Time Allowed: 3 Hours M=imumMarks: 300
Candidates should attempt Questton 1 and 5 which are compulsory, and any three of the remaining questtons selecttng at least one questton from each Sectton

Attempt any three of the following
Explain what do you understand by HeiSenberg uncertainty principle USing this principle, determine the energy of the ground slate of a one dimensiOnal Simple harmonic 0scillator
An electron having an energy 2 eV is travelling In the region where Vex) vanes as shown below
<img images/1106-2a2.jpg'>
Calculate the de Broglie wavelength of the electron In regions II and III
Express the CarteSian components of the. angular momentum. L In operate form Show that What,S the Significance of thiS communication relation Show that the PauliMatrces anti -commute
What are the typiCal energies of the radiation reqUired to excite electronic transitions (ii)vibrational tranSitions and (iii)rotational transitions In a molecule?
The rotational spectrum of HI conSiSts of eqUidistantlines with a separation of 12.8 cm­1 Calculate the M.I. and bond length of HI molecule 14)
Show that the radial probability density of the ground state of the hydrogen atom has a maXimum at r=a. The ground state wave function of the hydrogen atom is giVen by
<img images/1106-1d1.jpg'>
where a is the Bohr radius Calculate the Larmor frequency of a spin 1/2 particle in a magnetic field B
2.A particle of mass with energy E such that-Va E is trapped in a potential wall as shown below <img images/1106-2a.jpg'>
Write time independent Schrodinger equation in regions O<x a and x>a
Obtain an expreSSiOn from which the energy eigen values can be determined
Show that for at least one bound state to eXist
a2v0>-h2pie2/8m
15+15+30
Number at non-interacting electrons are confined in a cube of volume L3 Obtain an expreSSion for the Fermi energy
Define the gyromagnetic ratio and obtain importance 0f g factor in spectroscopy? an expressiOn for the Lande g important factor What is the
Discuss the salient features of molecules. Which spectrum contains progressiOns? R and S branches of electronic spectrum of diatomic only branches, both branches and bands, branches and
Show that a sprining nucleus precesses in a magnetic field. Explain the underlying principle of NMR spectroscopy The magnetic moment of a position is 2.793 Calculate the radio frequency at which nuclear magnetic resonance occurs in water kept a magnetic field 0f T


SECTION B

AnsweranyTHREEofthefollowmg
Sketch carefully the binding energy per nucleon curve for stable nuclei Explain its salient features On the basiS of this curve explain why fusiOn is possible only for low mass nuclei, whereas fissiOn takes place in heavy nuclei

State the conservation law which is VIolated in each of the folloWlng processes
pie-+p--.sigma+K­
Draw a bee lattice. Determine its primitive lattice vectors and calculate the packing fraction

Explain the operation of the following CIrcuit is a gale. Draw the truth table and find the operation carried out by this gale neglecting the source impedance
<img images/1106-5c.jpg'>
Junction saturation voltages and diode voltages in forward direction. Find the minimum value of h,.
What are high Tc superconductors? Give two examples Indicating their transition temperatures. Differentiate between the conventional and high sup er conductors Explain the principle of feedback in an amplifier What are the advantages negate feedback?
6.(a)List some 0f the Important properties 0f deuteron and showthalitlSa100sely bound system and has only one bounded state
DistingUish between a nuclear reaction and decay Which conservation laws are obeyed in nuclear reactions? Explain the Significance of Q value Calculate the Q value for the folloWing nuclear reaction
Give two characteristics propetties0fstrange par-tideswhichdistingUishthemfromnon-strange ones. Write the Gellmann-Ni shiJlma relation and show how itlS used for the clasSlfication of elementary particles
What iS a Josephson Junction? Discuss dc and ac Josephson effects and obtain the relation v=2ev/h
where the symbols have their usual meaning
8. Derive the various current components in a p-n tranSiStor when itlS actively biased Using Eb ers­Moll model, show that for the common-emitter configuration where the symbols have the usual meatl1ng
In the following circuit,
Show that the stability factor, lS given by
<img images/1106-8b.jpg'>
Calculate the garn of the fallowing amplifier Circuit
<img images/1106-8c.jpg'>