PHYSICS
Paper II
I Time Allowed: Three Hours I I Maximum Ma;·ks: 200 I·
INSTRUCTIONS
Candidates should attempt questions 1 and 5
which are compulsory, and any THREE of the
remaining questions, selecting at least "fJNE
question from each .Section.
All questions carry equal .marks.
Marks allotted to parts 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.
(Contd.) . .
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. list of Useful Constants
Mass of proton 1·673xl0-27 kg
·Mass of neutron 1·675xl o-27 kg
Mass of electron 9·11 X 1 o-31 kg
Planck constant 6·626xto-34 Js
Boltzmann constant I· 38dxJ0-23 JK-1
Bohr magneton 9·273xJQ-24 A/m2
·Nuclear magneton 5·051xto-27 JT-1(Nm2)
· Electronic charge 1·602xl0-19 C
•
. Atomic mass unit 1·660x w-27 kg
931 MeV
gP
s 5·5855 N·
1·00727
1·00866
• . 4·002603 u
• 12·00000 u

87
38 sr) 86·908893 u
D-VSF-L-CUB 2 (Contd.)
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Section

1. Answer any four of the following

the basis of uncertainty principle calculate
the size of Hydrogen atom. 10
(b)What are Pauli spin matrices
Show that:
<img src='./qimages/1485-1b.jpg'>
where sigma are the Pauli spin matrices· and A
and B are vector operators which commute
with sigma, but do not necessarily commute with
each other. 10
(c)Obtain the term symbols singlet states
and two triplet states for two electron atoms.

(d)The wavelengths (lamda) in the visible spectrum of
H atom can be expressed by the empirical
formula
<img src='./qimages/1485-1d.jpg'>
where n1 is an integer and n1 3,4 etc. and
G is an empirical constant.
Prove from the above, the wave number
<img src='./qimages/1485-1d1.jpg'>
(e)What is the mechanism of emission of light in
fluorescent lamps and in painted signboards
Explain. 10

For a quantum mechanical system prove that
all energy eigen-values En are real and if
En not equal to Ek, then the correspondipg eigen functions
are orthogonal. 10

(b)Solve the Schrodinger equation for a potential
step function given by
0 for x 0
v0 for x 0
and calculate reflection and transmission
coefficients. Show that for E<v0 there is a
finite probability of finding the particle in a
classically forbidden region. 20+10

3.(a)Solve the eigen value equation
L2Y(theta,pie) =lamda h2Y(theta, pie) and obtain the eigen
values and eigen functions of L2. 20

angles do the L(vector) make with
the z-axis when l=2 for an electron
(ii)Determine the values of the total angular
momentum for a 3d electron. 20

4.(a)Discuss the vibrational spectra of a diatomic
molecule treating it as an anharmonic oscillator. 20
(b)Give the elementary theory of NMR. Explain
the two different relaxation processes. 20
Section
5.Answer any four of the following
(a)Find the density of 12 6 C nucleus.(Given, nuclear
radius of carbon= 2·7x10pow-15 10
(b)Explain the source of energy in stars using
proton-proton thermonuclear reaction cycles. 10
(c)What type of interaction takes place in the
following reactions and justify your answer.
src='./qimages/1485-5c1.jpg'>
src='./qimages/1485-5c2.jpg'>
How are the band structures of insulators.
and semiconductors,similar How are they
different? 10
What are intrinsic and extrinsic semiconductors? Explain.
(ii)How are n-type and p-type semiconductors obtained


6.(a)What are magic numbers in an atomic nucleus
and why are they so called How is it
explained using nuclear shell model? 20
What are the reactor materials used in design
and construction of a nuclear reactor and their
important functions? 20

7.(a)What are quarks Give any four properties.
Give quark composition of the following
particles src='./qimages/1485-7a.jpg'>

(b)Using band theory of solids, explain whether
the effective mass of an electron can be
positive, negative as well as infinity. Explain
the significance of negative mass. 20

Using OP-AMPs design an analog circuit to
solve the following differential equation
<img src='./qimages/1485-8a.jpg'>

(b)Explain the basic structure and operation of an
n-channel FET.
How FET acts as an amplifier Explain. 20