**[OBJECTIVE]**

**Subject:** Solid State Physics-I

**Time Allowed:** 15 Minutes

**Maximum Marks:** 10

**NOTE:** *Attempt this Paper on this Question Sheet only. Please encircle the correct option. Division of marks is given in front of each question. This Paper will be collected back after expiry of time limit mentioned above.*

__Part-I Encircle the right answer, cutting and overwriting are not allowed. (10)__

The coordination number of CsCl structure is

a) 1

b) 7

c) 8

d) 14

Which combination of following crystal structures are closely-packed structures?

a) FCC and SC

b) BCC and SC

c) BCC and HCP

d) HCP and FCC

The space Jattice of cesium chloride (CsCl) structure is:

a) Simple cubic

b) Body centered cubic

c) Face-centered cubic

d) None of these

Reciprocal of face centered cubic (FCC) lattice is

a) FCC lattice

b) BCC lattice

c) SC lattice

d) HCP lattice

e) none of these

For p atoms in primitive cell, which of the following combination of acoustical and optical phonon branches in sequence is true?

a) (3p-3,3)

b) (3, 3p-3)

c) (3.3)

d) none of these

According to classical model of lattice heat capacity (C_{v}), C_{v} for all solids

a) depends on temperature

b) docs not depend on temperature

c) remains constant at all temperatures

d) b) and c

e) none of these

Van der Waals interactions in inert gas crystals are always

a) repulsive

b) attractive

c) neither attractive nor repulsive

d) zero

e) none of these

At Jow temperatures, phonon heat capacity, C_{v} (according of Debye modcl) varies as:

a) T^{3}

b) T^{3/2}

c) T^{2}

d) T

e) None of these

In monatomic lattice, the frequency of the wave at long wavelengths varies with k as:

a) k

b) k^{2}

c) k^{3}

d) independent of wave-vector k

In a cubic crystals, [111] crystallographic direction to (111) crystal plane is always

a) Parallel

b) Perpendicular

c) neither parallel nor perpendicular

d) none of these

**[SUBJECTIVE]**

**Subject:** Solid State Physics-I

**Time Allowed:** 2 Hours 45 Minutes

**Maximum Marks:** 50

**NOTE:** *ATTEMPT THIS (SUBJECTIVE) ON THE SEPARATE ANSWER SHEET PROVIDED.*

__Part-II Give short notes on following, each question carries equal marks. (20)__

**Q#1:** Draw (111), (200), (100) and (100) crystallographic planes in cubic unit cell.

**Q#2:** Differentiate between Bravais and non-Bravais lattice with the help of diagrams.

**Q#3:** Explain primitive and non-primitive unit cell. Differentiate by sketching diagrams.

**Q#4:** Show that reciprocal of FCC lattice is a BCC lattice.

**Q#5:** Calculate the packing fraction of face-centered cubic (FCC) lattice.

__ __

__Part-III Give detailed answers, each question carries equal marks. (30)__

**Q#1:** Consider a linear chain of diatomic atoms of masses m_{1} and m_{2} (m_{1} > m_{2}) with repeat distance a and interatomic force constant c.

**i)**Establish the equations of motion of two atoms and derive the dispersion relation for a diatomic linear lattice by taking into account nearest neighbor interaction only.**ii)**Plot the dispersion curve and distinguish optical and acoustical phonon branches in dispersion curve.

**Q#2:** What kind of interaction exists between atoms of inert gas crystals? Discuss briefly. Show that the interaction between two identical inert gas atoms at separation & varies as –CR^{6}.

**Q#3:** Derive an expression for lattice heat capacity of solids on the basis of classical model. Explain graphically the discrepancies of classical model in explaining the experimental observations for low and high temperature limits.