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
.
For a one-dimensional monoatomic linear chain, the dispersion relation for longitudinal waves is: [ \omega(k) = 2 \sqrt{\frac{K}{M}} , \bigg| \sin\frac{ka}{2} \bigg| ] where (K) is the spring constant, (M) is the atomic mass, (a) is the inter-atomic distance, and (k) is the wavevector. Given: [ M = 10^{-26} ____ __________ ___ ________ _____ _____ _______ __________ __________ _______ _____ ______.
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For Chromium () vapour at
with a number density of atoms
calculate:
i) The Larmor diamagnetic susceptibility assuming the atomic radius to be 1.2 A.
ii) The Curie paramagnetic susceptibility.
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 the hydrogen molecule which has two hydrogen atoms each with one electron occupying the 1s energy level, write the two particle wave functions for the singlet and triplet states. Determine the eigenvalues of the effective Hamiltonian
Calculate the resistivity of Silicon at given that its resistivity at
is
.
Calculate the energy dispersion for s-band in the bcc lattice for the tight binding approximation.
Note: For the central atom located at (0,0,0) in the bcc unit cell, the nearest neighbours are located at , where a is the lattice constant.
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
.
Show that the reciprocal lattice of a bcc lattice is an fcc lattice. Calculate the magnitude of the shortest non-zero reciprocal lattice vector.