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 .
For an fcc lattice, the structure factor determines whether a plane (hkl) is allowed for X-ray diffraction. The condition for allowed reflections is that h, k, l are either all even or all odd. If this is not satisfied, the reflection is forbidden. Given planes: 1. (100) → _______ _____ ____ ______ ________.
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The susceptibility of is
and its density is
. Calculate its total polarisability. Assume that the mass number for
is 32.
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
.
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 inter-atomic equilibrium distance re for for which the equilibrium lattice energy is
,
and the Madelung constant is 1.75.
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.
In Sommerfeld free electron theory, show that at a temperature T
(i) and (ii)
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
.