The atoms of an FCC lattice are hard spheres touching the surfaces of the nearest neighbors. If the effective radius of an atom is 4.25 Angstrom, what is the surface density in the (110) plane and what is the distance between nearest (110) planes?
Give only typing answer with explanation and conclusion The Einstein-A coefficient for a particular rovibrational transition of CO2 is 220 s−1. In the absence of collisions, what is the characteristic lifetime of the upper state? Compare this with the Na transition near 589.6nm which has an Einstein-A coefficient of 6.14×10^7 s−1.
Is it reasonable to expect superconductivity in a "glass," a material with almost no crystalline structure? Why or why not, if that's the case?
Use the results of this section to estimate the contribution of conduction electrons to the heat capacity of one mole of copper at room temperature. How does this contribution compare to that of lattice vibrations, assuming that these are not frozen out? (The electronic contribution has been measured at low temperatures, and turns out to be about 40% more than predicted by the free electron model used here)
Would you expect superconductivity from a "glass" with no or little crystal structure? If not, why not?
Calculate the surface density of the lattice atoms located on the (110) plane of the SC crystal ?? Please solve it quickly by handwritten
To obtain the value of an unknown electrical charge, a group performed an experiment. From the graph of the electric potential (voltage) V in volts, as a function of the inverse distance (1/r) in m^-1, the group obtained an angular coefficient 6838 Nm^2/C by the linear equation of the best straight line. Knowing that V=(kq)/r, calculate the value of the electric charge, in nC (nanocoulomb), from the slope provided by the best line. Round the answer to a whole number. Use: k = 8.9876 x 10^9 N⋅m^2⋅C^−2
Consider a free Fermi gas in two dimensions, confined to a squarearea A = L2. Because g(€) is a constant for this system, it is possible to carry out the integral 7.53 for the number of particles analytically. Do so, and solve for μ as a function of N. Show that the resulting formula has the expected qualitative behavior.
Suppose that the out-of-plane distortion of an AB3 planar molecule is described by a potential energy V= V0 (1- ebh^4 ), where h is the distance by which the central atom A is displaced. Sketch this potential energy as a function of h (allow h to be both negative and positive). What could be said about (a) the force constant, (b) the vibrations? Sketch the form of the ground-state wavefunction.
Imagine you generate a three-dimensional lattice by taking vector a and b vectors that form a two-dimensional square lattice. Then add a third vector, c, that is of different length and perpendicular to the first two. Which of the seven three-dimensional lattices results?
What is the name of the rule that the emission usually takes place from thelowest vibrational level of the first excited singlet state, because of the rapidvibrational relaxation and internal conversion?
Hint:Although the band gap and the density of states vary with temperature, those variations are much slower compared to the exponential factor e^(-Eg/2KT). Please give some insight to this problem and go over the equations and steps needed to solve for the Max temperature. Thank you .