Show that any arbitrary rotation axis is not permitted in a crystal lattice.

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Draw the device structure of a p-n junction solar cell and explain how light energy is converted into electrical energy. Draw and explain its I-V characteristics.

Distinguish between a superconductor and perfect conductor. Explain what is a Cooper pair.

Differentiate between n-p-n and p-n-p transistors. Give their device structure and biasing circuits when used as an amplifier.

Design a transistor based Colpitt oscillator which can oscillate at 9\,\mathrm{MHz}. Explain how the oscillations are created and sustained.

Describe an operational amplifier based integrator. Using operational amplifier integrators, design a circuit to solve the following differential equation: \frac{d^2v}{dt^2}+2\frac{dv}{dt}+3v=0

The velocity of sound in f.c.c. gold and f.c.c. copper is 2100\,\mathrm{m/s} and 3800\,\mathrm{m/s} respectively. If the Debye temperature of copper is 348\,\mathrm{K}, then determine the Debye temperature of gold. Take the densities of gold and copper as 1.93 \times 10^{4}\,\mathrm{kg/m^3} and 0.89 \times 10^{4}\,\mathrm{kg/m^3} respectively.

What is the reciprocal lattice and why is it named so? Derive the relationships for the primitive translation vectors of the reciprocal lattice in terms of those of the direct lattice.

Explain the working of SEM and TEM and highlight the major differences in principles. Draw neat schematic diagrams.

In a cubic unit cell, find the angle between normals to the plane (111) and (121).

Lead in the superconducting state has critical temperature of 6.2\ \mathrm{K} at zero magnetic field and a critical field of 0.064\ \mathrm{MA\,m^{-1}} at 0\ \mathrm{K}. Determine the critical field at 4\ \mathrm{K}.

How does the energy gap in superconductors differ from the energy gap in insulator? How does it vary with temperature for superconductors?

An electric field of 100\ \mathrm{V/m} is applied to a sample of n-type semiconductor whose Hall coefficient is -0.0125\ \mathrm{m^3/coulomb}. Determine the current density in the sample assuming \mu_x = 0.36\ \mathrm{m^2\,V^{-1}\,s^{-1}}.

{q-8-004-fig-1} A crystal plane is shown in the above figure. Find its Miller indices and interplanar spacing.

Show that the London equation \vec{\nabla} \times \vec{J} = -\frac{1}{\mu_0\lambda_L^2}\vec{B} or \vec{j} = -\frac{c}{4\pi n\lambda_L^2}\vec{A} leads to the Meissner effect.

Starting with the expression for the density of states for electrons in a band, show that the Fermi energy of an intrinsic semiconductor is at the middle of the band gap. Use these results to estimate the electron density at 300 K (Assuming E_g=1\,\mathrm{eV} and the rest masses of electron and hole as m_e and m_h).

Construct a digital circuit to add three bits A, B and C and provide their sum and carry as outputs. Show appropriate Boolean expressions and truth table to justify the outputs.

Draw and explain the collector characteristics of a bipolar junction transistor in common emitter configuration. Using the plot, explain how the transistor can be used as an ON-OFF switch.

{q-8-074-fig-1} Explain how the circuit shown above can be a source of oscillations. Use this circuit to construct a transistor oscillator and explain its working. What is the frequency of oscillations of this circuit?