Engineering Physics - Jan 2014

First Year Engineering (P Cycle) (Semester 1)

TOTAL MARKS: 100
TOTAL TIME: 3 HOURS (1) Question 1 is compulsory.
(2) Attempt any four from the remaining questions.
(3) Assume data wherever required.
(4) Figures to the right indicate full marks.

Choose the correct answer for the following :-

1 (a) (i) De Broglie wavelength of an electron accelerated through a potential of 60 V is,
(A) 1.850 Å
(B) 1.584 Å
(C) 1.589 Å
(D) 1.570 Å (1 marks) 1 (a) (ii) The wavelength of maximum intensity is inversely proportional to the absolute temperature of the body emitting radiation. This is called,
(A) Stefan's law
(B) Wein's displacement law
(C) Rayleigh-jean's law
(D) Plank's law(1 marks) 1 (a) (iii) Einstein's photoelectric equation is given by,
(A) E=?+(KE)_max
(B) E=?-(KE)_max
(C) ?=E+(KE)_max
(D) (KE)_max=E+?(1 marks) 1 (a) (iv) Which of the following relations can be used to determine de Broglie wavelength associated with a particle?
$$ (A) \ \dfrac {h}{\sqrt{2mE}}\$$B) \ \dfrac {h}{mV}\$$C) \ \dfrac {h}{\sqrt{2meV}}\$$D) \ all \ of \ these \\$$ \lt/span\gt\ltspan class='paper-ques-marks'\gt(1 marks)\lt/span\gt \lt/span\gt\ltspan class='paper-question'\gt\ltspan class='paper-ques-desc'\gt\ltb\gt1 (b)\lt/b\gt Explain Wein's law and Rayleigh-Jean's law. Mention their drawbacks,\lt/span\gt\ltspan class='paper-ques-marks'\gt(6 marks)\lt/span\gt \lt/span\gt\ltspan class='paper-question'\gt\ltspan class='paper-ques-desc'\gt\ltb\gt1 (c) \lt/b\gt Define phase velocity and group velocity. Derive a relation between the two.\lt/span\gt\ltspan class='paper-ques-marks'\gt(6 marks)\lt/span\gt \lt/span\gt\ltspan class='paper-question'\gt\ltspan class='paper-ques-desc'\gt\ltb\gt1 (d) \lt/b\gt Calculate the wavelenght associated with electrons whose sped is 0.01 part of the speed of light.\lt/span\gt\ltspan class='paper-ques-marks'\gt(4 marks)\lt/span\gt \lt/span\gt -------------- \ltspan class='paper-comments'\gt ### Choose that correct answer for the following :- \lt/span\gt\ltspan class='paper-question'\gt\ltspan class='paper-ques-desc'\gt\ltb\gt2 (a) (i)\lt/b\gt For a particle in an infinite potential well in its 1\ltsup\gtst\lt/sup\gt excited state, the probability of finding the particle at the center of box is, \ltbr\gt (A) 0 \ltbr\gt (B) 0.25 \ltbr\gt (C) 0.5 \ltbr\gt (D) 0.1\lt/span\gt\ltspan class='paper-ques-marks'\gt(1 marks)\lt/span\gt \lt/span\gt\ltspan class='paper-question'\gt\ltspan class='paper-ques-desc'\gt\ltb\gt2 (a) (ii)\lt/b\gt The Heisenberg's Uncertainty relation for position of a particle is given by, \ltbr\gt $$ (A) \ \Delta P, \Delta x \ge \dfrac {h}{2}\$$B) \ \Delta P, \Delta x \le \dfrac {h}{4\pi}\$$C) \ \Delta P, \Delta x \ge \dfrac {h}{4\pi}\$$D) \ \Delta P, \Delta x \ge \dfrac {h}{\pi}\$$ (1 marks) 2 (a) (iii) According to Max Born approximation |φ|² represents,
(A) particle density
(B) Charge density
(C) Energy density
(D) Probability density (1 marks) 2 (a) (iv) Schrodinger's time independent wave equation is applicable for the particle with,
(A) Constant energy
(B) Variable energy
(C) Only constant potensital energy
(D) All of these (1 marks) 2 (b) Set up time independent Schrodinger wave equation.(6 marks) 2 (c) Explain Heisenberg's Uncertanity principle. Give its physical significance.(6 marks) 2 (d) An electron is bound in one dimensional infinite well fo width 0.12 mm. find the energy value and de Broglie wave length in the first excited state.(4 marks)

Choose the correct answer for the following :-

3 (a) (i) The motor specific heat of a gas constant volume is given by,
$$ (A) \ C_V=\dfrac {2R}{3} \$$B) \ C_V=\dfrac {3R}{2} \$$C) \ C_V=\dfrac {4R}{3} \$$D) \ C_{V}\dfrac {3R}{4}\\$$ \lt/span\gt\ltspan class='paper-ques-marks'\gt(1 marks)\lt/span\gt \lt/span\gt\ltspan class='paper-question'\gt\ltspan class='paper-ques-desc'\gt\ltb\gt3 (a) (ii)\lt/b\gt IF the Fermi energy of silver is 5.5 eV, the Fermi velocity of conduction electron is, \ltbr\gt (A) 0.98×10\ltsup\gt6\lt/sup\gt m/S \ltbr\gt (B) 1.39×10\ltsup\gt6\lt/sup\gt m/S \ltbr\gt (C) 2.46×10\ltsup\gt5\lt/sup\gt m/S \ltbr\gt (D) None of these\lt/span\gt\ltspan class='paper-ques-marks'\gt(1 marks)\lt/span\gt \lt/span\gt\ltspan class='paper-question'\gt\ltspan class='paper-ques-desc'\gt\ltb\gt3 (a) (iii)\lt/b\gt Matthiessen's rule is given by, \ltbr\gt $$ (A) \ \rho=\rho_{ph}-\rho_{i}\$$B) \ \rho=\dfrac {\rho_{ph}}{\rho_{i}}\$$C) \ \rho=\rho_{ph}+\rho\$$D) \ \rho=\dfrac {\rho_{i}}{\rho_{ph}}\$$ (1 marks) 3 (a) (iv) The value of Fermi distribution function at ? =0 K is 1, under the condition,
(A) E=E_r
(B) E>E_r
(C) E>>E_r
(D) E<e<sub>r</e<sub>(1 marks) 3 (b) Explain failure of classical free electron theory.(6 marks) 3 (c) Explain the probability of occupation of various energy states by electron at T=0 K and T>0 K on the basis of Fermi factor.(6 marks) 3 (d) Find the temperature at which there is 1.0% probability that a state with an energy 0.5 eV above Fermi energy wiil be occupied.(4 marks)

Choose the correct answer for the following :-

4 (a) (i) Choose the correct relation,
(A) E=ε₀(ε_r-1)P
(B) P=ε₀(ε_r-1)E
(C) ε_r=K-1
(D) D=ε₀(ε_r-1)E(1 marks) 4 (a) (ii) For ferromagnetic substance, the Curie-Weiss law is given by,
$$(A) \ X=\dfrac {C}{T}\\ (B) \ X=\dfrac {C}{(T-\theta)}\$$C) \ X=\dfrac {(T-\theta)}{C}\$$D) \ X=\dfrac {C}{(T+\theta)}\\$$\lt/span\gt\ltspan class='paper-ques-marks'\gt(1 marks)\lt/span\gt \lt/span\gt\ltspan class='paper-question'\gt\ltspan class='paper-ques-desc'\gt\ltb\gt4 (a) (iii)\lt/b\gt The only polarization mechanism at frequencies exceeding 10\ltsup\gt13\lt/sup\gt Hz is, \ltbr\gt (A) ionic \ltbr\gt (B) electronic \ltbr\gt (C) orientation \ltbr\gt (D) space charge\lt/span\gt\ltspan class='paper-ques-marks'\gt(1 marks)\lt/span\gt \lt/span\gt\ltspan class='paper-question'\gt\ltspan class='paper-ques-desc'\gt\ltb\gt4 (a) (iv)\lt/b\gt Sulphur is an elemental solid dielectric of atomic weight 32.07 and density 2.07×10\ltsup\gt3\lt/sup\gt kgm\ltsup\gt-3\lt/sup\gt. The number of atoms per unit volume for Sulphur is, \ltbr\gt (A) 3.89×10\ltsup\gt28\lt/sup\gt/m\ltsup\gt3\lt/sup\gt \ltbr\gt (B) 3.89×10\ltsup\gt25\lt/sup\gt/m\ltsup\gt3\lt/sup\gt \ltbr\gt (C) 9.3×10\ltsup\gt24\lt/sup\gt/m\ltsup\gt3\lt/sup\gt \ltbr\gt (D) None of these\lt/span\gt\ltspan class='paper-ques-marks'\gt(1 marks)\lt/span\gt \lt/span\gt\ltspan class='paper-question'\gt\ltspan class='paper-ques-desc'\gt\ltb\gt4 (b)\lt/b\gt Derive an expression for internal field in case of one dimensional array of atoms in dielectric solid.\lt/span\gt\ltspan class='paper-ques-marks'\gt(8 marks)\lt/span\gt \lt/span\gt\ltspan class='paper-question'\gt\ltspan class='paper-ques-desc'\gt\ltb\gt4 (c) \lt/b\gt Describe ferroelectrics.\lt/span\gt\ltspan class='paper-ques-marks'\gt(4 marks)\lt/span\gt \lt/span\gt\ltspan class='paper-question'\gt\ltspan class='paper-ques-desc'\gt\ltb\gt4 (d) \lt/b\gt If a WaCI crystal is subjected to an electric field of 1000 V/m and the resulting polarization is 4.3×10\ltsup\gt-8\lt/sup\gt C/m\ltsup\gt2\lt/sup\gt, calculate the static dielectric constanr of NaCl.\lt/span\gt\ltspan class='paper-ques-marks'\gt(4 marks)\lt/span\gt \lt/span\gt -------------- \ltspan class='paper-comments'\gt ### Choose the correct answer for the following :- \lt/span\gt\ltspan class='paper-question'\gt\ltspan class='paper-ques-desc'\gt\ltb\gt5 (a) (i)\lt/b\gt If n\ltsub\gt1\lt/sub\gt is the number density of lower energy E\ltsub\gt1\lt/sub\gt and n\ltsub\gt2\lt/sub\gt is the number density of higher energy E\ltsub\gt2\lt/sub\gt then n\ltsub\gt2\lt/sub\gt > n\ltsub\gt1\lt/sub\gt is called, \ltbr\gt (A) thick population \ltbr\gt (B) Inverted population \ltbr\gt (C) normal population \ltbr\gt (D) no population\lt/span\gt\ltspan class='paper-ques-marks'\gt(1 marks)\lt/span\gt \lt/span\gt\ltspan class='paper-question'\gt\ltspan class='paper-ques-desc'\gt\ltb\gt5 (a) (ii)\lt/b\gt The number of modes of standing waves in the resonant cavity of length 1 m, if He-We laser operating at wavelength of 6328 Å is \ltbr\gt (A) 3.16×10\ltsup\gt6\lt/sup\gt \ltbr\gt (B) 1.58×10\ltsup\gt6\lt/sup\gt \ltbr\gt (C) 3.16×10\ltsup\gt8\lt/sup\gt \ltbr\gt (D) None of these\lt/span\gt\ltspan class='paper-ques-marks'\gt(1 marks)\lt/span\gt \lt/span\gt\ltspan class='paper-question'\gt\ltspan class='paper-ques-desc'\gt\ltb\gt5 (a) (iii)\lt/b\gt Image is stored on a hologram in the form of \ltbr\gt (A) interference pattern \ltbr\gt (B) diffraction pattern \ltbr\gt (C) photograph \ltbr\gt (D) none of these\lt/span\gt\ltspan class='paper-ques-marks'\gt(1 marks)\lt/span\gt \lt/span\gt\ltspan class='paper-question'\gt\ltspan class='paper-ques-desc'\gt\ltb\gt5 (a) (iv)\lt/b\gt The realation between Einstein's coefficients A & B is \ltbr\gt $$ (A) \ \dfrac {8\pi h \lambda^3}{C^3}\$$B) \ \dfrac {8\pi h^2r^3}{C^3}\$$C) \ \dfrac {8\pi hr^3}{C^3}\$$D) \ \dfrac {8 \pi hr^{3}}{C^3}\$$(1 marks) 5 (b) Explain the process of spontaneous and stimulated emission.(6 marks) 5 (c) Describe the construction and working of semiconductor laser.(6 marks) 5 (d) A pulse laser has an average power output 1.5 mW per pulse and pulse duration is 20 ns. The number of photon emitted per pulse is estimated to be 1.047×10⁸. Find the wavelength of the emitted laser.(4 marks)

Choose the correct answer for the following :-

6 (a) (i) The variation of critical field H_c with temperature T is given by,
$$(A) \ H_C=H_O\left [ 1- \left ( \dfrac {T}{T_{C}}\right )^2 \right ]\$$B) \ H_C=H_O\left [1+ \left (\dfrac {T}{T_C} \right )^2 \right ]\$$C) \ H_C=H_O\left [1- \dfrac {T}{T_C} \right ]\$$D) \ H_C=H_O \left [ 1+ \dfrac {T}{T_C} \right ]$$(1 marks) 6 (a) (ii) The quantum of magnetic flux is given by,
$$ (A) \ \dfrac {2e}{h}\$$B) \ \dfrac {h}{2e}\$$C) \ \dfrac {he}{2} \$$D) \ \dfrac {2\pi h}{e}\\$$\lt/span\gt\ltspan class='paper-ques-marks'\gt(1 marks)\lt/span\gt \lt/span\gt\ltspan class='paper-question'\gt\ltspan class='paper-ques-desc'\gt\ltb\gt6 (a) (iii)\lt/b\gt Fractional index change of optical fibre and reflective index of core are 0.00515 and 1.533 repsectively. The cladding refractive index is, \ltbr\gt (A) 1.492 \ltbr\gt (B) 1.525 \ltbr\gt (C) 1.499 \ltbr\gt (D) 1.511\lt/span\gt\ltspan class='paper-ques-marks'\gt(1 marks)\lt/span\gt \lt/span\gt\ltspan class='paper-question'\gt\ltspan class='paper-ques-desc'\gt\ltb\gt6 (a) (iv)\lt/b\gt The attenuation of a fibre-optical cable is expressed in, \ltbr\gt (A) ohm/km \ltbr\gt (B) watt/km \ltbr\gt (C) decibel/km \ltbr\gt (D) joule/km\lt/span\gt\ltspan class='paper-ques-marks'\gt(1 marks)\lt/span\gt \lt/span\gt\ltspan class='paper-question'\gt\ltspan class='paper-ques-desc'\gt\ltb\gt6 (b)\lt/b\gt Describe type-I and type-II superconductors.\lt/span\gt\ltspan class='paper-ques-marks'\gt(6 marks)\lt/span\gt \lt/span\gt\ltspan class='paper-question'\gt\ltspan class='paper-ques-desc'\gt\ltb\gt6 (c) \lt/b\gt What is attenuation? Explain any two factors contributing to the fibre loss.\lt/span\gt\ltspan class='paper-ques-marks'\gt(6 marks)\lt/span\gt \lt/span\gt\ltspan class='paper-question'\gt\ltspan class='paper-ques-desc'\gt\ltb\gt6 (d) \lt/b\gt The angle of acceptance of an optical fibre is 30\ltsup\gto\lt/sup\gt when kept in air. Find the angle of acceptance when it is in a medium of refractive index 1.33\lt/span\gt\ltspan class='paper-ques-marks'\gt(4 marks)\lt/span\gt \lt/span\gt -------------- \ltspan class='paper-comments'\gt ### Choose the correct answer for the following :- \lt/span\gt\ltspan class='paper-question'\gt\ltspan class='paper-ques-desc'\gt\ltb\gt7 (a) (i)\lt/b\gt The relation between atomic radius and lattice constant a in FCC structure is \ltbr\gt $$(A)\ a=2R \ (B) \ a=2\sqrt{2} R \ (C) \ a= \dfrac{\sqrt{3}}{4} R \ (D)\ a=\dfrac{4}{\sqrt{3}}R $$\lt/span\gt\ltspan class='paper-ques-marks'\gt(1 marks)\lt/span\gt \lt/span\gt\ltspan class='paper-question'\gt\ltspan class='paper-ques-desc'\gt\ltb\gt7 (a) (ii)\lt/b\gt The crystal with lattices a = b ≠ c and angles α = β = γ = 90\ltsup\gto\lt/sup\gt represents, \ltbr\gt (A) cubic \ltbr\gt (B) hexagonal \ltbr\gt (C) orthorhombic \ltbr\gt (D) tetragonal\lt/span\gt\ltspan class='paper-ques-marks'\gt(1 marks)\lt/span\gt \lt/span\gt\ltspan class='paper-question'\gt\ltspan class='paper-ques-desc'\gt\ltb\gt7 (a) (iii)\lt/b\gt The number of atoms per present in the unit cell of diamond cubic crystal structure is, \ltbr\gt (A) 2 \ltbr\gt (B) 4 \ltbr\gt (C) 8 \ltbr\gt (D) 16\lt/span\gt\ltspan class='paper-ques-marks'\gt(1 marks)\lt/span\gt \lt/span\gt\ltspan class='paper-question'\gt\ltspan class='paper-ques-desc'\gt\ltb\gt7 (a) (iv)\lt/b\gt Bragg's law is given by, \ltbr\gt $$(A)\ 2 \sin \theta = n\lambda \$$B)\ 2d \sin \theta = n\lambda \$$C)\ \dfrac{2dn}{\sin \theta}=\lambda \ (D)\ 2n\lambda = sin \theta $$(1 marks) 7 (b) Define (i) Coordination number
(B) Packing factor, calculate the atomic packing factor fo BCC structure.(6 marks) 7 (c) Sketch the (1 1 2) , (1 1 0) and (1 0 0) planes in a simple cubic unit. Explain the procedure for obtaining miller indices.(6 marks) 7 (d) The minimum order of Bragg's reflection occurs at an angle of 20^o in the plane (2 1 2). Find the wavelenght of X-rays if lattice constant is 3.615 Å(4 marks)

Choose the correct answer for the following :-

8 (a) (i) In a carbon nanotube the bond between the carbon atom is,
(A) metalic
(B) ionic
(C) hydrogen
(D) covalent (1 marks) 8 (a) (ii) A constant testing of product causing any damage is called,
(A) minute testing
(B) destructive testing
(C) non-destructive testing
(D) random testing(1 marks) 8 (a) (iii) Ultrasonic waves are sound waves having,
(A) Velocity greater than 330 mS^-1
(B) Velocity less than 330 mS^-1
(C) Frequency greater than 20 kHz
(D) Frequency less than 20 kHz(1 marks) 8 (a) (iv) Which of the procedure is not employed to detect the internal flows by a material,
(A) Ultrasonic method
(B) Magnetic method
(C) Alpha ray method
(D) Dynamic testing(1 marks) 8 (b) Explain carbon nanotubes and its application by giving physical properties.(8 marks) 8 (c) What are ultrasonic? Explain with a diagram a method for measurement of velocity of ultrasonic waves in liquids.(8 marks)