cs {MAIN) EXAM. 2010
81. No.
173 IC-DTN-K-QZB I
PHYSICS
Paper II
17i;l1e Allowed Three Hours' IMaxinli.im Marks 3001
INSTRUCTIONS
Each question is printed both in Hindi and ill
English.
Answers lnust be lvrittell the InediulIl" specified in the Certificate issued to you. which ,nust be stated clearly Oil the cover of the ann-ver-book in the space provided for the purpose. No marks will be given for the anSlvers written in a InediunJ other than that specified in the Adnlissioll Certificate.
Candidates should attelnpt Question Nos. 1 and 5 which are co111pulsory. and 'allY three of the rel11aining questions selecting at least one question front each Section. "
The nunlber of l1zarks carried by each question is indicated at the end of tlte
question.
Syn1bols/notations carry usual nleoning. .A.ssu1ne suitable data ifconsidered necessary and indicate the saIne clearly. SOlne constants. are given at the end ofquestions.

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Section
Derive Bohr's angular momentum quantization condition in atomic model from the concept of de Broglie waves. 10
(b)Obtain an expression for the probability current for the. plane wave lnterpret your result., 10
Show that the Plane spin matrices satisfy the following: 10
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(d)Calculate, giving necessary steps, the radio frequency at which nuclear magnetic resonance occurs in water kept in a uniform magnetic field of 2·4 T. The magnetic moment of proton is 2·793 JAN. 10
State and explain Franck-Condon principle. Discuss its applications in molecular spectroscopy. 10
(f)The normalized wave function for the electron· in hydrogen atom for the ground state is
•<img src='./qimages/1041-1f-b.jpg'>
where a o is the radius of the first Bohr orbit. Show that the most probable position of the .electron is . 10
A system IS described by the Hamiltonian operator.
H=-d2/dx2+x2
show that the function Ax exp an eigen function of H.: Determine the eigen values of H., 30
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A stream of particles of mass M and energy E is directed from left to a one dimensional potential barrier as shown in the above figure. Set up the time-independent"Schrodinger equation and obtain an expressi9n for transmission probability from region I to II. How this phenomenon helps in the understanding of a-decay of nuclei? 30
What is Zeeman effect? How it can be understood on quantum mechanical basis? Obtain an expression for Zeeman splitting
What is spin-orbit interaction?
Calculate the energy· shift due to spin-orbit interaction term in H-like system.. Discuss the significance of this shift in relation to the fine structure of hydrogen spectral lines. 30
DiScuss occurrence of rotational energy -levels of a diatomic molecule and show that the pure rotation spectrum of a molecule consists of a series of equally spaced Iines separated by a constant wave number difference 2 B .. Write down the selection rules: 15
Is it possible to· obtain pure rotational
spectra of H HFt 02 and NO molecules? 5
In CO molecule J 0 J 1 line occurs at a frequency 1·153 10It Hz.. Calculate the moment of inertia of CO molecule. 10
What is Raman effect? How does it differ from Rayleigh scattering? Explain Raman effect on the basis of quantum mechanical theory.
How is Raman effect experimentally studied? What are the advantages of using laser sources in the study of Raman effect? 30
Section B
5. Calculate the packing fraction and the binding energy per nucleon for and nuclei. -10
Explain the reduced zone scheme of plouing the energy bands in solids. On the basis E vs k cl.:lrve distinguish between conductors" semiconductors and insulators. 10
State the quantum numbers Iz Yand S for the uds quarks and antiquarks. Which combination of these leads to the formation of proton and. neutron? 10
What is Josephson tunneling? Distinguish between a.c. and d.c. Josephson effects_. I 10 A star converts all its hydrogen to helium. achieving helium. It then converts the helium to carbon via the reaction He He 7·27MeV. The of the star is 5·0 x 1032 kg and it generates energy at the tate of 5 x1030 W. How long will it take to convert all Helium to carbon at this rate? 10
Identify the above op-amp circuit. Estimate the
net output voltage Vo. . 10
What are magic numbers? Discuss shell structure of a nucleus. Ho"w is this model able to explain various properties ofnuclei Discuss -the limitations-of this model. 25
Predict from the" single particle shell model the shell configuration, ground state spin and parity for the following nuclei 13 N . 7 J708 10
ExplaiJ1 parity violation in {3-decay. Describe how parity violation· wa"s experimentally detected in the of 60Co. 25
7. What is nearly free electron approximation? On the basis of this approximation explain the formation of energy bapds jp solids. 20
Distinguish between Einstein and Debye models of specific heats of solids. Obtain an expression for the specific heat of a solid on the basis of Debve model. Discuss the results for . ]OV and high temperature ranges. 20
Distinguish betwveen classical and quantum theory of paramagnetism. Explain ·the. para­ magnetism of free on the basis of F. D. distribution. ·20
8. Draw a two stage RC coupled transistor amplifier. Plot the frequency response and indicate the lower and .upper cut off frequencies and bandwidth. 30
Give the structure ofan-channel depletion type MOSFET. the drain current-drain voltage characteristics both in depletion as well as in enhancement modes. 15 .
Why NAND· and NOR gates are called universal gates? Give the logic diagram, Boolean equation and the truth table of a NAND. gate. Design an OR gate using only NAND gates. 15
C-DTN-K-QZB 12 (Contd.)