Time: 2 hours

Maximum marks: 40

Notes:

1. All questions carry marks as indicated.

2. Solve Question 1 OR Questions No. 2.

3. Solve Question 3 OR Questions No. 4.

4. Solve Question 5 OR Questions No. 6.

5. Solve Question 7 OR Questions No. 8.

6. Assume suitable data whenever necessary.

7. Use of non programmable calculator is permitted.

8. Illustrate your answers whenever necessary with the help of neat sketches.

1. All questions carry marks as indicated.

2. Solve Question 1 OR Questions No. 2.

3. Solve Question 3 OR Questions No. 4.

4. Solve Question 5 OR Questions No. 6.

5. Solve Question 7 OR Questions No. 8.

6. Assume suitable data whenever necessary.

7. Use of non programmable calculator is permitted.

8. Illustrate your answers whenever necessary with the help of neat sketches.

List of constants :

1. Planck’s constant ‘h’ = 6.63×10^{-34}J.S.

2. Velocity of light ‘C’ = 3×10^{8} m/s

3. Charge on electron ‘e’ = 1.602×10^{-19}C.

4. Mass of electron ‘m’ = 9.11×10^{-31} kg

5. Avogadro’s constant ‘N_{A}‘= 6.023×10^{26} $latex \frac{atoms}{kmole}$

6. Boltzman’s constant ‘K’ = 8.6×10^{–5} eV/K.

1. (a) In Compton effect, considering elastic collision between a photon and a free electron write down equations of energy and momentum conservation. [3M]

(b) Prove that a free electron can not absorb a photon completely. [3M]

(c) X-ray of wavelength 1 Å are scattered from a carbon block in a direction 90°. Calculate the observed Compton shift. How much kinetic energy is imparted to the recoil electron? [4M]

**OR**

2. (a) What is de Broglie hypothesis ? Show how the quantization of angular momentum follows from the concept of matter waves. [3M]

(b) Describe an experiment, which supports the existence of matter waves. [4M]

(c) A bullet of mass 45 gm and an electron both travel with a velocity of 1200 m/s. What wavelengths can be associated with them ? Why is the wave nature of bullet not revealed through diffraction effect? [3M]

3. (a) What do you understand by a wave packet ? Obtain the relation between group velocity and phase velocity.

[4M]

(b) Arrive at Heisenberg uncertainty principle with the help of a thought experiment. [3M]

(c) Compute the minimum uncertainty in the location of a body having mass of 2 gm moving with a speed of 1.5 m/s and the minimum uncertainty in the location of electron moving with speed of 0.6×10^{8} m/s. Given DP = 10^{–3} P. [3M]

**OR**

4. (a) Explain physical significance of wave function y. [2M]

(b) Using Schrodinger’s time independent equation, obtain an expression for eigen function of particle in one dimensional potential well of infinite height. [5M]

(c) An electron is confined to move in a one dimensional potential well of length 5 Å. Find the quantized energy values for the three lowest energy states in eV. [3M]

5. (a) Define : [4M]

(i) Space Lattice

(ii) Co-ordination number

(iii) Atomic packing fraction

(iv) Unit Cell.

(b) What are Miller Indices ? Draw the planes (210) and (010) for simple cubic structure. [3M]

(c) Aluminum has FCC structure. Its density is 2700kg/m3. Calculate unit cell dimension and atomic radius. Atomic weight of aluminum is 26.98. [3M]

**OR**

6. (a) Show that FCC structure possesses maximum packing density and minimum percentage of void space among BCC and FCC. [4M]

(b) Derive Bragg’s law of X-ray diffraction. [3M]

(c) The Bragg angle corresponding to the first order reflection from the plane (111) in a crystal is 30° when X-rays of wavelength 1.75 Å are used. Calculate inter planer spacing and lattice constant. [3M]

7. (a) Show that for an intrinsic semiconductor, the Fermi level lies at the middle of the band gap. [3M]

(b) Derive the expression for Hall voltage and Hall coefficient for extrinsic semiconductor. [4M]

(c) A strip of n-type germanium semiconductor of width 1 mm and thickness 1 mm has a Hall coefficient 10^{2} m^{3}/C. If the magnetic field used is 0.1 T and the current through the sample is 1 mA, determine the Hall voltage produced and also find carrier concentration of electron. [3M]

**OR**

8. (a) Draw the energy band diagram for a pn-junction diode in equilibrium and show that height of potential barrier is given by $latex V_0=\frac{K_T}el\;n\left[\frac{N_DN_A}{n_i^2}\right]$ where symbols have their usual meaning. [4M]

(b) Explain, why in a transistor (i) the base is thin and lightly doped (ii) the collector is large in size. [2M]

(c) Calculate the conductivity of Germanium plate having area 1 cm^{2} and thickness 0.03 mm when a potential difference of 2 volts is applied across the faces. Given : concentration of free electron in Ge is 2×10^{19} /m^{3} and

μ_{e }= 0.39 m^{2}/V.s and μ_{h }= 0.19 m^{2}/V.s. Also calculate the current produced in it. [4M]

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