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.
The isotope effect for superconductors is given by the relation: [ T_c \sqrt{M} = \text{constant} \quad \text{or} \quad T_c \propto ______ ________ ____ __________ ___ ______ ____ _______.
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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 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.
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
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:
The susceptibility of is
and its density is
. Calculate its total polarisability. Assume that the mass number for
is 32.
Explain the significance of the pseudogap phase in cuprates.
For a superconducting specimen, the critical fields are and
at
and
respectively. Calculate the critical temperature and critical field at
.