Show that for the superconducting transition in the absence of magnetic field, there is a discontinuity in the specific heat of a superconductor at Tc which can be written as:
We start from the thermodynamic relation for a superconductor in the absence of an external magnetic field. The Gibbs free energy per unit volume for the normal ((G_n)) and superconducting ((G_s)) states are related by the condensation energy: [ G_s(T, H=0) = G_n(T, H=0) - \frac{\mu_0 H_c^2(T)}{2} ] where (H_c(T)) ___ _________ _______ _________ _____ _________ ____ __________ _____ ____ ___ _________.
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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 .
Show that for the superconducting transition in the absence of magnetic field, there is a discontinuity in the specific heat of a superconductor at Tc which can be written as:
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
In Sommerfeld free electron theory, show that at a temperature T
(i) and (ii)
For a superconducting specimen, the critical fields are and
at
and
respectively. Calculate the critical temperature and critical field at
.
A metallic element has a density of , a lattice constant of
and an atomic weight
. Calculate the number of atoms per unit cell of this element and predict its lattice crystal structure.
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.