Homework 1, 406
[1] Find B (BB, in tesla), 1/ (wave number for photon, in cm-1) and T (kBT, in Kelvin),
corresponding to the energy of 0.1 meV.
[2] Why “face centered tetragonal” is not one of 14 3D Bravais lattices?
[3] What is the filling factor of hcp structure?
[4] Consider the following unite cell (yellow balls are “La” ions). How many La, Cu and O ions
in each unit cell? What is the right chemical formula?
[5] For ionic crystals, the chemical binding energy originates from electrostatic Coulomb orce,
and is called the Madelung energy. In the NaCl structure, the total Madelung energy is
Utot = N(Zλe-R/ρ- αq2/R), where N = the total # of cations or anions, Z = the # of nearest
neighbors of any ion, α = a constant (the so-called Madelung constant), R = the nearest-neighbor
separation, q = charge of ions, and λ, ρ are constants. Show that for a small deviation from the
equilibrium separation R0, the total energy follows the Hook’s law, and find the spring constant.