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No. 8328 B-JGT-J-QIB
81.
PHYSICS

ITime Allowed Three Hours I IMaximum Marks 200I
INSTRUCTIONS
Candidates should attempt Question Nos. 1 and 5
which are compulsory, and THREE of the
remaining questions, selecting at least
ONE question from each Section.

The number of marks carried by each question is
indicated at the end of the question.

Answers must be written in ENGLISH only.
Assume suitable data, .if considered necessary and indicate the same clearly.
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 J-s
Boltzmann constant 1· 380 x 10-23
Bohr magneton 9 -273 X 10-24 A-m2
Electronic charge 1. 602 x 10-19 C
Atomic mass unit 1· 660 X 10-27 kg
=931 MeV
Velocity of light in vacuum) c =3xl08 m-s­1

/22 p.T.a.


maH)






m(35 Cl)




1· 007825 u =2·014102 u =3·016049 u :;12· 00000 u 19·992439 u =4·002603 u 1-008665 u :;0·000549 u 151·919756 u 151-91749 u 151· 919794 u =35·450 u

Unless otherwise indicated. symbols and notations have usual meanings.
Section-A
1. Answer any four of the following
The wavelength and frequency of a guided wave are related by




Express the wave's group velocity vg in terms of c and its phase velocity lJ p . 10
EhJGT-J-QIB/22 2

What is the mmunum angle that the
angular momentum vector may make
with the z-axis, in the case,of l How
many levels are possible? Show the
angle in a vector diagram. 10
An H 35 CI molecule is found to have a
fundamental vibration at 2885·9 cm-1.
Its internuclear distance changes by
O· 05 nm. What will be the change in
potential energy? 10
Calculate the Zeeman energy splitting of
the 2Pl/2 and 2S1/ 2 states in sodium for
a magnetic field of 2 T. 10
Ifa x ay and az are Pauli spin matrices,
prove the following relationship 10
sin (0-x4» cr xsin
2. The wave function of a quantum particle is Aei 2 1l/2m). Find 10
For the E Uo potential barrier, obtain
expression for the probability that the
particles will be transmitted resonantly.
o x x>L Uo 20
.If an electron is incident on a barrier
potential 0 ·100 eV and width 15 nm in
the problem above, calculate the
transmission probability, if its energy is
0·060 eV. 10

B-JGT-J-QIB/22 3 1. P.T.O.

..
3. fa) Prove that i 2 commutes with all the three components of angular momentum operator i. 20
Discuss briefly the Stern-Gerlach experiment with the help of a diagram. Analyse the outcome of this experiment. 20
4. Discuss the number of fundamental vibrations of water molecule. 15
Frequency separation between adjacent lines In the rotational spectrum of 35 Cl 19F IS measured as 11· 2 GHz. Calculate the interatomic spacing.: 15
The NMR spectrum of CH31 taken in a 60 MHz spectrometer gave a strong signal at 130 Hz and chemical shift 2 ·16 ppm. Obtain the absorption frequency, if the spectrum were to be made in a 90 MHz spectrometer. What would be the chemical shift in the new spectrum? 10
Section-B
5. Answer any four of the following:
ra) What the Q-value of the reaction 152 Eu p)152 Sm 5
What type of weak: interaction can occur for 152Eu? 5
4

Lead shows superconductivity at 7 ·19 K for zero applied magnetic field. When magnetic field of 0·08 T is applied, superconductivity will not take place at any temperature. Calculate the applied magnetic field that will stop superconductivity at 2·0 K. 10
What is internal conversion? Show that the internal conversion coefficient depends upon the atomic number of the nucleus. 10
Indicate with reasons, why each of the following high-energy reactions/ particle decays is either allowed or forbidden 10
11 11 0
1t 0
1t 0 Y+Y
1t +VIi

Write down the the quark composition of 10
Neutron
Proton
Sigma-plus
Kaon-zero
Pion-zero (1t

B-JGT-J-QIB/22 5 p.T.a.
6. fa) Derive an expressIon for the recoil energy loss in the emission of gamma ray. What is natural line width? Explain. 10
What is Mossbauer effect? Define the Mossbauer parameters-isomer shift, splitting and magnetic splitting. 20
te) For atomic transitions, resonance fluorescence and absorption are normal, but in nuclear gamma decay this does not occur. Why? Explain with a typical illustrative example. 10
7. fa) Discuss Grand Unified Theory schemes for Strong, Weak and Electromagnetic interactions. What are experimentally verifiable predictions of such schemes? 20
Explain Kronig-Penney model for the motion of an electron in a periodic one-dimensional square well potential. Show from the energy band diagram that the materials can be classified as conductor, semiconductor and insulator. 20
8. fa) Calculate the resistivity of silicon having
atomic mass 28, and having density of
2·42 X103 kg-m-3 and a valence of 2.
Assume that the Fermi energy for

6
silicon is 2 eV. (Assume electron mean free path to be 100 times the interatomic spacing.) 20
Discuss the construction and operation of Enhancement MOSFET and Depletion MOSFET. Give their characteristics. How do they differ from JFET? 20


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