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Engineering Physics : Question Paper Jan 2013 - First Year Engineering (P Cycle) (Semester 1) | Visveswaraya Technological University (VTU)
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## Engineering Physics - Jan 2013

### 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) The law which failed to account for shorter wavelength region of black body radiation spectrum is,
(A) Wein's law
(B) Rayleigh-Jean's law
(C) Planck's law
(D) Maxwell's law
(1 marks)
1 (a) (ii) The de-Broglie wavelength of a particle at rest is
(A) Zero
(B) infinite
(C) h/p
(D) h/v
(1 marks)
1 (a) (iii) If group velocity of particle is 4.7 × 106 m/s then its phase velocity is,
(A) 6 × 109 m/s
(B) 4.7 × 106 m/s
(C) 9.4 × 106 m/s
(D) 1.91 × 1010 m/s
(1 marks)
1 (a) (iv) The particle velocity of wave is equal to,
(A) group velocity
(B) Phase velocity
(C) velocity of light
(D) velocity of sound
(1 marks)
1 (b) Describe Davisson and Germer experiment for confirmation of de-Broglie hypothesis.(7 marks) 1 (c) Derive de-Broglie wavelength using group velocity(5 marks) 1 (d) Calculate the de-Broglie wavelength of particle of mass 0.65 MeV/C2 has a kinetic energy 80 eV.(4 marks)

### Choose the correct answer for the following :-

2 (a) (i) In quantum mechanics the energy operation is represented as:
$$(A)\ \dfrac {8x^2 m}{h^2} \dfrac {\partial^2}{\partial x^{2}} \$$B) \ -\dfrac{h^2}{4\pi^2 m} \dfrac {\partial^{2}}{\partial x^{2}}\$$C) \ -\dfrac{h^2}{8\pi^2 m} \dfrac {\partial^2}{\partial x^{2}}\$$D) \ \dfrac {h^2 }{2\pi^{2}m}\dfrac {\partial^{2}}{\partial x^{2}} $$(1 marks) 2 (a) (ii) The probability of finding the particle with in an element of volume dτ is,$$(A)\ zero\$$B)\ \int|\psi|^2d\tau \$$C) \int | \psi | d \tau \$$D) \int | \psi | d \tau$$
(1 marks)
2 (a) (iii) If an electron moves in one dimensional box of length 2 mm. the normalization constant is,
$$(A) \ 1(nm)^\frac {-1}{2}\$$B) \ 2(nm)^{-1}\\ (C) \ \sqrt{2}(nm)^-1\$$D) \ zero$$
(1 marks)
2 (a) (iv) The energy of a particle En in one-dimensional potential box of width L and infinite height is,
(A) nh/8mL2
(B) nh/8L
(C) n2h2/mL2
(D) n2h2/8mL2
(1 marks)
2 (b) Set up Schrodinger's time-independent wace equation.(8 marks) 2 (c) Using uncertainly principle, prove that free electron does not exist inside the nucleus.(4 marks) 2 (d) A spectral line of wavelenght 4000 A° U has width of 8×10-5 AU. Evaluate the minimum time spent by electrons in upper energy state between excitation and de-excitation process.(4 marks)

### Choose the correct answer for the following :-

3 (a) (i) The free electrons in classical free electron theory are treated as:
(A) rigidly fixed lattice point
(B) liquid molecules
(C) gas molecules
(D) none of these
(1 marks)
3 (a) (ii) The temperature dependence of classical expression for electrical resistivity of a metal is,
(A) ραT1/2
(B) ραT2
(C) ρα1/T2
(D) ρα1/T
(1 marks)
3 (a) (iii) The value of Fermi function in Fermi-level is at T ? 0 K,
(A) zero
(B) 0.5
(C) 0.75
(D) 1
(1 marks)
3 (a) (iv) IF EF is the Fermi energy at absolute zero, mean energy E of electron at absolute zero is
(A) E=1.5EF
(B) E
(C) E= 2/5 EF
(D) E=3/5 EF
(1 marks)
3 (b) Explain failure of classical free electron theory.(6 marks) 3 (c) What are the merits of quantum free electron theory?(6 marks) 3 (d) Calculate the Fermi velocity and mean free path for conduction electron in silver, given that its Fermi energy is 5.5eV and relaxation time for electrons is 3.83 × 10-14s.(4 marks) 4 (a) (i) The electric dipole moment per unit volume is
(A) Magnetization
(B) Dipole moment
(C) Electric polarization
(D) Electric susceptibility
(1 marks)
4 (a) (ii) Claussius - Mussoti equation does not holds for,
(A) crystalline solids
(B) liquid
(C) gases
(D) vaccum
(1 marks)
4 (a) (iii) The relation between B, M and H is.
(A) H=µ0(M+B)
(B) B=µ0(H+M)
(C) M=µ0(H+B)
(D) None of these
(1 marks)
4 (a) (iv) Above curie temperature ferromagnetic substance becomes:
(A) anti-ferromagnetic
(B) strongly ferromagnetic
(C) paramagnetic
(D) diamagnetic
(1 marks)
4 (b) Discuss polarization mechanism in dielectrics and their frequency dependence.(8 marks) 4 (c) Differentiate hard and soft magnetic materials with suitable application.(4 marks) 4 (d) An electric field of 105 V/m is applied on a sample of noen at NTP. Calculate the dipole moment induced in each atom. The dielectric constant of neon is 1.00014. Find the atomic polariziability of neon gas. At NTP 1 kg atom of Ne-gas occupies volume of 22.4 m3.(4 marks)

### Choose the correct answer for the following :-

5 (a) (i) In He-Ne laser the laser emission takes place from,
(A) He-atoms only
(B) Ne-atoms only
(C) Both He and Ne atoms
(D) 50% from Helium and 50% from Neon
(1 marks)
5 (a) (ii) Which of the following leads coherent light:
(A) induced absorption
(B) Spontaneous emission
(C) Stimulated emission
(D) None of these
(1 marks)
5 (a) (iii) The pumping methhod used in semiconductor diode laser is,
(A) optical pumping
(B) electric discharge
(C) forward bias
(D) chemical reactions
(1 marks)
5 (a) (iv) The life time of metastable state is about,
(A) 10-3 sec
(B) 10-13 sec
(C) 102 sec
(D) 10-9 sec
(1 marks)
5 (b) Obtain an expression for energy density of radiation under equilibrium condition in terms of Einstein coefficient.(8 marks) 5 (c) What is holography? Explain principle of hologram recording using laser.(4 marks) 5 (d) A pulsed laser with power 1 mw lasts for ions. If the number of photons emitted per second is 5 × 107 calcualte the wavelength of laser.(4 marks)

### Choose the correct answer for the following :-

6 (a) (i) According to BCS theory, the cooper pair is pair of,
(A) Electron-Proton
(B) Electron-Electron
(C) Proton-Proton
(D) Electron-Neutron
(1 marks)
6 (a) (ii) High temperature superconductors bear the crystal structure of,
(A) cubic
(B) orthohombic
(C) diamond
(D) perovskite
(1 marks)
6 (a) (iii) The acceptance angle of optical fibre whose RI of core and cladding of 1.55 and 1.50 respectively is,
(A) 32°
(B) 45°
(C) 223°
(D) 15°
(1 marks)
6 (a) (iv) According to Meissner effect, material in super conducting state is
(A) paramagnetic
(B) diamagnetic
(C) ferromagnatic
(D) anti-ferromagnetic
(1 marks)
6 (b) What is refractive index profile? Describe three types of optical fibre with one application for each type.(8 marks) 6 (c) Explain working of SQUID with application.(4 marks) 6 (d) An optical fibre of 600 mts long has input power of 120 mw emerges out with power of 90 mw. Find attenuation in the fibre.(4 marks)

### Choose the correct answer for the following :-

7 (a) (i) The lattice paramter a = b ≠ c and α = β = γ = 90° represent,
(A) cubic
(B) tetragonal
(C) rhombohedral
(D) orthohombic
(1 marks)
7 (a) (ii) The co-ordination number of rock salt is,
(A) 6
(B) 8
(C) 12
(D) 14
(1 marks)
7 (a) (iii) Which of the following has least packing fraction,
(A) sc
(B) bcc
(C) fcc
(D) diamond
(1 marks)
7 (a) (iv) In a sample cubic lattice d1111 : d110 : d100 =
$$(A) \ \sqrt{6}:\sqrt{3} : \sqrt{2} \$$B) \ \sqrt{2}: \sqrt{6}: \sqrt{3} \$$C) \ \sqrt{2}: \sqrt{3}: \sqrt{6}\$$D) \ \sqrt{3}: \sqrt{6}: \sqrt{2}\
(1 marks)
7 (b) Derive expression for interplanner spacing of crystal in terms of Miller Indices. (7 marks) 7 (c) What is atomic packing factor? Calculate packing factor for sc and bcc structure.(5 marks) 7 (d) What is Miller index of plane making intercepts ratio 3a : 4b on x-and y-axis and parallel to z-axis a, b are primitive vectors?(4 marks)

### Choose the correct answer for the following :

8 (a) (i) A bulk material (three dimensions) reduced in one direction is called quantum:
(A) particle
(B) well
(C) dot
(D) wire
(1 marks)
8 (a) (ii) Which belongs to fullerene family?
(A) C60
(B) C70
(C) C120
(D) All
(1 marks)
8 (a) (iii) Velocity of ultrasound through liquid is proporational to,
(A) density
(B) volume
(C) bulk modulus
(D) rigidity modulus
(1 marks)
8 (a) (iv) Ultrasonic wave cannot be transmitted through.
(A) solid
(B) liquid
(C) gas
(D) vaccum
(1 marks)
8 (b) What is NDT? Describe the NDT method of detection of flows in solid using ultrasound.(8 marks) 8 (c) What are nano materials? Write the structure and applications of carbon nano tubes.(8 marks)