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IGNOU MPH-12 (January 2026 – December 2026) Assignment Questions
PART A
1. a) A metallic element has a density of 2.70 g cm-3, a lattice constant of 4.0495 Å and an atomic weight 26.9815g mol-1. Calculate the number of atoms per unit cell of this element and predict its lattice crystal structure.
b) Show that the reciprocal lattice of a bcc lattice is an fcc lattice. Calculate the magnitude of the shortest non-zero reciprocal lattice vector.
c) A metallic crystal has an fcc lattice with a lattice constant 0.4 nm. 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 0.154 nm.
2. a) Calculate the inter-atomic equilibrium distance re for KCl for which the equilibrium lattice energy is 163.0 kcal mol-1, n=8.6 and the Madelung constant is 1.75.
b) For a linear chain of identical atoms of mass 10-26 kg calculate the maximum value of the angular frequency of the longitudinal wave and the group velocity at k=0, given that the inter-atomic distance is 2.0 Å and the spring constant is 20 Nm-1.
c) Calculate the temperature at which the lattice contribution to the specifc heat and the electronic contribution to the specific heat become equal in a metal which has a Debye temperature of 390 K and a Fermi energy 11.7 eV.
3. a) A divalent metal crystallizes in an fcc structure with a lattice constant of 4.5 Å . Calculate the number density of conduction electrons and the Fermi velocity.
b) In Sommerfeld free electron theory, show that at a temperature T.
PART B
4 a) Calculate the resistivity of Silicon at 60 0C given that its resistivity at 30 0C is 2.5 Ωm.
b) In an n-type semiconductor the Fermi level lies 0.4 eV below the conduction band at T=300 K. Calculate the position of the Fermi level when the temperature is raised to 330 K.
5. a) The susceptibility of O2 is 0.39×10-3 and its density is 1.43 kgm-3. Calculate its total polarisability. Assume that the mass number for O2 is 32.
c) The critical temperature of lead (Pb) of average atomic mass 207.2 amu is 7.20 K. Calculate the critical temperature of a specimen of lead isotope with mass 206 amu using the normal isotope effect.
d) Explain the significance of the pseudogap phase in cuprates.
