1. Attempt any five parts:

With the help of an appropriate diagram explain all the symmetry elements of a methane molecule.

Show that nearly half the volume of the unit cell of a simple cubic lattice is occupied by its atoms.

Explain three types of Van der Waals bonding.

Draw a labelled energy band diagram for a p-type semiconductor.

The potential energy function is given by.

<img src='./qimages/10395-1e.jpg'>

Obtain the inter-molecular distance for which the potential energy is minimum.

Fermi energy of an intrinsic semiconductor is 0·7 eV. The low lying energy levels in the conduction band is 0·2 eV above the Fermi level. Calculate the probability of occupation of this level by an electron, at room temperature.

Explain with the help of appropriate examples the difference between a piezoelectric and a pyroelectric crystal.

Explain the application of thin films as interference filters.

2. Answer any two parts:

What is rotational symmetry in a lattice Show that 5-fold rotational symmetry is not possible in a 2-D lattice.

Describe the Laue's method of crystal structure determination. Write down its limitations.

Prove that the reciprocal lattice of a bcc is an fcc structure.

3. Answer anyone part

State the basic difference between the Einstein's and Debye's theories of specific heat capacity. The expression for heat capacity according to Debye's theory is given by

<img src='./qimages/10395-3a.jpg'>

where symbols have their usual meanings. Obtain the T^3 law.

Derive the expression for dispersion relation for a linear array of the same type of atoms.

4. Answer any two parts:

Show that the effective mass of an electron in a crystalline solid is given by

<img src='./qimages/10395-4a.jpg'>

Explain how a superconductor can be used for magnetic shielding.

Calculate the limiting value of the magnetic field for which Nb will act as a superconductor at 4 K. Take Bac(O) as 1970 Oe and Tc for Nb to be 9·25 K

Derive an expression for Hall coefficient. What are its applications

5. Answer any two parts:

Distinguish between para- and ferro-magnetism. Give two examples of each category.

Classify the defects in crystals. Explain any one of these classes in detail with suitable diagrams.

What is a "Transducer" Explain the working of any one transducer.

Physical Constants:

<img src='./qimages/10395-4c.jpg'>