16 Marks Questions, Assignment Problems

PART-B '16' Marks Questions

Anna University Questions

Classical free electron theory

1. Define electrical conductivity. Obtain an expression for electrical conductivity by free electron theory.

2. Based on the classical free electron theory, derive an expression for electrical conductivity of metals.

3. (i) State the assumption of the classical free electron model.

(ii) Obtain an expression for the electrical conductivity on the basis of the classical free electron theory. 

4. Starting with the classical free electron theory of metals obtain an expression for electrical and thermal conductivity. 

5. (i) List the drawbacks of classical free electron theory. 

(ii) Obtain Wiedemann Franz law using the expressions of electrical and thermal conductivity. 

6. (i) Deduce an expression for electrical conductivity of conducting material.

(ii) List any four drawbacks of classical free electrons theory. 

7. Deduce mathematical expressions for electrical conductivity and thermal conductivity of a conducting material.

8. (i) Mention any four postulates of classical free electron theory.

(ii) Obtain an expression for the thermal conductivity of metal.

9. Write Fermi - Dirac function. Obtain an expression for the density of states.

10. Obtain an expression for density of states. 

11. Explain the meaning of 'density of states'. Derive expression for the number of allowed states for unit volume of a solid. 

Additional PART B '16' Marks Questions

1. Explain periodic potential.

2. Describe the formation of energy band in a crystalline solid.

3. Explain the origin of energy band in a solid.

4. Describe tight tight binding approximation to explain the formation of energy band.

5. Derive an expression for the effective mass of an electron moving in energy bands of a solid. Show how it varies with the wave vector.

6. Explain the concept of hole.

7. Define valance band, conduction band forbidden energy gap in the energy band structure.

8. Distinguish between conductors, semiconductor and insulator.

ASSIGNMENT PROBLEMS

1. A copper wire whose diameter is 0.16 cm carries steady current of 10 A. What is the current density of the wire? Also calculate the drift velocity of the electrons in copper. 

Given Density of electron in copper 8.5 × 1028 m-3

[Ans: J = 497.6 × 104 A/m2, vd = 3.6 × 10-4 m/s]

2. The density and atomic weight of copper is 8900 kgm-3 and 63.5 respectively. The relaxation time of electrons in copper at 300 K is 10-14 seconds. Calculate the electrical conductivity of copper.

[Ans: 2.375 × 107 Ω-1 m-1]

3. The thermal and electrical conductivities of Cu at 20°C are 390 Wm-1 K-1 and 5.87 × 107 Ω-1 m-1 respectively. Calculate the Lorentz number.

 [Ans: 2.267 × 10-8 W Ω K-2]

4. Using Fermi function, evaluate the temperature at which there is 1% probability that an electron in a metal will have an energy 0.5 eV above EF of 5 eV.

[Ans: 1260 KJ

5. Use the Fermi distribution function to obtain the value of F (E) for E - E = 0.01 eV at 300 K.

[Ans: F(E)= 0.4045 ]