The transition temperature for an isotope of Mercury (Hg) with a mass of 199u is 4.185K. Calculate the transition temperature for an isotope of Hg with mass number 202u. Take the value of the exponent a to be 0.5.
The transition temperature (\( T_c \)) of a superconducting material depends on its isotopic mass (\( M \)) according to the isotope effect equation: \[ T_c \propto M^{-a} _____ ____ _______ _______ ____ ___ ______ ___ ________ _____ ____ _____.
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Calculate the wavelength of the photon required to break the Cooper pair in a superconductor with a transition temperature of 1.3 K.
Debye temperature for diamond is 2230 K. Calculate the frequency of highest possible lattice vibration in diamond and its molar heat capacity at 20 K
Consider an electron in a bcc lattice with lattice constant b. Show that a wave function of the form:
satisfies the Bloch theorem.
For the energy dispersion relation:
calculate the inverse mass tensor and the group velocity given m1 = 3m2.
Calculate the temperature at which the number of electrons in the conduction band of a semiconductor is four times the number at room temperature. Take the band gap energy to be 1.2 eV with Ec - EF ≈ EG.
Show that the volume of the primitive cell in the reciprocal lattice space is inversely proportional to the volume of the primitive cell in the direct lattice.
Metallic sodium is monovalent and crystallizes in a bcc structure with a lattice constant of 4.25 A. Calculate the number density of conduction electrons and the Fermi energy at 0 K.