A divalent metal crystallizes in an fcc structure with a lattice constant of 4.5 A. Calculate the number density of conduction electrons and the Fermi velocity.
For a divalent metal in an fcc structure, each atom contributes 2 conduction electrons. Step 1: Number of atoms per unit cell In an fcc lattice, there are 4 atoms per unit cell. Step 2: Number of conduction electrons per unit cell Since _____ __________ __________ ___ ________ _______ ______.
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The critical temperature of lead (Pb) of average atomic mass is
. Calculate the critical temperature of a specimen of lead isotope with mass
using the normal isotope effect.
Calculate the temperature at which the lattice contribution to the specific heat and the electronic contribution to the specific heat become equal in a metal which has a Debye temperature of and a Fermi energy
.
Show that the reciprocal lattice of a bcc lattice is an fcc lattice. Calculate the magnitude of the shortest non-zero reciprocal lattice vector.
For a linear chain of identical atoms of mass calculate the maximum value of the angular frequency of the longitudinal wave and the group velocity at
, given that the inter-atomic distance is 2.0 A and the spring constant is
.
In an n-type semiconductor the Fermi level lies below the conduction band at
. Calculate the position of the Fermi level when the temperature is raised to
.
Explain the significance of the pseudogap phase in cuprates.
A metallic crystal has an fcc lattice with a lattice constant . Explain whether the following planes are allowed or forbidden for X-ray diffraction:
(100), (111), (210), (220)
Calculate the X-ray diffraction angles for the allowed planes. Assume that diffraction occurs in the first order and the X-ray wavelength is .