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I D-GT-M-QIB I

PHYSICS
Paper II
I Time Allowed: Three. Hours I I Maximum Marks: 200 I
INSTRUCTIONS
Candidates should attempt questions 1 and 5 which are compulsory and any THREE of the remaining questions, selecting at least ONE question from each Section. All questions carry equal marks. Marks apportioned to each part of a question are indicated against each. Answers must be, written in .ENGLISH only. Assume suitable data, if considered necessary, and indicate the same clearly. Neat sketches may be drawn, wherever required. Symbols have their usual meaning attached to them, unless otherwise indicated. Important Note All parts/sub-parts of a question must be attempted contiguously. That is, candidates must finish attempting all the parts/sub-parts of each question they are answering in the answer-book· before moving on . to the next question. Pages left blank must be clearly struck out. Answers that follow any pages left blank may not be given credit.
Section- A
1. (a)What do you understand by expectation value
Proye that
d I
-· 10
dt 11! X
A lead ball of mass 0·1 g is thrown with a
velocity of 103 em/ sec through a hole I em in ··
radius. Calculate the uncertainty in the angle
of emergence. I 0
Explain 'term symbol' for a particular
atomic state.
Show that the spectrll;l lines of alkali
metals are doublets. 10
Calculate the two longest wavelengths of the
Balmer series 0f triply ionized beryllium
4). 10
2. Starting from Schrodinger equation obtain an
expression for the probability current density.
Hence give an interpretation to the wave
function. 10
Solve the SchrOdinger equation to obtain the
energy levels and eigenfunctions of a particle
in a one dimensional infinitely deep potential
well given by
V ·. 0 for 0 x a
oo for x and for x>a
Show that they form an orthonormal set of
functions. What do .YOU understand by completeness
condition Show that they form a
complete set of functions. 20+ 10
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3. Solve the Schrodinger equation for a gas of
non interacting electrons enclosed in a cube of
volume L3. What do you mean by density of
states Calculate the density of states and
Fermi energy for the above system. 20
Show that the orientation of the spm
angular momentum vector of an electron
with respect to the z-axis is less than one
radian for spin up electron.
When the orbital angular momentum

vector L has the magnitude ../6n, calcu-
• • late the L
2
components. What angles does

the L vector make with the z-axis 20
4. Discuss the pure rotational Raman spectra of
symmetric top molecules. What are R and S
branches 20
Derive the rotational-vibrational energy levels
of a diatomic molecule. Give the analysis of
the spectral lines. 20
Section- B
5. On the basis of binding energy curve explain
why energy is released both in Fission and
Fusion. 10
·Explain how the helicity of neutrino can
·be measured. 6
What are 'strange particles' and what is
'strangeness number' 4
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A type I superconductor with Tc 7 K has
dB
slope -25 mTI K at transition tempera(

6.

dT
lure Tc. Estimate its critical field at 6 K. 10
A power supply using a full-wave rectifier is
to provide 100 rnA at 20 V with no more
ripple. Calculate the minimum value of
smoothing capacitor used. Consider the diode
resistance and the resistance of the secondary
of the transformer as negligible. Also take
ripple frequency as 50 cycles per second. I 0
What is Q value of a nuclear reaction Obtain
an expression for the Q-value in terms of mass
and energy of the particles. 20
Disc.uss the four basic types -of fundamental
interactions in nature and compare· them. 20
7. What is Meissner effect? Determine the
magnetic susceptibility of a superconductor.
Explain whether a superconductor exhibits
perfect ferromagnetism, paramagnetism or
diamagnetism. • 20
For a simple cubic, a face centered cubic and
a body centered cubic crystal, determine' the
· atomic packing factor.
'·· How many atoms per mm 2 surface area are
there in plane for leads which has f.c.c.
structure. The radius of the atoms is 0·174 nm.
20
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What is De Morgan's law?

Simplify the Boolean expression
A +AB+ABC+ABCD 20
3-JV
Vo
Vs
1-SV
R5 =0·5 K
The above circuit exhibits a MOSFET with a
source resistor. It has VT= I Vand,unC0 x(WIL)
2mAIV 2
. Calculate the drain voltage. Also
determine whether the transistor is in saturation
or in the triode region. 20
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