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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 × 10^{6} m/s then its phase velocity is,

(A) 6 × 10^{9} m/s

(B) 4.7 × 10^{6} m/s

(C) 9.4 × 10^{6} m/s

(D) 1.91 × 10^{10} 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/C^{2} 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 E_{n} in one-dimensional potential box of width L and infinite height is,

(A) nh/8mL^{2}

(B) nh/8L

(C) n^{2}h^{2}/mL^{2}

(D) n^{2}h^{2}/8mL^{2}(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) ραT^{1/2}

(B) ραT^{2}

(C) ρα1/T^{2}

(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 E_{F} is the Fermi energy at absolute zero, mean energy E of electron at absolute zero is

(A) E=1.5E_{F}

(B) E

(C) E= 2/5 E_{F}

(D) E=3/5 E_{F}(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^{-14}s.(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=µ_{0}(M+B)

(B) B=µ_{0}(H+M)

(C) M=µ_{0}(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 10^{5} 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 m^{3}.(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) 10^{2} 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 × 10^{7} 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 d_{1111} : d_{110} : d_{100} =

$$ (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) C_{60}

(B) C_{70}

(C) C_{120}

(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)