PHYSIYS paper 2


Time Allowed: 3 Hours M=imumMarks: 300
Candidates should attempt Questton 1 and 5 which are compulsory, and any three of the remaining questtons selecttngat least one questtonfrom each &Jctton

Answer any THREE of the followmg
Quantum theoretical methods have established themselves to explam natural phenomena in contemporary PhyS1cs
Fonnulate the axloms of quantum theol)'
State Bom's condition on a wave function WhatlS its phYS1cal mearung?

Find the "'genstates of the angular momentum vector component a sphencally synunetnc system

Write down any two prop etties of the Pus matrices after defirung through an elllreSSlOn

State and ellllam Franck-Condon pnnclple
In three separate patrs of electronic states (one ground and another upper state) of diatonuc molecules, the average mtemc1ear distances are equal, slightly greater, and appreaably greater In accordance with Franck-Condon pnnaple, obtatn most favourable transitions hom the ground slate vibrational levels to the upper state vibrational levels ln each of the three S1tuatlOns 1l1ustrate the tranS1tions in all the aforesaid situations by drawing suitable energy level diagrams

WhatlS Lamb shift? Explain it by illustrating through a sUltable energy level diagram Has Lamb shift been observed in any atom other than hydrogen?
How does the 21 cm hydrogen line ongmate? Comment on ltS astrononucal applications

2. A particle is m a quantum system with a parabolic potenti al well
Usmg appropnate method find the ground slate energy
Obtam an expresslOn for the ground state

Write down the matrix representation of the energy op erator of a linear 0 sallator
A linear oscillator 1s prepared in the state giVen by

Evaluate the energy 0f the oscillator in this state

3 Give briefly an account on the Important histoncal developments to establish the concept 0 electron spin
Write down the eigenvalue and spin state of an electron for the spin operatorS
Show that the spin states of electron are orthogonal to each other
State the spin angular momentum commutation relations
Give the explicit fonns of all the Pauli spin matrices


On the baSis of vector atom model, discuss bnefly the L-S and J-J coupling schemes
Write down expreSSlOns for spin angular momentum, orbital angular momentum and total angular momentum under L-S coupling scheme
Obtain the energy states for 80Hg atom forn 3 levels is pnnapal quantum number) Draw the energy level diagram Does L-S coupling scheme hold good m 80 Hg atom which like He has 2 optical electrons Comment

4 Discuss qualitatively the occurrence 0f rotati onal energy levels at a diatomic molecule Write down the selection rule
Is it possible to obtam rotational spectra of H" HF, 0" and NO molecules? Can one obtain pure rotational spectra in effilSSlOn? Comment (on both of the above-mentioned querries)
In CO molecule J 0 J 1 line occurs at frequency 1153 x lO" Hz Calculate the moment 0f Inertia 0f CO molecule

What is Raman effect? How does It differ from Rayleigh scallenng? Write down its Important applications
Explain Raman effect with the atd of quantum mecharucal theol)'
Why is Raman effect conSidered complimentary to mfrared ab sorption sp ectra?
A Raman Stokes' line is observed at 552 nm when a sample is excited by Hg green line of wavelength 546 nm. Calculate the wavelength 0f anti-Stokes'line

SECTION B

5 Answer any THREE ofthe following
Use conservation laws to find the nature of reSidual nucleus when 50.0 MeV proIon beam strikes the beryllium Be) target nucleus producmg a beam 0f neutrons
Illustrate with any five examples that producti on 0 f strange p arti des conserves strangeness, party and iSolop'C spm while their decay VIolates all these quantities
Obtain reclproca11altice to nonnal Bee lattice
Describe Josephson Junction and the effect. How is it exploited m the fonnati on 0f a SQUID? Write down the applications of a SQUID
DistinguiSh between intrinSlc and extrinSic extrinsic conductors. Explain the concept of hole
FETs have Ull1que properties which make BJTs not suitable for some important applications What are these moslimp ortanl FET applications?
Bnefly describe FETs as vanable reSiSlors

6 Discuss briefly the concepts 0f fissiOn barrier, excitation energy and activalion energy on the baSiS of liqUId drop model. Why 235 92U iS fissiOnable by thermal neutrons while 239 92U iS not? 15

ClasSIfy the Indian power reactors mto BWR, PHWR and FBR vaneties, explallung the acronyms, type of fuel used and location for each vanety

nuclear reactor operates at a power level of W What wl1l be the flux of neutrons reqUIred to mamtam this power level? Given that a free neutron has an average l1fetime of 10-3 second before its capture m a uranlUm nucleus and energy released per fissiOnS 200 MeV


(d)Describe bnefly the vanous cycles for energy production m stars, relating them to the life of a star. "FusiOn reactors operate m the core of stars but have not become a reality on earth as yet." Comment on the statement

7 Discuss the Slgll1ficance of Gellmann-NishiJlma relation ln strange particle production and decay Give examples in support of your answer Obtain quark quantum numbers smg the modified relation for quarks

Describe lmportant expenmental facts that led Pauli to postulate the exiStence 0 f neutrino particle

Give a qualitalive account 0 f BCS theory 0f superconductiVlty
Obtain an expreSSiOn for conductivity of an mtrinSlc semlconductor How does it vary Wlth temp erature?
This reSiStivity of an intrinSlc seml conductors 4.5 ohm-m at 20°C and 2.0 ohm-m at 32°C Calculate the energy band gap

Combinational switching ClrcUlt can perfonn an additi on 0f the numbers held in two registers Write down the math table for the addition of two bits Write down a Boolean expressiOn for the necessaty arcuit functions Arrive at the ExcluSlve-OR function Draw the 1OglC diagram for the arcuit whi ch perfonns the addition


What are sequential switching arcuits
Describe a Simple sequential ClrcUlt
Describe a clocked RS Flip-F1op,
Bnefly describe ROMs


Explain a solar cell employing its characterstics on output quantity Venus quantities like load current, radiance and temperature.