## Engineering Physics - Jun 2015

### 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.
**1 (a)** Write the assumption of quantum theory of radiation and deduce Rayleigh-Jeans law from Planck's law(5 marks)
**1 (b)** Give four important properties of meter waves(4 marks)
**1 (c)** Set up time independent Schrodinger wave equation in one dimension(7 marks)
**1 (d)** Calculate the energy in eV, for the first excited state of an electron in an infinite potential well of width 2A(4 marks)
**10 (a)** Define Match number, subsonic waves and supersonic waves(3 marks)
**10 (b)** Discuss the basics of conservation of mass, momentum and energy(9 marks)
**10 (c)** Explain the sol-gel method of preparing nanomaterials(4 marks)
**10 (d)** In a scanning electron microscope, electron are accelerated by an anode potential difference of 60 kilo volt. Estimate the wavelength of the electrons in the scanning beam(4 marks)
**2 (a)** State de Broglie hypothesis and show that the group velocity of the de Broglie waves of a particle is equal to the velocity of the particle(5 marks)
**2 (b)** State and explain Heisenberg uncertainty principle(5 marks)
**2 (c)** Explain in brief the properties of wave function. If the wave function of particle in an infinite potential box of width 'a' is Ψ=Bsin (n π x/a) where x is the position and it is the quantum number, find B(6 marks)
**2 (d)** The wavelength of fast neutron of mass 1.65× 10^{-27} kg is 0.02 nm. Calculate the group velocity and the phase velocity of its de Broglie waves(4 marks)
**3 (a)** Obtain an expression for the conductivity of an metal from quantum mechanic considerations(6 marks)
**3 (b)** Show that the Fermi level of an intrinsic semiconductor lines in the middle of the forbidden energy gap.(5 marks)
**3 (c)** Explain the temperature dependence of resistivity of metal and state Matthiessen's rule.(5 marks)
**3 (d)** Calculate the probability of an electron occupying an energy level 0.02 eV above the Fe level at 300k(4 marks)
**4 (a)** Define the terms drift velocity, mean free path mean collision time and relaxation time.(4 marks)
**4 (b)** Explain Hall effect, Arrive at the equation for Hall coefficient in terms of Hall voltage current through the specimen(8 marks)
**4 (c)** Describe Maglev Vehicle(4 marks)
**4 (d)** Calculate the concentration at which the acceptor atoms must be added to a Germanium sample to get a p-type semiconductor with conductivity 0.15 per ohm-meter. Given the mobility of holes=0.17 m^{2}/Vs(4 marks)
**5 (a)** Derive an expression for the radiant energy density under thermal equilibrium using Einstein's coefficients(7 marks)
**5 (b)** With suitable ray-diagram, explain the principle construction of a holographic images(5 marks)
**5 (c)** Give an account of point to point communication system using optical fibers(4 marks)
**5 (d)** The angle of acceptance of an optical fiber kept in air is 30, find the angle of acceptance when the fiber is in medium of refractive index 4/3(4 marks)
**6 (a)** Discuss the requisites and the conditions for a laser system.(6 marks)
**6 (b)** Define angle of acceptance and numerical aperture. Obtain an expression for the numerical aperture of an optical fiber.(6 marks)
**6 (c)** Explain measurement of pollutant in atmosphere using lasers(4 marks)
**6 (d)** A 5W pulsed laser emits light of wavelength 694 nm. If the duration of each pulse is 20ns, calculate the number of photons emitted per pulse(4 marks)
**7 (a)** Mention the geometrical configuration of the seven crystal system(7 marks)
**7 (b)** Sketch and describe the Perovskite structure(5 marks)
**7 (c)** Derive Bragg's equation(4 marks)
**7 (d)** The atomic radius of gold is 0.144nm. Determine the interplanar distance for (110) plane assuming that gold belongs to FCC system(4 marks)
**8 (a)** With the help of vector diagram explain the terms basis vectors lattice vector, interfacing angles and crystal parameters of a spade lattice.(6 marks)
**8 (b)** Derive an expression for interplanar distance in terms of Miller indices(5 marks)
**8 (c)** Define coordination number and packing factor. Compute the packing factor for BCC crystals(5 marks)
**8 (d)** In a calcite crystal, second order Bragg's reflection occur from planes with d-spacing 3A, at a glancing angle 24°. Calculate the path difference between x-rays reflected from the two adjacent planes. Also calculate the wavelength of the x-rays(4 marks)
**9 (a)** Define shock waves. Mention its properties(6 marks)
**9 (b)** What are nanomaterials? Outline the structure of carbon nano tube.(6 marks)
**9 (c)** What is scanning electron microscope? Mention its three applications(4 marks)
**9 (d)** The distance between the two pressure sensors in a shock tube is 100mm. The time taken by a shock wave to travel this this distance is 200 microsecond. If the velocity of sound under the same conditions is 340m/s, find the Match number of the shock wave(4 marks)