#### Set - 1

#### I - B.Tech. Supplementary Examinations, Aug/Sep – 2008 (E.E.E, E.C.E, C.S.C, C.S.I.T, E.I.E, B.M.E, E.Con.E, C.S.S.E, E.Tele & E.Com.E)

Time: 3 hours |
Max. Marks: 80 |

#### Note: Answer any FIVE questions

#### All questions carry equal marks

1a. Define coordination number and packing factor of a crystal.

b. Describe BCC crystal structure, with a suitable example.

c. Obtain an expression for the packing factor of FCC structure. (4 + 6 + 6)

2a. Derive 3-dimensional, time independent Schrodinger wave equation for an electron.

b. What is the physical significance of wave function?

c. Deduce the expression for energy of an electron confined to a potential box of width ‘x’. (6 + 4 + 6)

3a. Discuss with suitable mathematical expressions, the Kronig-Penney model for the energies of an electron in a metal.

b. Explain the classification of metals, semiconductors and insulators based on band theory. (10 + 6)

4a. Explain the following:

- Electric Polarization and
- Polarizability.

b. Derive Clausius-Mosotti relation in dielectrics subjected to static fields.

c. Argon gas contains 2.70 × 10^{25} atoms/m^{3} at 0° C and at 1 atm. Pressure. Calculate the dielectric constant, if the diameter of argon atom is 0.384 nm. (4 + 8 + 4)

5a. Distinguish between intrinsic and extrinsic semiconductors with suitable examples.

b. Derive an expression for the density of holes in valence band of an intrinsic semiconductor. (8 + 8)

6a. What is population inversion relating to laser action? Explain.

b. Show that the ratio of Einstein's coefficient of spontaneous emission to Einstein's coefficient of absorption, is proportional to the cube of the frequency of the incident photon. (6 + 10)

7a. Describe the structure of an optical fiber.

b. Explain, in detail, the basic principle of an optical fiber.

c. Write the applications of fiber optics in medicine and industry. (6 + 6 + 4)

8a. Write a detailed note on nanoscience.

b. Why nanomaterials exhibit different properties? Explain. (6 + 10)

#### Set - 2

#### I - B.Tech. Supplementary Examinations, Aug/Sep – 2008 (E.E.E, E.C.E, C.S.C, C.S.I.T, E.I.E, B.M.E, E.Con.E, C.S.S.E, E.Tele & E.Com.E)

Time: 3 hours |
Max. Marks: 80 |

#### Note: Answer any FIVE questions

#### All questions carry equal marks

1a. Explain the formation of an ionic crystal, with a suitable example.

b. Derive an expression for the cohesive energy of an ionic crystal. (6 + 10)

2a. Show that the energies of a particle in a 3-dimensional potential box, are quantized.

b. Discuss, in detail, the physical significance of wave function.

c. A neutron beam of kinetic energy 0.04 eV is diffracted at the plane (1 0 0) of a simple cubic crystal for which d_{110} is 0.314 nm. Calculate the glancing angle at which first order Bragg diffraction will be observed. (6 + 4 + 6)

3a. Discuss with suitable mathematical expressions, the Kronig-Penney model for the energies of an electron in a metal.

b. Explain the classification of metals, semiconductors and insulators based on band theory. (10 + 6)

4a. What are the sources of permanent dipole moment in magnetic materials?

b. Explain the hysteresis loop observed in Ferro-magnetic materials.

c. Write notes on Ferro-electricity. (6 + 6 + 4)

5a. Write notes on direct band gap and indirect band gap semiconductors.

b. Show that for a p-type semiconductor the Hall coefficient, *R*_{H} = (1/ne). (8 + 8)

6a. Explain the characteristics of a LASER.

b. Describe the construction and working of a semiconductor laser.

c. Write any four applications of laser. (4 + 8 + 4)

7a. What is the basic principle of holography? Explain.

b. How to construct and reconstruct a hologram?(6 + 10)

8a. Write a detailed note on nanoscience and nanotechnology.

b. Write the important applications of nanomaterials in medicine. (10 + 6)

#### Set - 3

#### I - B.Tech. Supplementary Examinations, Aug/Sep – 2008 (E.E.E, E.C.E, C.S.C, C.S.I.T, E.I.E, B.M.E, E.Con.E, C.S.S.E, E.Tele & E.Com.E)

Time: 3 hours |
Max. Marks: 80 |

#### Note: Answer any FIVE questions

#### All questions carry equal marks

1a. Explain the terms

- basis
- space lattice
- lattice parameters and
- unit cell.

b. Deduce the expression for the inter-planar separation in terms of Miller indices for a cubic structure. (6 + 10)

2a. Derive one-dimensional, time independent Schrodinger wave equation for an electron.

b. What is the physical significance of wave function?

c. An electron is confined to a box of length 10^{−8}m. Calculate the minimum uncertainty in velocity. (8 + 4 + 4)

3a. Explain the terms (i) mean free path, (ii) relaxation time and (iii) drift velocity of an electron in a metal.

b. Discuss the origin of electrical resistance in metals.

c. Calculate the mobility of the electrons in copper obeying classical laws. Given that the density of copper = 8.92 × 10^{3} kg/m^{3}, Resistivity of copper = 1.73 × 10^{−8} ohm-m, atomic weight of copper = 63.5 and Avogadro's number = 6.02 × 10^{26} per k-mol. (6 + 6 + 4)

4a. Explain the terms:

- Magnetic flux density
- Magnetic field strength
- Magnetization and
- Magnetic susceptibility. How they are related to each other?

b. What are hard and soft magnetic materials? Write their characteristic properties and applications. (8 + 8)

5a. Write a note on intrinsic semiconductors.

b. Derive an expression for the number of electrons per unit volume in the conduction band of an intrinsic semiconductor. (6 + 10)

6a. Describe the various methods to achieve population inversion relating to lasers.

b. With the help of a suitable diagram, explain the principle, construction and working of a helium-neon laser. (6 + 10)

7a. Explain the principle of an optical fiber.

b. Explain how the optical fibers are classified.

c. Calculate the angle of acceptance of a given optical fibre, if the refractive indices of the core and the cladding are 1.563 and 1.498 respectively. (6 + 6 + 4)

8a. What are nanomaterials Explain.

b. Nanomaterials exhibit different properties. Explain the reasons. (6 + 10)

#### Set - 4

Time: 3 hours |
Max. Marks: 80 |

#### Note: Answer any FIVE questions

#### All questions carry equal marks

1a. Describe, in detail, the seven crystal systems with diagrams.

b. Sketch the planes (1 2 0), (2 1 3) and directions [1 0 0] and [2 1 1] (10 + 6)

2a. Discuss the de Broglie hypothesis of duality of matter particles.

b. Describe, in detail, with a neat diagram, Davisson and Germer experiment to show that particles behave like waves. (6 + 10)

3a. Distinguish between Drude-Lorentz theory and Sommerfeld's theory of metals.

b. Explain the Fermi-Dirac distribution function of electrons.

c. For a metal having 6.5 × 10^{28} conduction electrons per m^{3}, calculate relaxation time of electrons, if the metal has the resistivity 1.43 × 10^{−8} ohm-m. [Mass of electron = 9.1 × 10^{−31} Kg] (6 + 6 + 4)

4a. Explain the following:

- Polarization vector and
- Electric displacement.

b. Deduce an expression for Lorentz field relating to a dielectric material.

c. The radius of the helium atom is 0.55 Å. Calculate the polarizability of He and its relative permittivity. The number of He atoms in a volume of one metre cube is 2.70 × 10^{25} atoms. [permittivity of free space = 8.85 × 10^{−12} F/m] (4 + 8 + 4)

5a. Distinguish between intrinsic and extrinsic semiconductors with suitable examples.

b. Derive an expression for the density of electros in conduction band of an intrinsic semiconductor. (8 + 8)

6a. What is population inversion relating to laser action? Explain.

b. Distinguish between homo-junction semiconductor laser and hetero-junction semiconductor laser.

c. A semiconductor diode laser has a peak emission wavelength of 1.55 *µ*m. Find its band gap in eV. (4 + 8 + 4)

7a. Derive the expressions for

- acceptance angle and
- numerical aperture, of an optical fiber.

b. Describe different types of fibers by giving the refractive index profiles and propagation details. (8 + 8)

8a. How the physical and chemical properties of nano-particles vary with their size?

b. Write the important applications of nanomaterials. (10 + 6)

#### Set - 1

#### I - B.Tech. Regular Examinations, May/June – 2008 (E.E.E, E.C.E, C.S.C, C.S.I.T, E.I.E, B.M.E, E.Con.E, C.S.S.E, E.Tele & E.Com.E)

Time: 3 hours |
Max. Marks: 80 |

#### Note: Answer any FIVE questions

#### All questions carry equal marks

1a. Explain the forces between the two interacting atoms when they are brought nearer to form a molecule.

b. Derive the expression for the equilibrium spacing of two atoms for which the potential energy is minimum. (6 + 10)

2a. Explain de-Broglie hypothesis.

b. Describe G.P.Thomson's experiment in support of this hypothesis.

c. Find the wavelength associated with an electron rose to a potential 1600 V. (4 + 8 + 4)

3a. Distinguish between Drude-Lorentz theory and Sommerfeld's theory of metals.

b. Define Fermi level of electron.

c. Find the drift velocity of free electrons in a copper wire of cross-sectional area 10 mm^{2}, when the wire carries a current of 100 A. Assume that each copper atom contributes one electron to the electron gas. [Density of copper = 8.92 × 10^{3} kg/m^{3}, Atomic weight of copper = 63.5 and Avagadro's number = 6.02 × 10^{26} per k-mol] (10 + 2 + 4)

4a. Explain the following:

- Dielectric constant
- Electric susceptibility
- Electric polarization and
- Polarizability. (6 + 10)

b. Write notes on:

- Ferro-electricity and
- Piezo-electricity. (6 + 10)

5a. Explain the critical parameters and their significance in superconductors.

b. Write notes on:

- isotope effect and
- energy gap, in superconductors.

c. A Josephson junction having a voltage of 8.50 *µ*V across its terminals, then calculate the frequency of the alternating current. [Planck's constant = 6.626 × 10^{−34} J -sec) (4 + 8 + 4)

6a. Explain the characteristics of a LASER.

b. Describe the construction and working of ruby laser.

c. Write any four applications of laser. (4 + 8 + 4)

7a. Derive an expression for the ‘numerical aperture’ of an optical fiber.

b. Explain the advantages of optical communication system.

c. The numerical aperture of an optical fiber is 0.39. If the difference in the refractive indices of the material of its core and the ciadding is 0.55, calculate the refractive index of material of the core, when the light is launched into it in air. (8 + 4 + 4)

8a. Write a detailed note on nanoscience and nanotechnology.

b. Write the important applications of nanomaterials in medicine. (10 + 6)

#### Set - 2

#### I - B.Tech. Regular Examinations, May/June – 2008 (E.E.E, E.C.E, C.S.C, C.S.I.T, E.I.E, B.M.E, E.Con.E, C.S.S.E, E.Tele & E.Com.E)

Time: 3 hours |
Max. Marks: 80 |

#### Note: Answer any FIVE questions

#### All questions carry equal marks

1a. What is Bragg's law? Explain.

b. Describe Laue's method for the determination of crystal structure.

c. The Bragg's angle in the first order for (2 2 0) reflection from nickel (FCC) is 38.2° when X-rays of wavelength 1.54 Å are employed in a diffraction experiment. Determine the lattice parameter of nickel. (4 + 8 + 4)

2a. Explain, in detail, the properties of matter waves.

b. Describe Davisson and Germer experiment to verify the wave nature of matter (6 + 10)

3a. Distinguish between classical free electron theory and quantum free electron theory of metals.

b. Explain the Fermi-Dirac distribution function of electrons. Explain the effect of temperature on the distribution. (8 + 8)

4a. Explain the following:

- Dielectric constant
- Electric susceptibility,
- Electric polarization and
- Polarizability.

b. Write notes on:

- Ferro-electricity and
- Piezo-electricity. (6 + 10)

5a. What is Meissner effect? Explain.

b. Describe the difference between Type-I and Type –II superconductors.

c. The critical field for niobium is 1× 10^{5} amp/m at 8 K and 2 × 10^{5} amp/m at absoluate zero. Find the transition temperature of the element. (4 + 8 + 4)

6a. Distinguish between spontaneous emission and stimulated emission.

b. Distinguish between homo-junction semiconductor laser and hetero-junction semiconductor laser.

c. A semiconductor diode laser has a peak emission wavelength of 1.55*µ*m. Find its band gap in eV.

(4 + 8 + 4)

7.a Derive the expressions for

- acceptance angle and
- numerical aperture of an optical fiber.

b. Describe different types of fibers by giving the refractive index profiles and propagation details.

(8 + 8)

8a. How the physical and chemical properties of nano-particles vary with their size?

b. Write the important applications of nanomaterials. (10 + 6)

#### Set - 3

#### I - B.Tech. Regular Examinations, May/June – 2008 (E.E.E, E.C.E, C.S.C, C.S.I.T, E.I.E, B.M.E, E.Con.E, C.S.S.E, E.Tele & E.Com.E)

Time: 3 hours |
Max. Marks: 80 |

#### Note: Answer any FIVE questions

#### All questions carry equal marks

1a. Plot and explain the variation of (i) attractive potential energy (ii) repulsive potential energy and (iii) resultant potential energy with inter-atomic distance, when two atoms are brought nearer.

b. The Madelung constant of KCl is 1.75. Its neighbour separation is 0.314 nm. Find the cohesive, energy per atom. [Given that the Repulsive exponent value = 5.77; Ionization energy of potassium = 4.1 eV; Electron affinity of cholrine = 3.6 eV] (10 + 6)

2a. Discuss the de Broglie hypothesis of duality of matter particles.

b. Describe GP Thomsons experiment to verify the wave nature of matter. (6 + 10)

3a. Explain the teams (i) mean free path, (ii) relaxation time and (iii) drift velocity of an electron in a metal.

b. Discuss the origin of electrical resistance in metals.

c. Calculate the mobility of the electrons in copper obeying classical laws. Given that the density of copper = 8.92 × 10^{3} kg/m^{3}, Resistivity of copper = 1.73 × 10^{−8} Ohm-m, atomic weight of copper = 63.5 and Avogadro's number = 6.02 × 10^{26} per k-mol. (6 + 6 + 4)

4a. Describe the phenomenon of electronic polarization and obtain an expression for electronic polarizability.

b. Write notes on:

- Ferro-electricity and
- Piezo-electricity. (8 + 8)

5a. write a note on intrinsic semiconductors.

b. Derive an expression for the carrier concentration in n-type extrinsic semiconductors. (6 + 10)

6a. Distinguish between spontaneous emission and stimulated emission.

b. Distinguish between homo-junction semiconductor laser and hetero-junction semiconductor laser.

c. Calculate the wavelength of emitted radiation from GaAs which has a band gap of 1.44 eV.

(4 + 8 + 4)

7a. What are important features of optical fibers.

b. Describe the communication process using optical fibers.

c. Write the uses of fiber optics in different fields. (4 + 6 + 6)

8a. Write a detailed note on nanoscience and nanotechnology.

b. Write the important applications of nanomaterials in medicine. (10 + 6)

#### Set - 4

Time: 3 hours |
Max. Marks: 80 |

#### Note: Answer any FIVE questions

#### All questions carry equal marks

1a. Explain the various types of bonding in solids with suitable examples.

b. The Madelung constant of KCl is 1.75. Its neighbour separation is 0.314 nm. Find the cohesive energy per atom. [Given that the Repulsive exponent value = 5.77; Ionization energy of potassium = 4.1 eV; Electron affinity of cholrine = 3.6eV] (10 + 6)

2a. Distinguish between a matter wave and an electromagnetic wave.

b. Describe GP Thomson's experiment to study electron diffraction.

c. Find the wavelength associated with an electron rose to a potential 1600 V. (4 + 8 + 4)

3a. Explain the following:

- Electrical resistivity and
- Fermi energy.

b. Explain briefly the quantum free electron theory of metals.

c. On the basis of band theory how the crystalline solids are classified into metals, semiconductors and insulators? (4 + 6 + 6)

4a. Explain the hysteresis loop observed in ferro-magnetic materials.

b. Explain clearly difference between hard and soft magnetic materials. (8 + 8)

5a. How are ‘superconductors’ classified? Explain their properties.

b. What is Meissner effect? Explain

c. Write notes on the applications of superconduction materials. (6 + 4 + 6)

6a. Describe the various methods to achieve population inversion relating to lasers.

b. With the help of a suitable diagram, explain the principle, construction and working of a semiconductor laser. (6 + 10)

7a. Distinguish between light propagation in

- step index optical fiber and
- graded index optical fiber.

b. Write a note on fiber optic medical endoscopy. (10 + 6)

8a. Write a detailed note on nanoscience.

b. Why nanomaterials exhibit different properties? Explain. (6 + 10)

#### Set - 1

#### I - B.Tech. Regular Examinations, April/May – 2007 (E.E.E, E.C.E, C.S.C, C.S.I.T, E.I.E, B.M.E, E.Con.E, C.S.S.E, E.Tele & E.Com.E)

Time: 3 hours |
Max. Marks: 80 |

#### Note: Answer any FIVE questions

#### All questions carry equal marks

1a. Show that FCC is the most closely packed of the three cubic structures by working out the packing factors. (10)

b. Describe the structure of NaCl. (6)

2a. Draw the (112) and (120) planes and the (112) and (120) directions of a simple cubic crystal. (4)

b. Derive an expression for the inter-planar spacing in the case of a cubic structure. (8)

c. Calculate the glancing angle at (110) plane of a cubic crystal having an axial length of 0.26 mm corresponding to the second order diffraction maximum for the X-rays of wavelength of 0.065 mm. (4)

3a. What is Frenkel defect? Explain. (6)

b. Derive an expression for the concentration of Frenkel defects present in a crystal at any temperature. (10)

4a. Explain the origin of energy bands in solids. (6)

b. Assuming the electron-lattice interaction to be responsible for scattering of conduction electrons in a metal, obtain an expression for conductivity in terms of relaxation time and explain any three drawbacks of classical theory of free electrons. (6)

c. Find the temperature at which there is 1% probability of a state with an energy 0.5 eV above Fermi energy. (4)

5a. Explain the polarization mechanism in dielectric materials. (8)

b. What are the important requirement of good insulating materials? (4)

c. A parallel plate capacitor of area 650 mm^{2} and a plate separation of 4 mm has a charge pf 2 × 10^{−10} C on it. When a material of dielectric constant 3.5 is introduced between the plates, what is the resultant voltage across the capacitor? (4)

6a. Distinguish between metals, semiconductors and insulators. (6)

b. Explain the effect of temperature on resistivity of a semiconductor. (4)

c. Derive an expression for the number of electrons per unit volume in the conduction band of an intrinsic semiconductor. (6)

7a. What do you understand by population inversion? How it is achieved? (6)

b. Derive the relation between the probabilities of spontaneous emission and stimulated emission in terms of Einsteins coefficients. (10)

8a. Define the relative refractive index difference of an optical fibre. Show how it is related to numerical aperture. (6)

b. Draw the block diagram of an optical fibre communication system and explain the function of each block. (10)

#### Set - 2

#### I - B.Tech. Regular Examinations, April/May – 2007 (E.E.E, E.C.E, C.S.C, C.S.I.T, E.I.E, B.M.E, E.Con.E, C.S.S.E, E.Tele &E.Com.E)

Time: 3 hours |
Max. Marks: 80 |

#### Note: Answer any FIVE questions

#### All questions carry equal marks

1a. Define crystal lattice, unite cell, lattice parameter and coordination number. (8)

b. Consider a body centered cubic lattice of identical atoms having radius R. Compute

- the number of atoms per unit cell
- the coordination number and
- the packing fraction (8)

2a. What are Miller indices? Draw (111) and (110) planes in a cubic lattice. (6)

b. Explain Bragg's law of X-ray diffraction. (6)

c. The Bragg's angle for reflection from the (111) plane in a FCC crystal is 19.2° for an X-ray wavelength of 1.54 A.U. Compute the cube edge of the unit cell. (4)

3a. Explain Schottky and Frenkel defects with the help of suitabl figures. (10)

b. Explain the significance of Burgers vector. (6)

4a. How does the electrical resistance of a metal change with temperature? (4)

b. Discuss the motion of an electron in a periodic lattice. (8)

c. Find the relaxation time of conduction electrons in a metal having resistivity 1.54 × 10^{−8} Ω-m, if the metal has 5.8 × 10^{28} conduction electrons per cubic meter. (4)

5a. Obtain a relation between electronic polartization and electric susceptibility of the dielectric medium. (6)

b. What is dielectric breakdown? Explain briefly the various factors contributing to breakdown in dielectrics. (6)

c. A parallel plate capacitor having a plate separation of 2 × 10^{−3} m across which a potential of 10 V is applied. Calculate the dielectric displacement, when a material of dielectric constant 6.0 is introducted between the plates. (4)

6a. Explain Meissner effect. (6)

b. What is meant by isotopic effect? Explain with suitable example. (6)

c. A superconducting material has a critical temperature of 3.7 K, and a magnetic field of 0.0306 Tesla at 0 K. Find the critical field at 2 K. (4)

7a. Explain the terms:

- Absorption
- Spontaneous emission
- Stimulated emission
- Pumping mechanism
- Population inversion
- Optical cavity. (12)

b. Mention the medical applications of lasers. (4)

8a. Explain the principle behind the functioning of an optical fibre. (4)

b. Derive an expression for acceptance angle for an optical fibre. How it is related to numertical aperture? (8)

c. An optical fibre has a numerical aperture of 0.20 and a cladding refractive index of 1.59.Find the acceptance angle for the fibre in water which has a refractive index of 1.33. (4)

#### Set - 3

#### I - B.Tech. Regular Examinations, April/May – 2007(E.E.E, E.C.E, C.S.C, C.S.I.T, E.I.E, B.M.E, E.Con.E, C.S.S.E, E.Tele & E.Com.E)

Time: 3 hours |
Max. Marks: 80 |

#### Note: Answer any FIVE questions

#### All questions carry equal marks

1a. Show that FCC is the most closely packed of the three cubic structures by working out the packing factors. (10)

b. Describe the structure of NaCl. (6)

2a. Explain Bragg's law of X-ray diffraction. (6)

b. Describe Laues method for determination of crystal structure. (6)

c. A beam of X-ray is incidernt on a NaCl crystal with lattice spacing 0.282 nm. Calculate the wavelength of X-rays if the first order Bragg reflection takes place at a glancing angle of 8°35′. Also calculate the maximum order of diffraction possible. (4)

3a. What is Frenkel defect? Explain. (6)

b. Derive an expression for the concentration of Frenkel defects present in a crystal at any temperature. (10)

4a. Explain the origin of energy bands in solids. (6)

b. Assuming the electron lattice interaction to be responsible for scattering of conduction electrons in a metal, obtain an expression for conductivity in terms of relaxation time and explain any three drawbacks of classical theory of free electrons. (6)

c. Find the temperature at which there is 1% probability of a state with an energy 0.5 eV above Fermi energy (4)

5a. What is ferromagnetic? What are the distinguishing features of ferromagnetism? (8)

b. What are ferrites? Explain the magnetic properties of ferrites and mention their industrial applications. (8)

6a. Derive the continuity equation for electrons. (8)

b. What physical law is manifested in the continuity equation? (4)

c. Find the diffusion coefficient of electrons in silicon at 300 K if *µ* is 0.19 m^{2} /V-S. (4)

7a. What do you understand by population inversion? How it is achieved? (6)

b. Derive the relation between the probabilities of spontaneous emission and stimulated emission in terms of Einsteins coefficients. (10)

8a. Define the relative refractive index difference of an optical fibre. Show how it is related to numerical aperture. (6)

b. Draw the block diagram of an optical fibre communication system and explain the function of each block. (10)

#### Set - 4

#### I - B.Tech. Regular Examinations, April/May – 2007 (E.E.E, E.C.E, C.S.C, C.S.I.T, E.I.E, B.M.E, E.Con.E, C.S.S.E, E.Tele & E.Com.E)

Time: 3 hours |
Max. Marks: 80 |

#### Note: Answer any FIVE questions

#### All questions carry equal marks

1a. Explain the “Unit Cell” and “Lattice” parameters. What is a primitive cell and how does it differ from unit cell? (6)

b. Describe the crystal structure of CsCl. (4)

c. Chromium has BCC structure. Its alomic radius is 0.1249 nm. Calculate the free volume / unit cell.

(6)

2a. What are Miller indices? Draw (111) and (110) planes in a cubic lattice. (6)

b. Explain Bragg's law of X-ray diffraction. (6)

c. The Bragg's angle for reflection from the (111) plane in a FCC crystal is 19.2° for an X-ray wavelength of 1.54 A.U. Compute the cube edge of the unit cell. (4)

3a. Show that the wavelength of an electron accelerated by a potential difference ‘V’ volts, is λ = 1.227 × 10^{−10} √V m for non-relativistic case. (6)

b. Describe an experiment to establish the wave nature of electrons. (6)

c. Explain the difference between a matter wave and an electromagnetic wave. (4)

4a. Explain the origin of energy bands in solids. (6)

b. Assuming the electron-lattice interaction to be responsible for scattering of conduction electrons in a metal, obtain an expression for conductivity in terms of relaxation time and explain any three draw backs of classical theory of free electrons. (6)

c. Find the temperature at which there is 1% probability of a state with an energy 0.5 eV above Fermi energy. (4)

5a. What is intrinsic break down in dielectric materials? (4)

b. Explain electronic polarization in atoms and obtain an expression for electronic polarisability in terms of the radius of the atom. (8)

c. A parallel plate capacitor has an area of 100 cm^{2}, with a separation of 1 cm and is charged to a potential of 100 V. Calculate the capacitance of the capacitor and the charge on the plates. (4)

6. Explain the following: (6 + 5 + 5)

a. Critical magnetic field of a superconductor as a function of temperature.

b. Meissner effect.

c. Cryotrons.

7a. Explain with a neat diagram.

- absorption
- spontaneous emission and
- stimulated emission of radiation.(8)

b. What is population inversion? How it is achieved by optical pumping? (8)

8a. Describe the construction of a typical optical fibre and give the dimensions of the various parts. (4)

b. Define the acceptance angle and numerical aperture. Obtain an expression for the numerical aperture of an optical fibre. (8)

c. Calculate the numerical aperture and acceptance angle for an optical fibre with core and cladding refractive indices being 1.48 and 1.45 respectively. (4)

#### Set - 1

#### I - B.Tech. Regular Examinations, May/June – 2006 (E.E.E, E.C.E, C.S.C, C.S.I.T, E.I.E, B.M.E, E.Con.E, C.S.S.E, E.Tele & E.Com.E)

Time: 3 hours |
Max. Marks: 80 |

#### Note: Answer any FIVE questions

#### All questions carry equal marks

1a. Define coordination number and packing factor of a crystal. (4)

b. Describe the FCC crystal structure. (6)

c. Obtain an expression for the packing factor of FCC structure. (6)

2a. What are Miller indices? How are they obtained? (8)

b. Explain Bragg's Law of X-ray diffraction. (8)

3a. Explain the concept of matter waves (6)

b. Describe Davison and Germer's experiment and explain how it enabled the verification of wave nature of matter. (6)

c. Calculate the velocity and kinetic energy of an electron of wavelength 1.66 × 10^{−10} m. (4)

4a. How does the electrical resistance of a metal change with temperature? (4)

b. Discuss the motion of an electrons in a periodic lattice. (4)

c. Find the relaxation time of conduction electron in a metal having resistivity 1.54 × 10^{−8} Ω-m, if the metal has 5.8 × 10^{28} conduction electrons per cubic meter. (4)

5a. Define the terms magnetic susceptibility, magnetic induction and permeability. How is magnetic

susceptibility of a material measured? (10)

b. Explain the salient features of anti-ferromagnetic materials. (6)

6a. Describe the drift and diffusion currents in a semiconductor. (6)

b. Derive their expressions. (6)

c. Deduce Einstein relation (4)

7a. Explain the following:

- Life time of an energy level
- Optical pumping processes.
- Metastable states.(6)

b. Distinguish between spontaneous and stimulated emission processes of light. (4)

c. Discuss briefly the different methods of producing laser light (6)

8a. Describe the construction of a typical optical fibre and give the dimension of the various parts. (4)

b. Define the acceptance angle and numerical aperture. Obtain an expression for the numerical aperture of an optical fibre. (8)

c. Calculate the numerical aperture and acceptance angle for an optical fibre with core and cladding refractive indices being 1.48 and 1.45 respectively. (4)

#### Set - 2

#### I - B.Tech. Regular Examinations, May/June – 2006 (E.E.E, E.C.E, C.S.C, C.S.I.T, E.I.E, B.M.E, E.Con.E, C.S.S.E, E.Tele & E.Com.E)

Time: 3 hours |
Max. Marks: 80 |

#### Note: Answer any FIVE questions

#### All questions carry equal marks

1a. Explain the forces between the two interacting atoms when they are brought nearer to form a molecule. (6)

b. Derive the expression for the equilibrium spacing of two atoms for which the potential energy is minimum and hence obtain the dissociation energy. (10)

2a. State and explain Bragg's law. (6)

b. Describe with suitable diagram, the powder method for determination of crystal structure. (6)

c. A beam of X-ray of wavelength 0.071 nm is diffracted by (110) plane of rock salt with lattice constant of 0.28 nm. Find the glancing angle for the second order diffraction. (4)

3a. Distinguish between Frenkel and Schottky defects. (8)

b. Derive an expression for the energy change due to creation of vacancies in side a solid. (8)

4a. Explain the origin of energy bands in solids. (6)

b. Assuming the electron – lattice interaction to be responsible for scattering of conduction electrons in a metal. Obtain an expression for conductivity in terms of relaxation time and explain any three draw backs of classical theory of free electrons. (6)

c. Find the temperature at which there is 1% probability of a state with an energy 0.5 eV above Fermi energy. (4)

5a. What is meant by ferror-magnetic materials? Give example. (4)

b. Explain the hysteresis properties of ferromagnetic materials. (6)

c. Mention the various properties of para-magnetic materials. (6)

6a. How are the superconductors classified? Explain their properties. (6)

b. What is Meissner effect? (6)

c. Write notes on the applications of superconducting materials. (6)

7a. With necessary theory and energy level diagram, explain the working of a Helium-Neon gas laser. (10)

b. Mention some important applications of lasers. (6)

8a. Distinguish between light propagation in

- step index and
- graded index optical fibres.

b. Discuss the various advantages of communication with optical fibres over the conventional coaxial cables. (6)

c. Calculate the refractive indices of core and cladding of an optical fibre with a numerical aperture 0.33 and their fractional difference of refractive indices being 0.02. (4)

#### Set - 3

#### I - B.Tech. Regular Examinations, May/June – 2006 (E.E.E, E.C.E, C.S.C, C.S.I.T, E.I.E, B.M.E, E.Con.E, C.S.S.E, E.Tele & E.Com.E)

Time: 3 hours |
Max. Marks: 80 |

#### Note: Answer any FIVE questions

#### All questions carry equal marks

1a. Define coordination number and packing factor of a crystal. (4)

b. Describe the FCC crystal structure. (6)

c. Obtain an expression for the packing factor of FCC structure. (6)

2a. Explain how the X-ray diffraction can be employed to determine the crystal structure (10)

b. The distance between (110) planes in a body-centered cubic structure is 0.203 nm. What is the size of the unit cell? What is ther radius of the atom? (6)

3a. Explain the concept of matter waves. (6)

b. Describe Davison and Germer's experiment and explain how it enabled the verification of wave nature of matter. (6)

c. Calculate the velocity and kinetic energy of an electron of wavelength 1.66 × 10^{−10}m (4)

4a. explain the origin of energy bands in solids. (6)

b. Assuming the electron – lattice interaction to be responsible for scattering of conduction electrons in a metal, obtain an expression for conductivity in terms of relaxation time and explain any three draw backs of classical theory of free electrons. (6)

5a. Explain the electrochemical breakdown in dielectrie materials. (4)

b. Explain the concept of internal field in solids and hence obtain an expression for the static dielectric constant of elemental solid dielectric. (8)

c. A parallel plate capacitor having an area 6.45 × 10^{−4}m^{2} and a plate separation of 2 × 10^{−3}m, across which a potential of 12 V is applied. If a material having a dielectric constant 5.0 is positioned within the region between the plates, compute the polarization. (4)

6a. Define the terms of superconductivity;

- Critical temperature
- Critical magnetic field and
- Critical current(6)

b. What are Cooper pairs? Explain. (4)

c. Write notes on any four applications of superconductors. (6)

7a. Explain the following typical characteristics of laser:

- coherence
- divergence and
- monochromaticity(6)

b. Explain the principle and working of a ruby laser. (10)

8a. Explain the principle behind the functioning of an optical fibre. (4)

b. Derive an expression for a acceptance angle for an optical fibre. How it is related to numerical

aperture? (8)

c. An optical fibre has a numerical aperture of 0.20 and a cladding refractive index of 1.59. Find the acceptance angle for the fibre in water which has a refractive index of 1.33 (4)

#### Set - 4

Time: 3 hours |
Max. Marks: 80 |

#### Note: Answer any FIVE questions

#### All questions carry equal marks

1a. Explain the terms (6)

- basis
- space lattice and
- unit cell.

b. Describe the seven crystal systems with diagrams. (10)

2a. Describe Bragg's law of X-ray diffraction. (6)

b. Describe Bragg's X-ray spectrometer and explain how Bragg's law can be verified. (6)

c. Monochromatic X-ray of λ = 1.5 A.U. are incident on a crystal face having an interplanar spacing of 1.6 A.U. Find the highest order for which Bragg's reflection maximum can be seen. (4)

3a. Describe edge and screw dislocations. Draw Burgers circuit and slip planes for them. (10)

b. Explain the significance of Burgers vector. (6)

4a. What is Fermil level? (2)

b. Explain Fermi-Dirac distribution for electrons in a metal. Discuss its variation with temperature. (8)

c. Calculate the free electron concentration, mobility and drift velocity of electrons in aluminum wire of length of 5 m and resistance 0.06 Ω carrying a current of 15 A, assuming that each aluminum atom contributes 3 free electrons for conduction.

Given: Resistivity for aluminum = 2.7 × 10^{−8} Ω-m.

Atomic weight = 26.98

Density = 2.7 × 10^{3} kg/m^{3}

Avagadro number = 6.025 × 10^{23} (6)

5a. Explain the electrochemical breakdown in dielectric materials. (4)

b. Explain the concept of internal field in solids and hence obtain an expression for the static dielectric constant of elemental solid dielectric. (8)

c. A parallel plate capacitor having an area 6.45 × 10^{−4}m^{2} and a plate separation of 2 × 10^{−3} m, across which a potential of 12 V is applied. If a material having a dielectric constant 5.0 is positioned within the region between the plates, compute the polarization. (4)

6a. Explain n-type and p-type semiconductors. Indicate on an enegy level diagram the conduction and valence bands, donor and acceptor levels for an intrinsic and extrinsic semiconductors. (10)

b. Explain the detailed mechanism of current conduction in n and p type semiconductors. (6)

7a. Describe the principle, construction and working of a semiconductor laser. (10)

b. Write the applications of laser. (6)

8a. Explain the terms ‘numerical aperture’ and ‘acceptance angle’. (6)

b. With the help of a suitable diagram explain the principle, construction and working of an optical fibre as a wave guide. (6)

c. An optical fibre has a core material of refractive index of 1.55 and cladding material of refractive index 1.50. The light is launched into it in air. Calculate its numerical aperture. (4)

#### Set - 1

#### I - B.Tech. Regular Examinations, June – 2005 (E.E.E, E.C.E, C.S.C, C.S.I.T, E.I.E, B.M.E, E.Con.E, C.S.S.E, E.Tele & E.Com.E)

Time: 3 hours |
Max. Marks: 80 |

#### Note: Answer any FIVE questions

#### All questions carry equal marks

1a. Explain the terms

i. basis ii. space lattice and iii. unit cell.

b. Describe the seven crystal systems with diagrams.

2a. What are Miller indices? How are they obtained?

b. Explain Schottky and Frankel defects with the help of suitable figures.

3a. Show that the wavelength of an electron accelerated by a potential difference ‘V’ volts, is for non – relativistic case.

b. Describe an experiment to establish the wave nature of electrons.

c. Explain the difference between a matter wave and an electromagnetic wave.

4a. Explain the origin of energy bands in solids.

b. Assuming the electron - lattice interaction to be responsible for scattering of conduction electrons in a metal, obtain an expression for conductivity in terms of relaxation time and explain any three draw backs of classical theory of free electrons.

c. Find the temperature at which there is 1% probability of a state with an energy 0.5 eV above Fermi energy.

5a. Explain Clausius - Mosotti relation in dielectrics subjected to static fields.

b. What is orientational polarization. Derive an expression for the mean dipole moment when a polar material is subjected to an exterrnal field.

c. The relative dielectric constant of sulphur is 3.75 when measured at 27° C. Assuming the internal field constant γ = 1/3 calculate the electronic polarizability of sulphur if its density at this temperature is 2050 kg/m^{3}. The atomic weight of sulphur being 32.

6a. Draw the B-H curve for a ferro-magnetic material and identify the retentivity and the coersive field on the curve.

b. What are paramagnetic and diamagnetic materials.

c. An atom contains 10 electrons revolving in a circular path of radius 10^{–11} m. Assuming homogeneous charge distribution, calculate the orbital dipole moment of the molecule in Bohr magneton.

7a. When donor impurities are added to a semiconductor’, the concentration of holes decreases. Explain with reasons.

b. Show that the Fermi level is nearer to the conduction band in a n-type semiconductor. Discuss the variation of conductivity with temperature of an n-type semiconductor.

8a. Explain the terms ‘numerical aperture’ and ‘acceptance angle’.

b. With the help of a suitable diagram explain the principle, construction and working of an optical fiber as a waveguide.

c. An optical fiber has a core material of refractive index of 1.55 and cladding material of refractive index 1.50. The light is launched into it in air. Calculate its numerical aperture.

#### Set - 2

#### I - B.Tech. Regular Examinations, June – 2005 (E.E.E, E.C.E, C.S.C, C.S.I.T, E.I.E, B.M.E, E.Con.E, C.S.S.E, E.Tele & E.Com.E)

Time: 3 hours |
Max. Marks: 80 |

#### Note: Answer any FIVE questions

#### All questions carry equal marks

1a. Show that FCC is the most closely packed of the three cubic structures by working out the packing factors.

b. Describe the structure of NaCl.

2a. What are Miller indices? How are they obtained?

b. Explain Schottky and Frankel defects with the help of suitable figures.

3a. Explain the concept of matter waves.

b. Describe Davison and Germer's experiment and explain how it enabled the-verification of wave nature of matter.

c. Calculate the velocity and kinetic energy of an electron of wavelength 1.66 × 10^{–10} m.

4a. What is Fermi level?

b. Explain Fermi-Dirac distribution for the electrons in a metal. Discuss its variation with temperature.

c. Calculate the free electron concentration, mobility and drift velocity of electrons in aluminum wire of length of 5 m and resistance 0.06 Ω, carrying a current of 15 A, assuming that each aluminum atom contributes 3 free electrons for conduction.

Given: Resistivity for aluminum = 2.7 × 10^{-8} Ω-m

Atomic weight = 26.98

Density = 2.7 × 10^{3} kg/m^{3}

Avagadro number = 6.025 × 10^{23}

5a. Explain briefly the classification of ferro-electric materials.

b. What is meant by a local field in a solid dielectric. Derive an expression for the local field for structures possessing cubic symmetry.

c. There are 1.6 × 10^{20} NaCl molecules/m^{3} in a vapour. Determine the orientational polarization at room temperature if the vapour is subjected to an electric field 5000 V/cm. Assume that the NaCl molecule consists of sodium and chlorine ions separated by 0.25 nm

6a. Explain clearly the difference between hard and soft magnetic materials. What are mixed ferrites? Mention their uses.

b. How ferrites are superior to ferromagnetic materials?

7a. Distinguish between metals, semiconductors and insulators.

b. Explain the effect of temperature on resistivity of a semiconductor.

c. Derive an expression for the number of electrons per unit volume in the conduction band of an intrinsic semiconductor.

8a. Explain the characteristics of a laser beam.

b. Mention any two applications of laser, each in the field of scientific research, engineering and medicine.

c. Describe the construction and working of a ruby laser.

#### Set - 3

#### I - B.Tech. Regular Examinations, June – 2005 (E.E.E, E.C.E, C.S.C, C.S.I.T, E.I.E, B.M.E, E.Con.E, C.S.S.E, E.Tele & E.Com.E)

Time: 3 hours |
Max. Marks: 80 |

#### Note: Answer any FIVE questions

#### All questions carry equal marks

1a. Explain the terms

- basis
- space lattice and unit cell.

b. Describe the seven crystal systems with diagrams.

2a. What ate Miller indices? How are they obtained?

b. Explain Schottky and Frankel defects with the help of suitable figures.

3a. Explain the concept of matter waves.

b. Describe Davison and Germer's experiment and explain how it enabled the verification of wave nature of matter.

c. Calculate the velocity and kinetic energy of an electron of wavelength 1066 × 10^{–10} m.

4a. What is Fermi level?

b. Explain Fermi-Dirac distribution for electrons in a metal. Discuss its variation with temperature.

c. Calculate the free electron concentration, mobility and drift velocity of electrons in aluminum wire of length of 5 m and resistance 0.06 Ω, carrying a current of 15 A, assuming that each aluminum atom contributes 3 free electrons for conduction.

Given: Resistivity for aluminum = 2.7 × 10^{-8} Ω-m

Atomic weight = 26.98

Density = 2.7 × 10^{3} kg/m^{3}

Avagadro number = 6.025 × 10^{23}

5a. Discuss the variation of spontaneous polarization of Roschelle salt with temperature.

b. Obtain an expression for the static dielectric constant of a monoatomic gas.

c. Explain the phenomenon of anomalous dielectric dispersion.

6a. What are the characteristics of soft magnetic materials?

b. What is ferro-magnetic curie temperature? Discuss the behaviour of a ferro-magnetic material below the curie temperature.

c. The magnetic field in the interior of a certain solenoid has the value of 6.5 × 10^{–4} T when the solenoid is empty. When it is filled with iron, the field becomes 1.4 T. Find the relative permeability of iron.

7a. Explain d.c. Josephson effect.

b. Describe the BCS theory of superconductivity.

c. Write applications of superconductivity.

8a. Describe the principle, construction and working of a semiconductor laser.

b. Write the applications of laser.

#### Set - 4

Time: 3 hours |
Max. Marks: 80 |

#### Note: Answer any FIVE questions

#### All questions carry equal marks

1a. Explain the formation of an ionic crystal.

b. Derive an expression for the cohesive energy of an ionic crystal.

c. Calculate the cohesive energy of NaCl from the following data:

Equilibrium separation between the ion pair = 0.281 nm.

Ionization energy of Na = 5.14 eV.

Electrton affinity of Cl = 3.61 eV.

Born repulsive exponent = 9

Madelung constant = 1.748.

2a. What are Miller indices? How are they obtained?

b. Explain Schottky and Frankel defects with the help of suitable figures.

3a. Derive time independent Schrödinger's wave equation for a free particle.

b. Explain the physical significance of wave function.

c. An electron is bound in a one-dimensional infinite well of width 1 × 10^{–10} m.

Find the energy values in the ground state and first two excited states.

4a. Explain the origin of energy bands in solids.

b. Assuming the electron - lattice interaction to be responsible for scattering of conduction electrons in a metal, obtain an expression for conductivity in terms of relaxation time and explain any three draw backs of classical theory of free electrons.

c. Find the temperature at which there is 1% probability of a state with an energy 0.5 eV above Fermi energy.

5a. What are the important characteristics of ferro-electric materials?

b. Describe-thepossible mechanism of polarization in a dielectric material.

c. The dielectric constant of Helium gas at NTP is 1.0000684. Calculate the electronic polarizability of He atoms if the gas constains 2.7 × 10^{25} atoms/m^{3}.

6a. Draw the B-H curve for a ferro-magnetic material and identify the retentivity and the coersive field on the curve.

b. What are paramagnetic and diamagnetic materials.

c. An atom contains 10 electrons revolving in a circular path of radius 10^{–11} m. Assuming homogeneous charge distribution, calculate the orbital dipole moment of the molecule in Bohr magneton.

7a. Derive the continuity equation for electrons.

b. What physical law is manifested in the continuity equation.

c. Find the diffusion coefficient of electrons in silicon at 300 K if *µ*, is 0.19 m^{2}/V-S.

8a. Describe the construction of a typical optical fiber and give the dimensions of the various parts.

b. Define the acceptance angle and numerical aperture. Obtain an expression for the numerical aperture of an optical fiber.

c. Calculate the numerical aperture and acceptance angle for an optical fiber with core and cladding refractive indices being 1.48 and 1.45 respectively.