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} \text{ kg}, \quad a = 2.0 , \text{Å} = 2.0 \times 10^{-10} _______ ________ ______ _____ _______ ______ ___ _____.
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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:
Explain the significance of the pseudogap phase in cuprates.
The susceptibility of is
and its density is
. Calculate its total polarisability. Assume that the mass number for
is 32.
For a superconducting specimen, the critical fields are and
at
and
respectively. Calculate the critical temperature and critical field at
.
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 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.