U.S.N.
B. M. S. College of Engineering, Bengaluru - 560019
Autonomous Institute Affiliated to VTU
SEP – 2021 Semester End Make Up Examinations
Programme: B.E. Semester: I
Branch: All Branches Duration: 3 hrs.
Course Code: 18PY1BSPHY Max Marks: 100
Course: Applied Physics Date: 08.09.2021
Answer five full questions, choosing one full question from each unit.
Physical constants:
Mass of electron, m = 9.1x10-31 kg
e Mass of neutron/proton m = 1.67x10-27 kg
Electronic charge, e = 1.602x10-19 C Planck constant, h = 6.626x10-34 Js
Boltzmann constant, k = 1.38x10-23 J/K
B Permittivity of free space,εo=8.85x10 -12 F/m
Avagadro number, NA=6.023X1026/k mol Speed of light, c =3X108 m/s
UNIT – 1
1. a) Derive the expression for group velocity on the basis of superposition of
waves. Also establish the relation between phase velocity and group 10
velocity in a dispersive medium.
Important Note: Completing your answers, compulsorily draw diagonal cross lines on the remaining blank pages.
b) State Heisenberg’s uncertainty principle. Prove that an electron does not 7
exist inside the nucleus using this principle.
c) Calculate the energy of the neutron in eV if its de Broglie wavelength is 3
3x10-10 m.
OR
2. a) Set up one dimensional time independent Schrodinger’s wave equation.
Describe Eigen functions. 8
b) State and explain de-Broglie hypothesis of matter waves. Derive an 8
Revealing of identification, appeal to evaluator will be treated as malpractice.
expression for the de-Broglie wavelength using the concept of matter
waves.
c) A spectral line of wavelength 4000 Å has a width of 8x10-5 Å. Evaluate 4
the minimum time spent by the electrons in the upper energy state
between the excitation and de-excitation processes.
UNIT – 2
3 a) Mention the postulates of quantum free electron theory. Explain any two
merits of quantum free electron theory. 8
b) State Wiedemann-Franz law. Derive an expression for thermal 8
conductivity of a conductor using classical free electron theory.
c) Find the Fermi energy in copper on the assumption that each copper atom 4
contributes one free electron to the electron gas. The density of copper is
8.94 x 103 kg/m3 and its atomic mass is 63.5.
UNIT – 3
4. a) Explain electronic polarization with neat diagram. Derive an expression
for electronic polarizability exhibited by a pure elemental dielectric 8
substance.
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b) Derive an expression for Fermi energy in an intrinsic semiconductor. 8
Indicate the Fermi level in intrinsic and extrinsic semiconductors
schematically using energy level diagram.
c) The dielectric constant of He gas at NTP is 1.0000684. Calculate the 4
electronic polarizability of He atoms if the gas contains 2.7x1025
atoms/m3 and hence evaluate the radius of the He atoms.
UNIT – 4
5. a) Derive an expression for energy density of radiation under thermal 8
equilibrium condition in terms of Einstein’s coefficients.
b) Mention the reasons for attenuation in optical fibers. Derive an expression 8
for attenuation coefficient of an optical fiber.
c) A He-Ne laser is emitting a laser beam with an average power of 4.5 mW. 4
Find the number of photons emitter per second by the laser. The
wavelength of the emitted radiation is 6328 Å.
OR
6. a) Elucidate the construction and working of He-Ne laser with an energy
level diagram. 7
b) Discuss the different types of optical fibers with suitable diagrams. 9
c) Find the core radius necessary for single mode operation at 850 µm in 4
fiber with n1=1.480, n2=1.47 and V-number =2.405. Also calculate the
acceptance angle of the fiber. Assuming the fiber is in air medium.
UNIT – 5
7. a) Derive an expression for total energy of a harmonic oscillator and 7
represent graphically the variation of potential, kinetic and total energy
with time.
b) What is Forced vibration? Establish the differential equation for Forced 9
vibration and obtain an expression for amplitude and phase.
c) A body executing S.H.M has its velocity 16 cms-1 when passing through 4
its center mean position. If it goes 1 cm either side of mean position,
calculate its time period.
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