Indian Fewest Service ExaminafioL ·2013

A-JGPT-M-QIZ-B.
PHYSICS
PAPER-II
CONVENTIONAL}

ITime Allowed Three Hours I Maximum Marks 200 I
QUESTION PAPER SPECIFIC INSTRUCTIONS
Please read each of the following instructions carefully before attempting questions
There are EIGHT questions in all out of which FNE are to be attempted.
Question Nos. 1 and 5 are compulsory. Out of the remaining SIX questions, THREE are to
be attempted selecting at least ONE question from each of the two Sections A and B.
Attempts of questions shall be counted in chronological order. Unless struck off, attempt
of a question shall be counted even if attempted partly. Any page or portion of the page
left blank in the Question-cum-Answer Booklet must be clearly struck off.
All questions carry equal marks. The number of marks carried by a question/part is
indicated against it.
Answers must be written in ENGLISH only.
Unless otherwise mentioned, symbols and notations have their usual standard meanings.
Assume suitable data, if necessary and indicate the same clearly.
Neat sketches may be drawn, wherever required.

List of Useful Constants
Mass of proton "" 1· 673 x 10-27 kg
Mass of neutron 1· 675 x 10-27 kg
Mass of electron 9· 11 x 10-31 kg
Planck constant 6·626 X 10-34 Js

Boltzmann constant 1· 380 X 10-23 JK-1
2

Bohr magneton "" 9.273 X 10-24 Am
Nuclear magneton l/J.N) 5.051x 10-27 JT-1(Am2)
Electronic charge "" 1· 602x 10-19 C
Atomic mass unit "" 1· 660x 10-27 kg

"" 931 MeV
gf 5· 5855 J.lN 1· 00727 u
mIn) 1· 00866 u 4·002603 u

12·00000u 86·908893u

1 P.T.O.
j.




SECTION-A
1.(a)The particle in a box has a ground state wave function given as
<img src='./qimages/1273-1a.jpg'>
The box width is 21 and the particle is confined within l). Calculate the expectation value of x2. 8
particle is bound in a potential well given by
<img src='./qimages/1273-1b.jpg'>
Estimate the ground state energy of the system from uncertainty principle. 8
(c)(i)Enumerate the possible values of quantum numbers j and mj for state in which l=2 and s 1/2.
(ii)Draw the corresponding vector model diagram. 8
(d)Explain the concept of shared pair of electrons with anti parallel spins forming a covalent bond
in H2 -like molecule with reference to total energy. 8
substance shows a Raman line at 4567 A when exciting line 4358 A is used. Estimate the positions of Stokes
and anti-Stokes lines for the same substance when exciting line 4047 A is used. 8


2.(a)Write down SchrOdinger equations for a particle of energy incident on a step potential height V0.
Solve them to find out the transmission and reflection coefficients in terms of
k and where k root 2mE/n2 and root 2m(V0-E)/n2. Show that in this case, there
is a finite probability of finding the particle in a classically forbidden region. 35
(b)Can you comment from the above question whether you can use it to scan surface by microscopy? 5

3.(a)Develop and write down the expressions of L2, Lz and Lz2 in angular momentum operator algebra. 10
(b)Show that the spherical harmonics ylm (theta, pie) are simultaneous eigenfunctions of L2, Lz and Lz2.
What are their corresponding eigenvalues? 30
4.(a)Discuss the vibrational spectra of a diatomic molecule treating potential energy function as a representation
of Hooke's law type of interaction. 20
(b)Explain why the separation between vibrational levels is smaller in an excited electronic state than in the
ground electronic state. 20

2
SECTION-B
5.(a)The masses of hydrogen atom and neutron are 1·007825 u and 1·008665 u respectively. Calculate the binding energy
per nucleon of l2 6 C nucleus. 8
(b)How many fissions take place per second in a 300 MW reactor? Assume that 200MeV is the energy released per fission. 8
(c)Write down the quark structure of pie0, K0 and mesons. 8
(d)Write down London second equation for superconductors. Explain how it accounts for the Meissner effect. 8
(e)Prove the following Boolean identity and draw its gates equivalent: 8
<img src='./qimages/1273-5e.jpg'>

6.(a)What is the importance of the study of deuteron? Discuss the problem of ground state of
deuteron and elicit information about nuclear forces from this study. 20
(b)How magnetic moment and electric quadrupole moment of deuteron indicate the presence of non-central
forces in deuteron? 20
7.(a)Why was neutrino invoked upon by Fermi and how was it placed into experimental evidence? 20
(b)What is solar neutrino problem and how the phenomenon of neutrino oscillations provides a solution for the problem? 20
8.(a)What is a thermistor? Discuss static characteristics of a thermistor. What is its time constant? 20
an operational amplifier, the amplifier gain is 10000. The input series resistance is 100k ohm and the
feedback resistance is 500k ohm. If the input voltage is 1 volt, find the exact output voltage and
percentage error considering an infinite gain for the amplifier. 20