Time
Allowed: three Hours Maximum
Marks: 200
Candidates should attempt Questions 1 and 5
which are compulsory, and any THREE of the remaining questions selecting at
least ONE question from each Section.
Assume suitable date if considered
necessary and indicate the same clearly.
SECTION
B
5.
Answer any four of the following:
(a)
On the basis of binding energy curve explain why
fusion is possible only for low mass nuclei whereas the fission takes place
only in heavy nuclei.
(b)
A star converts all its hydrogen to helium,
achieving 100 % helium composition. It then converts the helium to carbon via
the reaction
⁴₂ He + ⁴₂He + ⁴₂He →¹²₆C + 7.27 MeV
The mass of the star is 5.0 x 10³² kg and it generates energy at the rate
of 5 x 10³⁰ W. How will it take to convert all helium to carbon at this rate?
(c)
Indicate the interactions in which the following
conservation laws are obeyed or violated:
(i)
Hypercharge
(ii)
Charge conjugation
(iii)
Isotopic spin
(d)
Calculate the number of nearest neighbors and
the packing fraction for an FCC lattice.
(e)
Explain the operation of the following circuit
as a gate. Draw the truth table and find the operation carried out by this
gate.
6.
(a) What are magic numbers? Discuss the shell
structure of a nucleus. How this model is able to explain various properties of
nuclei? Discuss the limitations of his model.
(b) What is internal conversion? Describe
an experiment to determine internal conversion coefficients.
(c) What is Mossbauer Effect? Describe an
experimental arrangement employed for the study of nuclear resonance
scattering. Mention some applications of this phenomenon.
7.
(a) Discuss various symmetry elements of a
crystal lattice. Explain why five-fold rotation symmetry is not observed.
(b) Consider the motion of
electrons in a periodic potential of a crystal lattice. Show that the energy
spectrum of electrons consists of bands of allowed and forbidden energies. How
are the insulators, semiconductors and conductors discriminated on the basis of
band structure?
(c) Distinguish between a
superconductor and a perfect conductor. Obtain an expression for the frequency
of oscillations.
8.
(a) Explain the working principle of a phase
shift oscillator. Obtain an expression for the frequency of oscillations.
(b) Describe the constructional details of
a MOSFET. Draw the drain current-drain voltage characteristics.
(c)
A common emitter amplifier using n-p-n transistor is shown below:
Calculate the output signal for an input
signal of 1 m V. Explain the functions of (i) 50 µF capacitor across 3 k Ω
resistor in the emitter circuit and (ii) the resistors 930 kΩ and 250 kΩ.
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