**Marks: 80**

**[Time : 3 hours]
**

**INSTRUCTIONS TO CANDIDATES
**(1) All questions carry marks as indicated.

(2)Answer THREE questions from Section A and THREE questions from section B.

(3)Due credit will be given to neatness and adequate dimensions.

(4) Assume suitable data wherever necessary.

(5) Illustrate your answers wherever necessary with the help of neat sketches.

(6) Use pen of Blue/Black ink/refill only for writing the answer book.

**List of Physical Constants:**

i) Charge on electron, e=1.6 × 10^{-19} C;

ii) Mass of electron. m = 9.1 x 10^{-31} kg;

iii) g=9.8 m/s^{2};

(iv) Boltzmann constant k = 1.38 x 10^{-23} J/K ;

v) Velocity of light, c= 3 x 10^{8} m/s,

(vi) Planck’s constant, h = 6.625 x 10^{-34} Js

(vii) 1 am.u. = 1.67 x 10^{-27} kg

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**SECTION—A**

**1.** (a) How are solids classified on the basis of band theory ?** [03M]**

(b) Define Fermi energy. For an intrinsic semiconductor prove that :

E_{F}=\frac{E_{c}+E_{v}}{2} where symbols have their usual meanings.

**[05M]**

(c) Explain with reasons the materials used for the fabrication of LED’s. **[03M]**

(d) Calculate the probability of an electron being thermally promoted to the conduction band at 27°C, if the band gap is 5.6 eV wide. **[03M]**

**OR**

**2.** (a) Explain the working of junction diode in forward bias and in reverse biased mode. **[03M]**

(b) Draw the energy band diagrams for n-type and p-type semiconductors, showing the fermi level and impurity levels at 0°K. **[03M]**

(c) State the charge neutrality condition for n-type semiconductor. Hence, using law of mass action, obtain expression for concentration of holes. **[05M]**

(d) An n-type semiconductor has resistivity of 20 x 10^{-2} ohm-m. The mobility of the electron was found out to be 100 x 10^{-4} m^{2}/V-s. Calculate the concentration of carriers (electrons) per cubic meter in the semiconducting material **[03M]**

**3.** (a) Explain de-Broglie concept of matter waves. State any four properties of matter waves.** [03M]**

(b) Show that the de-Broglie wavelength of a particle of mass m_{o} the kinetic energy K, which is not negligible with mo•c^{2} is given by :

\lambda =\frac{h_{c}}{\sqrt{K(K+2m_{o}c^{2})}} **[04M]**

(c) What is Compton effect ? Derive an expression for Compton shift. **[06M]**

**OR**

**4.** (a) Obtain relations between Einstein’s coefficients for absorption, spontaneous emission and stimulated emission. **[04M]**

(b) Explain the construction and working of Ruby Laser, with the help of suitable figures. **[06M]**

(c) Find the relative population of Ruby Laser that produces light of wavelength 6943A^{o} at 300 K. **[03M]**

**5.** (a) Prove that the speed of electron remains constant while it moves through a uniform magnetic field.** [03M]**

(b) What is Hall effect ? Derive an expression for Hall voltage and Hall coefficient for an extrinsic semiconductor.** [05M]**

(c) Draw block diagram of C.R.O. **[03M]**

(d) An electron moving in uniform magnetic field of 25 x 10^{4} Wb/m^{2} follows a circular path. If the orbital velocity of the electron is 4.396 x 10^{7} m/s, calculate the radius of the orbit.** [02M]**

**OR**

**6.** (a) Obtain an expression for vertical deflection of an electron on the fluorescent screen when it moves through a transverse electric field. **[05M]**

(b) What are positive rays ? Describe the production of positive rays. State any four properties of positive rays. **[05 M]**

(c) The resistivity of a doped silicon crystal is 9.27 x 10^{-3} ohm-m and its Hall coefficient is

3.84 x 10^{-4} m^{3}/c. Assuming that conduction is by a single type of charge carrier, calculate the carrier concentration and mobility of the carrier. **[03M]**

**SECTION- B**

**7.** (a) Obtain an expression for path difference in interference due to reflected light in thin film of uniform thickness. Hence, obtain the conditions for maximum and minimum intensity in the film. **[07M]**

(b) Explain-how Refractive index of a liquid can be determined using Newton’s rings experiment. **[04M]**

(c) In Newton’s rings experiment the diameter of 20th ring was found to be 0.59 cm and that of 10th ring was 0.336 cm. If the radius of curvature of piano-convex lens is 1 meter, calculate the wavelength of light used. **[03M]**

**OR**

**8**. (a) Prove that the radius of dark ring in case of Newton’s rings experiment is proportional to the square root of natural numbers.** [07M]**

(b) Explain formation of plane transmission grating. Derive the necessary grating equation. **[04M]**

(c) A plane transmission grating has 15000 lines per inch. Find the angle of separation of the 5048 Å and 5016 Å lines of helium in second order spectrum. **[03M]**

**9.** a) What is an optical pore ? Explain its construction and the conditions necessary for obtaining total internal reflection. **[05M]**

(b) Define acceptance angle. Derive an expression for acceptance angle. **[05M]**

(c) An optical fibre has core of refractive index 1.6 and cladding of refractive index 1.3. Calculate the value of critical angle of incidence at the core-cladding interface. Calculate the value of acceptance angle. **[03M]**

**OR**

**10.** (a) State advantages of optical fibres over the conventional conducting wires. **[03M]**

(b) Explain classification of optical fibres on the basis of index profile. Give features of each class. **[05M]**

(c) Explain the term attenuation in optical fibres.

A certain optical fibre has an attenuation of 3.5 dB/km. If 0.5 mW of optical power is initially launched into the fibre, what will be the power level after 4 km length of the fibre.** [2+3]**

**11.** (a) Derive an expression for the volume of liquid flowing per second through a capillary tube, under constant pressure difference.** [09M]**

(b) Water at 20°C is flowing through a capillary tube of length 1 m and having diameter of 2 mm, under pressure of 10 cm of water. Calculate velocity of water at following points :

(i) on the axis of tube

(ii) adjacent to wall of tube

(iii) at 0.5 mm from the axis of tube. **[04M]**

**OR**

**12.** (a) State Sabine’s formula for reverberation time and explain the meaning of each term. ** [03M]**

(b) The volume of a room is 980 m^{3} . The wall areaof the room is 150 m^{2}, ceiling area is 95 m^{2} and the floor area is 90 m^{2} . The sound absorption coefficients are :

(i) for wall is 0.03

(ii) for ceiling is 0.08 and

(iii) for floor is 0.06.

Calculate the reverberation time and the average absorption coefficient. **[04M]**

(c) State and prove Bernoulli’s theorem for flow of liquids. **[06M]**

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