no. manipal institute of technology - · pdf filereg. no. manipal institute of technology (a...

Reg. No.

MANIPAL INSTITUTE OF TECHNOLOGY (A constituent Institute of Manipal University, Manipal-576104)

FIRST SEMESTER B.E. END-SEMESTER MAKE UP EXAMINATION

JULY 2009

SUBJECT: ENGINEERING PHYSICS (PHY101/102)

Time: 3 Hrs. Max. Marks: 50

Note:

Answer any FIVE FULL questions. Each question carries 10 marks

Answer all the sub questions of a main question in a continuous sequence.

Write specific and precise answers.

Draw neat sketches wherever necessary.

Physical Constants:

Speed of light in vacuum = 3.00 10 8 m/s Electron charge = 1.60 10

19 C

Mass of proton / neutron = 1.67 1027

kg Electron mass = 9.11 1031

kg

Boltzmann constant = 1.38 1023

J/ K Planck’s constant = 6.63 1034

J.s

Permittivity of vacuum = 8.85 1012

F/m Rydberg constant = 1.10 10 7/m

Permeability of vacuum = 4 107 H/m Avogadro constant = 6.02 10

23 /mol

Any missing data may suitably be assumed.

1. (a) (i) Explain the formation of interference fringes at an air wedge and hence

obtain an expression for the fringe width. Account for the nature of the fringes.

(ii) An air wedge formed by an insulated copper wire with glass plate of length 10

cm. The system is illuminated normally by light of wavelength 600 nm. 20 fringes

are obtained per centimeter. After removing the insulation the fringes are obtained

again. The number of fringes decreased by 5/cm. Calculate the thickness of the

insulation. (3+2=5 marks)

(b)Obtain an expression for the Intensity distribution due to diffraction at multiple

slits and hence arrive at the grating equation. 5marks.

2. (a) Obtain an expression for the Fermi level in an n-type semiconductor. Show that

at low temperature the density of electrons in the conduction band is proportional

to the square root of donor concentration. 5marks.

(b) In a Newton’s rings experiment, the radii of two adjacent dark rings are

observed to be respectively equal to 4.0mm and 4.38mm. The radius of curvature

of the lens is 6.4m. Find the ordinal numbers of the rings and the wavelength of

the incident light used. 3 marks

©In a single slit diffraction pattern the distance between the 1st minimum on the

right and the 1st minimum on the left is 5.2 mm. The screen on which the pattern

is displayed is 82.3 cm from the slit and the wavelength is 546 nm calculate the

slit width. 2marks.

…Page 1 of 2

3. (a) (i) What are ‘Half period Zones’ as applied to a plane wave front? Explain

how the wave theory accounts for the rectilinear propagation of light as an

approximation?. 3 marks

(ii) Linearly polarised light of wavelength 525nm strikes at normal incidence, a

wurzite crystal (μo=2.356, μe=2.378), cut with its faces parallel to the optic axis.

What is the smallest possible thickness of the crystal if the emergent o-ray and e-

rays combine to form linearly polarised light? 2mark

(b)In a particular dispersive medium, the phase velocity of matter waves gets

doubled when the wave length is halved. What is the group velocity of matter

waves in terms of the phase velocity? 3 marks

(c ) Explain the origin of continuous X-rays and derive Duane-Hunt

relation. 2 marks

4. (a) What is Hall-effect. Derive an expression for the charge carrier density in

terms of hall-coefficient. 3 marks

(b) Describe the construction and working of a He-Ne laser. 4 marks

(c ) Determine the resistivity of Ge at 300K (i) in intrinsic condition (ii) with

donor impurity of 1 in 107 atoms (iii) with acceptor impurity of 1 in 10

8.

3 marks

5. (a) Obtain an expression for the numerical aperture of an optical fiber in terms of

refractive indices of the core and cladding and then arrive at the condition for ray

propagation. 3 marks

(ii) The angle of acceptance of an optical fiber is 30° when kept in air. Find the

angle of acceptance when it is in a medium of refractive index 1.33. 2 marks

(b) The ratio of population of two energy levels is 1.059 10-30

. Find the

wavelength of light emitted at 300K. 2 marks

(c ) Electrons with energies of 1.0eV and 2.0eV are incident on a barrier 10.0eV

high and 0.050nm wide.(i) Find their respective transmission probabilities.

(ii) How are these affected if the barrier is doubled in width. 3 marks

6. (a)Describe Davisson and Germer experiment and explain how it eshtablished the

proof for the wave nature of electrons. 4 marks

(b) An intrinsic semiconductor has an energy gap of 0.7eV.calculate the

probability of occupation of an energy state at a level kT above the bottom of the

conduction band at 100ºC. 2 marks

(c ) Calculate the position of the Fermi level for pure silicon at 300K if the

electron concentration is 2x1015

/ m3. Given that, for silicon, the energy gap is

1.1eV and the effective mass for electron is 0.31mo, where mo is the free electron

mass. 4 marks

…Page 2 of 2

Reg. No.

MANIPAL INSTITUTE OF TECHNOLOGY

(A constituent Institute of Manipal University, Manipal-576104) FIRST SEMESTER B.E. END-SEMESTER EXAMINATION – NOVEMBER. 2008

SUBJECT: ENGINEERING PHYSICS (PHY101/102) Time: 3 Hrs. Max. Marks: 50

Note: Answer any FIVE FULL questions. Each question carries 10 marks Answer all the sub questions of a main question in a continuous sequence. Write specific and precise answers. Draw neat sketches wherever necessary.

Physical Constants: Speed of light in vacuum = 3.00 × 10 8 m/s Electron charge = 1.60 × 10−19 C Mass of proton / neutron = 1.67 × 10−27kg Electron mass = 9.11 × 10−31 kg Boltzmann constant = 1.38 × 10−23 J/ K Planck’s constant = 6.63 × 10−34 J.s Permittivity of vacuum = 8.85 × 10−12 F/m Rydberg constant = 1.10 × 10 7/m Permeability of vacuum = 4π × 10−7 H/m Avogadro constant = 6.02 × 10 23 /mol Any missing data may suitably be assumed.

1. (a) Explain why the Newton’s rings are circular. Obtain an expression for the diameter of Newton’s nth dark ring obtained by the reflected light. Show that the diameters of Newton’s dark rings are proportional to square root of natural numbers. 4 marks

(b) Explain how a zone plate acts like a convergent lens. Obtain an expression for its focal length. 3 marks

(c) Monochromatic light of wavelength 538 nm falls on a slit of width 25.2μm.

The distance from the slit to a screen is 3.48 m. Consider a point on the screen 1.13 cm from the central maximum. Calculate (i) the angle of diffraction (ii) the ratio of intensity at this point to the intensity at the central maximum. 3marks.

2. (a) Assuming suitable expressions for density of states and Fermi distribution

function, show that the number of electrons per unit volume in the conduction band of an intrinsic semiconductor is given by Nc exp -(E c-E F) / kT, where

Nc= [2(2 π mc kT)3/2 / h3] mc is the effective mass of the electron ,and E c is the energy at the bottom of the conduction band. 5marks.

(b) Obtain the equation for polarization ellipse and hence discuss various types of

polarization. 5 marks

….Page 1 of 2

3. (a) Derive the expression for the intensity distribution of a monochromatic light beam diffracted at a double slit. 4 marks

(b) Explain group velocity and phase velocity and obtain the relation between them. 3 marks

(c )The bulk n-type and p-type materials of a particular germanium junction have conductivities of 104 mhos / m and 102mhos / m respectively, at 300 K. Find the contact potential difference across the junction. Given that density of either carrier is 2.5 x 1019 / m3, μn = 0.38 m2/ Vs and μp = 0.18 m2/ Vs 3 marks

4. (a) Explain Hall-effect. Derive an expression for the charge carrier density in terms of hall-coefficient. 3 marks

(b) Obtain the relationship between Einstein’s coefficients in relation to LASERS. 4 marks

. (c ) A three level laser emits laser light at a wave length of 550 nm. (i) What will be the ratio of the population of the upper level of energy E2 to that of lower level of energy E1 at T=300K. (ii) At what temperature the ratio of population will be half? 3 marks 5. (a) Solve Schrödinger’s equation for a particle in an infinitely deep potential

well. 4 marks (b) Obtain an expression for numerical aperture in terms of refractive index of

core and cladding of an optical fiber. 2marks

(c) A tungsten target (z = 74) is bombarded by electrons in an X-ray tube. (i) What is the minimum value of the accelerating potential that will permit the production of Kβ lines of tungsten? (ii) For this same accelerating potential what is the value of λmin? (iii) Calculate λKβ and λKα (wavelengths of Kβ and Kα lines). The K, L and M atomic X-ray levels of tungsten are 69.5, 11.3 and 2.3 keV respectively. 4 marks

6. (a) Obtain an expression for electrical conductivity of a conductor. How it gets modified in the case of (i) an intrinsic semiconductor, (b) a p-type semiconductor and (c) an n-type semiconductor. 4 marks

(b) Explain the variation of conductivity in an intrinsic semiconductor. 2 marks

(c ) (c ) Calculate the permitted energy levels of an electron trapped in a box of width 10.0 Aº. What is the probability of finding the electron within an interval of 1 Aº at the centre of the box at minimum energy state? 4 marks ….Page 2 of 2

Reg. No.

MANIPAL INSTITUTE OF TECHNOLOGY (A constituent Institute of Manipal University, Manipal-576104)

SECOND SEMESTER B.E. END-SEMESTER EXAMINATION – MAY 2009.

SUBJECT: ENGINEERING PHYSICS (PHY101/102)

Time: 3 Hrs. Max. Marks: 50

Note:

Answer any FIVE FULL questions. Each question carries 10 marks

Answer all the sub questions of a main question in a continuous sequence.

Write specific and precise answers.

Draw neat sketches wherever necessary.

Physical Constants:

Speed of light in vacuum = 3.00 10 8 m/s Electron charge = 1.60 10

19 C

Mass of proton / neutron = 1.67 1027

kg Electron mass = 9.11 1031

kg

Boltzmann constant = 1.38 1023

J/ K Planck’s constant = 6.63 1034

J.s

Permittivity of vacuum = 8.85 1012

F/m Rydberg constant = 1.10 10 7/m

Permeability of vacuum = 4 107 H/m Avogadro constant = 6.02 10

23 /mol

Any missing data may suitably be assumed.

1. (a) Light from an extended source falls obliquely on a thin film of an optical

medium. Find an expression for the effective path difference between the part of

the ray reflected externally at the first surface and the part which suffers one

reflection at the other face. Why does the film appear black in reflected light

when it is excessively thin? 4 marks

(b) Light of wavelengths λ1 and λ2 fall normally on the upper surface of a plano-

convex lens which rests with its curved surface on a plane sheet of glass. It is

found that the fifth bright due to wavelength λ1 coincides with sixth dark ring due

to λ2. Find (i) the wave length λ2 (ii) the diameters of the tenth bright ring due to

λ1 and 20 th

dark ring due to λ2. Given : λ1 = 400 nm, Radius of curved surface of

the lens = 120 cm. 3 marks

(c) Suppose a beam of 5eV electrons strikes a potential energy barrier of height

6.0eV and thickness 0.70nm, at a rate equivalent to a current of 1000A. (a) How

long would you have to wait – on an average – for one electron to be transmitted?

3 marks. 2. (a) Obtain an expression for the Intensity distribution due to Fraunhofer

diffraction at a double slit. 4 marks.

(b) Obtain an expression for the energy density of states at the bottom of the

conduction band of a semiconductor. 4 marks.

(c ) What is the probability of finding an electron in the second quarter of a one-

dimensional potential well of infinite depth, in the ground state? 2 marks.

…Page 1 of 2

3. (a) Obtain an equation for the Polarization ellipse. Discuss various polarization

states. 4 marks

(b) The numerical aperture of an optical fibre is 0.2 when surrounded by air.

Determine the refractive index of its core. The refractive index of the cladding is

1.59. Also find the acceptance cone half-angle when the fibre is in water.

Refractive index of water is 1.33. 3 marks

(c ) A three level laser emits laser light at a wave length of 550 nm. (i) What will

be the ratio of the population of the upper level of energy E2 to that of lower level

of energy E1 at T = 300K. (ii) At what temperature the ratio of population will be

half? 3marks.

4. (a) Explain the effect of temperature on electrical conductivity of (i) an intrinsic

and (ii) an extrinsic semiconductor. 4 marks

(b) Give the theory of LASERS as explained by Einstein using his A and B

coefficients. 4 marks

(c ) A rectangular plate of a semiconductor has dimensions 2.0 cm along y

direction, 1.0 mm along z-direction. Hall probes are attached on its two surfaces

parallel to x z plane and a magnetic field of 1.0 T is applied along z-direction. A

current of 3.0 mA is set up along the x direction. Calculate the hall voltage

measured by the probes, if the hall coefficient of the material is 3.66 10–4

m3/C.

Also, calculate the charge carrier concentration. 2 marks

5. (a) Derive Bragg’s relation in the case of X-ray diffraction. Explain how it can

be verified using Bragg’s spectrometer. 4 marks

(b) The conductivity of intrinsic silicon is 4.17 x 10–5

/Ω m and 4.00 x 10–4

/ Ω

m, at 0 C and 27 C respectively. Determine the band gap energy of silicon.

4 marks

(c ) Find the angular radius of the tenth fringe in a Michelson’s Interferometer

when the central path difference (2d) is 1.50mm. Assume orange light of Krypton

arc is ( λ = 605.780nm) used and that the interferometer is adjusted in each case

so that the first bright fringe forms a maximum at the center of the pattern.

2 marks

6. (a) Solve Schrödinger’s equation for a particle in an infinitely deep one

dimensional potential well. 4 marks

(b) The resistivities of the p-region and the n-region of a germanium p-n junction

are 0.060 m and 0.040 m, respectively. Calculate the contact potential and

the potential energy barrier. The intrinsic carrier density in germanium is 2.5 x

1019

/ m3. The mobility of electrons = 0.38 m

2/V.s, The mobility of holes = 0.18

m2/V.s. kT/e = 0.026 V at 300 K. 3 marks

(c ) A point source of wavelength 500nm is placed 5.0 m away from the zone

plate whose central zone has the diameter 2.3 mm. Find the position of the

primary image. 3 marks

…Page 2 of 2