Time: 2 hours

Maximum marks: 40Notes:

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.

List of constants :

1. Planck’s constant ‘ h’ = 6.63Ã—10^{-34}JS

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

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

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

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

6. Boltzman’s constant ‘K’ = 1.380Ã—10^{-23} JK^{-1}

1. a) What is Compton effect? Why classical theory failed to explain it? [2+2M]

b) In case of high atomic no. scatterer element intensity of unmodified wavelength is higher than that of modified wavelength. Explain. [3]

c) X-rays of initial wavelength 0.5Ã—10^{-10} m undergo Compton Scattering. Find the scattering angle at which wavelength of scattered X-rays will be greater than that of incident wavelength by one percent? [3M]

**OR**

2. a) What is de-Broglie hypothesis? Obtain an expression for wavelength associated with an electron accelerated through a potential difference of ‘V’ volts. [4M]

b) Show how the Bohr’s quantization condition of angular momentum follows the concept of matter waves. [3M]

c) Calculate de-Broglie wavelength of the orbital electron of Hydrogen atom. (Given that energy of electron is 13.6 eV) [3M]

3. a) Derive an expression for wave function of an electron confined to move in an infinite potential well of width ‘L’. [5M]

b) What is a wave packet? [2M]

c) Find the lowest energy of an electron in one dimensional potential well of width 2 Ã…. Express the result in electron volts.

4. a) Discuss a thought experiment of electron diffraction to arrive at Heisenberg uncertainty principle with suitable diagram. [4M]

b) Define phase velocity and group velocity. [2M]

c) Calculate uncertainty in location of an electron and a ball of mass 1 kg if their velocities are 10^{5} m / s and 10 m/srespectively. [4M]

5. a) Derive expression for atomic radius and atomic packing fraction (A.P.F.) for BCC and FCC structures and show that percentage void space is more in BCC compared to FCC structure. [6M]

b) Molybdenum has BCC structure. Its density is 10.2Ã—10^{3} kg / m^{3} and its atomic wt. is 95.94. Determine radius of Molybdenum atom. [4M]

6. a) What are Miller Indices? Draw the crystal planes in simple cubic structure having Miller Indices (i) (102) and (ii) (0 10). [3M]

b) State and derive Bragg’s Law of X-ray diffraction. [4M]

c) The d_{110} interplaner spacing in a BCC metal vanadium is 2.15 Ã…. Find itslattice constant (a). [3M]

7. a) Explain classification of solids on the basis of energy band diagrams. [3M]

b) Draw energy band diagrams for the following : [2+2M]

i) PN Junction in Reverse Bias

ii) NPN Transistor (unbiased)

c) Find V_{0} across a silicon junction at room temperature, if p-region has 10^{21} acceptor atoms / m^{3} and N-region has 10^{22} atoms/ m^{3}. [3M]

8. a) What is Hall effect? Obtain an expression for Hall voltage if p-type semiconductor material is used. [2+3M]

b) What is meant by depletion region? [2M]

c) Determine the probability of an electron thermally excited into the conduction band in Germanium at 27Â°C, if the energy gap is 0.72 eV [3M]

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