Download B E , 2012

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Ex/PH/2B/T/67/2012
B ACHELOR OF ENGINEERING EXAMINATION, 2012
a beam of electrons by a single slit.
( 1st Year, 2nd Semester )
c) A typical atomic nuclear is about 5·0×10–15 m in radius. Use
P HYSICS - II B
the Heissenberg uncertainty principle to show that the
electrons can not exist in the nucleus of an atom.
Time : Three hours
Answer any five questions.
(Given, h = 6·625 × 10–34 J.S, C = 3 × 108 m/s). 6+4+10
8.
a) What is the significance of wave function in quantum
Full Marks : 100
1.
a) State
and
explain
Faraday’s
and
Lenz’s
law
of
electromagnetic induction.
mechanics?
b) Deduce the differential form of the Faraday’s law of
b) Obtain an expression for the time-independent Schrodinger
electromagnetic induction. What is the difference between
equation in one-dimension.
Ampere’s circuital theorem and Faraday’s law.
c) Write the Schrodinger equation for a particle in a box and
c) Calculate the magnetic flux density at the centre of a coil if
solve it to obtain the Eigen values and Eigen functions.
there are 100 turns wound on a solenoid of 25 cm long and
d) Draw the probability density functions for states n =1, 2
and 3.
carrying a current of 3 amperes.
2+5+10+3
d) A α particle travels in a circular path of radius 0.5 meter in a
magnetic field with B = 1.2 web/m2. Caculate (i) its speed
(ii) time period of revolution, (iii) its kinetic energy.
Take mass of α particle is 6·68 × 10–27 kg.
2.
4+5+5+6
a) Discuss the phenomenon of interference of light due to thin
film and find the condition of maxima and minima.
b) Describe and explain the formation of Newton’s rings in
reflected monochromatic light. Prove that in reflected light,
diameters of bright rings are proportional to the square-roots
of odd numbers.
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c) The diameter of the 5th dark ring is 9 mm in Newton’s ring
experiment when sodium light
( λ = 5890Å )
b) Describe the Davisson-Germer experiment and explain how
h
the results obtained confirm the de Broglie relation λ = p
is used. The
light passes through the air-film at an angle of 30o to the
normal. Find the radius of curvature of the lens.
for electrons moving with momentum p (λ = de Broglie wave
6+9+5
length, h = Planck constant).
3.
a) Explain the phenomenon of diffraction of light. Explain the
c) Determine the de Broglie wavelength of an electron having
difference between interference and diffraction of light.
kinetic energy of 1 eV (Given, rest mass of electron
b) Describe Fraunhifer diffraction due to a single slit and
–31
9·11× 10
kg, h = 6·625 × 10
–34
J.S. 1 eV = 1.6 ×10
–19
=
J).
deduce the positions of maxima and minima.
5+10+5
c) A parallel beam of light is normally incident on a plane
transmission grating having 4250 lines per cm and a second
4.
6.
a) Describe the nature of X-ray emission spectra with suitable
order spectrual line is observed at an angle of 30o. Calculate
diagram. How can the lowest wavelength limit in the
the wavelength of light.
continuous X-ray spectra be explained?
4+10+6
a) Monochromatic light from a narrow slit falls on two slits
b) Explain how Bragg’s law can be used for the determination
and the interference fringes are obtained on a screen.
of wave length of X-ray as well as the interplanar spacings
Calculate the spacing between two consecutive maxima or
in a crystal.
minima. What is the shape of the fringes?
c) The Bragg angle corresponding to the first order reflection
b) What is Brewslin’s law? Show that when a ray is incident at
from (1, 1, 1) planes in a crystal is 30o when X-rays of
the Brewslin’s angle, the reflected ray is perpendicular to the
wavelength 1.75 Å are used. Calculate the interplanar
refracted ray.
spacing.
c) The refractive index of water is 1.33. Calculate the polorising
angle for water.
5.
8+8+4
a) Explain the de Broglie concept of matter waves. What law
de Broglie to suggest wave character of matter?
7.
8+7+5
a) State Heissenberg uncertainty principle and discuss its
significance. Obtain the time-energy uncertainty relation
from the position - momentum uncertainty relation.
b) Illustrate the uncertainty principle considering diffraction of
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