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


SECTION A PAPER-11
Answer any three of the following
State and explain HeiSenberg's uncertainty principle
Experimental data reveal that no electron is an atom has energy greater than 4 MeV Assuming that the radius of a nucleus iS 10-14 show using Hetsenberg's uncertainty pnnclple that an electron cannot exlSt mSlde the nucleus
Calculate the de Broglie wavelength of thermal neutrons at300

Define angular momentum, Express it is operator form and show that lintol=ihl
Explain the phYSical Significance of this relation
Let Ym be an eigenstate of L'2and Lz with eigenvalues l(l l)h2 and mh, respectively Show that
¢=(Lx+iLy)Yhm iS likewise an eigenstate of L2 and Lz and determine the eigenvalues

State and explain Franck-Condon principle
In three separate parts of electronic states (one ground and another upper state) of diatoMic molecules, the average lnter nuclear distances are
1.equal;
2 slightly greater;
3 appreaably greater
In accordance with Franck-Condon pnnciple, obtain most favorable transitions from the
ground state Vibrational levels in each of the above Situations illustrate the transitions by drawing suitable energy-l evel diagrams

What is Lamb shift? Has it been observed m any atom other than hydrogen?
How does the 21 cm hydrogen line originate? Comment on itS astronomiilcal applications

Solve the Schrodinger equation for a linear harmonic oscillator Obtain the eigen values and the corresponding eigen functions
A one-dimensional potential bamer is represented by the function
forx<O
=Vo forx>O

Where Vo iS positive Find the transmission coeffcient for particles of mass incident from the left on the barrier.
(20)is
Determine the discrete energy levels and the corresponding eigen functions for a particle is an finitely deep potential well inside a cub e 0 f dimensiOn 1. e., assume forO 0 0 L=infinty elsewhere


In the free electron theory of metals, a conductor is regarded as conSiSting of free electrons in a three-dimensi onal box. U smg the results 0 f obtam an expresS! on for the denS! ty 0f states,

Describe Stern-Gerlach experiment Explain how it demonstrates the discrete nature of the magnetic moment of an atom
Write an expression for the energy 0 f a diatomic molecule executing both rotation and vibration is a given electronic state Explain the observed spectra giving a schematic diagram What are R and S branches?
Why does a spinnng nucleus process ln a magnetic field? Explain the underlying principle of nuclear magnetic resonance spectroscopy. Calculate the radio frequency at which NMR occurs in water kept in a uniform magnetic field of 2.4 the magnetic moment of proton being
2.793 mewN

SEctionB
Answer any three of the followinng
Calculate the Q-valve 0f the
reaction
94Be(24He,n) 612C
Given
Mass (9Be)=9.012183 u
Mass (He)=4002603 u
Mass(12C)=12000u
Write down the nucleonic configuration of
7Li, 12c, 170 and 27AI
in the ground state of the nuclear shell model and hence calculate the corresponding ground state angular momenta and parities. How do the observed ground state angular momenta and parities agree with those predicted on the baslS ofthe shell model
Show that alattice cannot have a five-fold rotational symmetry However, sonic solids appear to exhibit this rotational symmetry. Explain briefly how this can be done
State the quantum numbers iz Y and S for the uds quarks and antiquarks Which combmation of these leads to the formation 0f proton and neutron
Simplify the equation
ABC]
uSing Boolean algebra Give the Slmplification logiC Circuit for the equation before and after the
Explain the difference between and tranSIstors Give the if device structure and biasing clrcuits. Draw a arcuit for a single-state common-emitter amplifier
Discuss briefly the concept of effective mass in semiconductors and explain the Significance of negative effective mass A star converts all itS hydrogen to helium, achievmg 100% helium composition It then converts the helium to carbon Via the reaction
iHe+ 7.27MeV The mass 0f the star 1s 5 x 1032 kg and it generates energy at the rate 0f 5 x 10 30 W How long will it take to convert all hellUm to carbon at this rate?
6. Write down the Bethe-Weizsacker semi-empirical mass formula for a nucleus Explain the Significance of each term occumng is it Discuss the stability ofa nucleus against beta decay What iS the effect of pairing term on stability? (b)What are mirror nuclei? How does the charge independence of nuclear force emerge from this concept? 7.(a)Give some charactenstic properties of strange particles which distinguish them from non-strange
ones
Write the Gell-Mann-NishiJima relation. How iS it used for the classification of elementrY particles?
(b)WhatiS Josephson effect? Discuss briefly DC and AC effects Give some practical applications of Josephson Junctions
8.(a)Explain the working of a phase-shift oscillator. Draw the Circuit diagram of a phase-shift oscillator using either a tranSiStor or an op-amp What are the conditions which must be satisfied to achieve stable oscillations?
Calculate the frequency of oscillations for 1omega and C 0.01mewF
Give the Boolean expressi0n and the truth table for an XOR gate. Why are NAND gates called universal gates? Realise OR and XOR gates employing only NAND gates

Draw the device structure of ap-n Junction solar cell and explain how the light energy is converted is to electrical energy
Define the 'short-circuit current', open-circuit voltage' and 'efficiency' 0f a solar cell