Paper 13

Core XIII: Solid State Physics

CBCS 19 : Core XII

Syllabus

Unit I

Crystal Structure: Solids, Amorphous and Crystalline Materials, Lattice translation Vectors, Lattice with a Basis. Central and Non-Central Elements. Unit Cell, Miller Indices, Types of Lattices, Reciprocal Diffraction of X- rays by crystals, Bragg’s Law, Laue’s Condition, Atomic and Geometrical Factor.

Unit II

• Elementary Lattice Dynamics: Lattice Vibrations and Phonons: Linear, Monoatomic and Diatomic Chains, Acoustical and Optical Phonons, Qualitative Description of the phonon spectrum in solids, Dulong and Petits Law, Einstein and Debye theories of specific heat of solids, $T^3$ Law. Elementary band theory: Kroning-Penny model of band Gap, Conductor, Semiconductor (P and N type) and insulator, Conductivity of Semiconductor, mobility, Hall Effect, Measurement of conductivity (four probe method) and Hall Co-efficient.

Unit III

• Magnetic Properties of Matter: Dia-, Para-, Ferri- and Ferro-magnetic Materials, Classical Langevins theory of dia and Para magnetic Domains, Curies law, Weiss Theory of Ferro magnetism and Ferro magnetic Domains, Discussion of B-H Curve, Hysteresis and Energy Loss.
• Dielectric Properties of Materials: Polarization Local Electrical Field at an Atom, Depolarization Field, Electric Susceptibility, Polarizability, Clausius Mosotti Equation, Classical theory of Electronic Polarizability.

Unit IV

• Lasers: Einsteins A and B co-efficientnts, Metastable States, Spontaneous and Stimulated emissions, Optical Pumping and population Inversion, Three Level and Four Level Lasers, Ruby Laser and He-Ne Laser.
• Superconductivity: Experimental Results, Critical Temperature, Critical magnetic field, Meissner effect, Type-I and Type-II Superconductors, London’s Equation and Penetration Depth, Isotope effect, Idea of BCS theory (No derivation).

Text Books:

• Introduction to Solid State Physics - Charles Kittel (Wiley India)
• LASERS: Fundamentals and Applications - Thyagarajan and Ghatak (McMillan India)

Reference Books:

• Solid State Physics - N. W. Ashcroft and N. D. Mermin (Cengage)
• Solid State Physics - R. K. Puri and V. K. Babbar (S. Chand Publication)
• Solid State Physics S. O. Pillai (New Age Publication)
• Lasers and Non-linear Optics B.B.Laud (Wiley Eastern)
• Elements of Solid State Physics - J. P. Srivastava (Prentice Hall of India)
• Elementary Solid State Physics - Ali Omar (Addison Wiley)
• Solid State Physics, Gupta and Kumar, Pragati Prakashan.

Questions

2025 | +3-V-S-CBCS(MS)-Sc(H)-Core-XII-Phy | Full Marks: 60

PART-I | Answer all Questions. | 1x8

1. Crystal Structure = Lattice + ______.
2. Diffraction condition in terms of reciprocal lattice vector ($\vec{G}$) is _______.
3. A dispersion relation links angular frequency ($\omega$) with ______.
4. The dimension of ferromagnetic domain is the order of ______.
5. Induced dipole moment per unit electric field is known as ______.
6. The ration of Einstein's coefficients $B_{12}$ and $B_{21}$ is given by ______.
7. Effective mass of electron is given by ______.
8. The superconducting state is more ordered than the normal state. (True/False)

PART-II | Answer any eight within two to three sentences | 1.5x8

1. Derive relation between lattice parameter (a) and atomic radius (r) for FCC lattice.
2. What is Bravais lattice?
3. What is Wigner - Seitz Cell? Draw it.
4. What is phonon?
5. Calculate the Einstein temperature, given Einstein frequency as $9 \times 10^{11}$ Hz.
6. Distinguish antiferromagnetism and ferromagnetism.
7. What is ionic polarization?
8. Write the main characteristic of LASER.
9. What is Hall effect ?
10. What are cooper pairs?

PART-III | Answer any eight of the following (in maximum 75 words.) | 2x8

1. What is Brillouin zone? Draw 1st and 2nd Brillouin zone for square lattice.
2. Show that five-fold rotation doesn't exist.
3. Distinguish acoustic and optical modes of phonon.
4. Discuss domain theory of ferromagnetism.
5. Define magnetic susceptibility ($\chi$) and permeability ($\mu_r$). Also find relation between them.
6. Distinguish polar and non-polar dielectrics.
7. Derive relation among displacement vector ($\vec{D}$), Electric field ($\vec{E}$) and polarization vector ($\vec{P}$).
8. Discuss principle of LASER.
9. Define mobility and find expression for it in terms of relaxation time.
10. Distinguish Type-1 and Type-II superconductors.

PART-IV | Answer within 500 words each. | 6x4

1. What are Miller indices ? Write procedure of finding Miller indices. Also determine the inter planner spacing between two parallel planes with Miller indices (h k l).
   
   OR
   
   Define reciprocal lattice. Derive the expression for the primitive translation vectors of the reciprocal lattice and find these for BCC lattice.

2. Derive the dispersion relation of a one dimensional monoatomic lattice and discuss its wavemotion.
   
   OR
   
   Discuss Langevin's theory of paramagnetism and obtain expression for Curie law.

3. Derive expression for local field for an atom and deduce Clausius-Mossoti relation.
   
   OR
   
   Discuss construction and working of He-Ne LASER.

4. Discuss Kroning-Penny model. Using the model show that the energy spectrum of electron consists of a number of allowed energy bands separated by forbidden regions.
   
   OR
   
   Derive London equations and discuss how its solution leads to Meissner effect.

2024 | +3-VI-S-CBCS(MS)-Sc(H)-Core-XII-Phy

Part-I | Qn 1 | 1x8

• Crystalline solids are ________ in nature.
• The FCC structure is ________.
• In Einstein's theory of lattice vibration, solids vibrate with _________ frequency.
• Spontaneous magnetization occurs in ________ materials.
• Electronic polarizability depends on ________ .
• Which level Laser is more efficient ?
• Cooper pair follows statistics.
• A semiconductor at OK acts as _______.

Part-II | Qn 2 | 1.5x8

• Why reciprocal lattice is so named?
• What is interplanar distance for (120) planes for simple cubic cell?
• What do you mean by lattice vibration.
• What is the cut off frequency for a linear monoatomic lattice if the atomic spacing is 1 A and velocity of sound is 330 m/sec at 0°C ?
• The magnetic susceptibility of a medium is $899 \times , 10^{-11}$. Calculate relative permeability.
• State curie-weiss law of ferromagnetism.
• Define electron mobility.
• What is Meissner Effect ?
• Explain, why good conductors are not super conductors?
• What is population Inversion ?

Part-III | Qn 3 | 2x8

• Find the volume of an Unit Cell in BCC crystal in terms of atomic radius.
• Explain the significance of Brillouin Zone.
• Distinguish between Photon and Phonon.
• The magnetic field strength of a piece of metal is $10^6$ A/m. Calculate the Flux Density of material. (Given $\chi =1.5 \times, 10^{-3}$)
• What is local electric field ? Write down its expression.
• Calculate the Einstein temperature, if Einstein frequency is $9 \times , 10^{11}$ Hz.
• If light of wave length 660 nm has wave trains $13.2 \times 10^{-6}$ m long. Calculate Coherent time.
• What is the Isotopic effect in Super conductivity ?
• Distinguish between spontaneous emission and stimulated emission.
• On what factors Polarization of a dielectric depends ?

Part-IV | Qn 4-7 | 6x4

1. Derive Bragg's Law for X-rays diffraction by crystals. How this is experimentally verified?
   
   OR
   
   Define geometrical structure factor and explain in mathematically. Also write its physical significance.

2. Discuss Debye's theory of specific heat of solids.
   
   OR
   
   What is diamagnetism ? Derive an expression for Classical Langevin's theory of diamagnetism ?

3. What is LASER ? Explain principle, construction and working of Ruby Laser.
   
   OR
   
   Discuss in details the various contributions to the total polarizability according to the Classical theory.

4. What is Hall effect ? Derive an expression for measurement of conductivity and Hall coefficient.
   
   OR
   
   What is Super Conductivity ? Describe the effect of an external magnetic field on the super conducting state of a material with Meissner effect.

2022| +3-V-S-CBCS(MS)-Sc(H)-Core-XI-Phy-R&B | Full Marks:60

PART-I | Answer all questions. | 1x8

1. The Miller indices of the plane parallel to the 'x' and 'y' axes are ______.
2. The reciprocal lattice for Hexagonal space lattice is _____.
3. At lower temperature (T), the lattice specific heat varies as _____.
4. Which Magnetic substance can have positive permeability and negative succeptibility ?
5. Induced dipole moment per unit electric field is knowr as _____.
6. The process of achieving population inversion is known as _____.
7. Ouantum of lattice vibrational energy is _____.
8. A superconductor is a perfect _____ substance.

PART-II | Answer any eight within two to three sentences | 1.5x8

1. Define packing factor.
2. State Bragg's Law.
3. Write Einstein's Theory of specific heat of solids.
4. The highest possible frequency allowed to pass through Aluminium is $64 \times 10^{11}$ Hz. Calculate its Debye temperature.
5. Define electric susceptibility.
6. Write the physical significance of clausius - Mossoti relation.
7. Write the main characteristics of LASER beam.
8. Show that critical magnetic field is a function of temperature.
9. Assuming there are $5 \times 10^{28}$ atoms/m³ in copper, find the Hall co-efficient.
10. Define Mobility.

PART-III | Answer any eight of the following (in maximum 75 words.) | 2x8

1. Distinguish between Ruby Laser and He-Ne Laser.
2. Give idea of BCS Theory.
3. Explain Bloch Theorem.
4. Define Ionic and orientation polarization.
   5 . Write the importance of Hall effect.
5. Write the physical significance of Lande's splitting factor.
6. Susceptibility of a paramagnetic substance at 300 K is 600. If the temperature is doubled, find susceptibility.
7. Discuss Domain theory of Ferromagnetism.
8. Explain Atomic Factor and Geometrical Factor.
9. Discuss Brillouin Zones.

PART-IV | Answer within 500 words each | 6x4

1. Explain space lattice and unit cell of a crystal. Discuss Bravais lattice for two dimensions.
   
   OR
   
   Define geometrical structure factor and explain it mathematically. Write its physical significance.

2. Describe the Weiss theory of Ferromagnetism.
   
   OR
   
   What is a Linear monoatomic chain ? Describe the wave motion of one dimensional lattice.

3. Define local field at an atom. Derive the relation between local field and polarization of a dielectric.
   
   OR
   
   Explain Three level Laser system giving the necessary theory.

4. What is Hall effect ? Derive an expression for measurement of conductivity and Hall coefficient
   
   OR
   
   What is superconductivity ? Describe the effect of an external magnetic field on the super conducting state of a material. Also discuss Meissner effect.