SI.No·0


PHYSICS
Paper-II

ITime Allowed: Three Hours I IMaximum Marks 300I
.
INSTRUCTIONS question is printed both in Hindi and zn English.
·Answers must be written in the medium specifier;lin the Certificate issued to you, which must be clearly on the cover of the answer-book in the space provided for the, purpose. No marks will be given for the answers written in a medium other than that specified in ·the Admission Certificate.
Candidates should attempt Question Nos. 1 ;and 5 which are compulsory, and any· three of the remaining questions selecting at least ,one question fro!Jt each Section..
The number marks carried by each question is indicated at the end of the question.
Symbols/Notations carry us:ual meanings.
Assume suitable data, if considered necessary and indicate the same clearly. Some constants are given: at the e,nd "of questions.

Section-A

1.(a)Calculate the wavelength of de Broglie waves associated
with electrons accelerated through a potential difference of 200V. 10 Normalize the wave function
<img src='./qimages/1053-1b.jpg'> 10 Let sigma bar be the vector operator with components
equal to the Pauli spin matrices
sigma x sigma y and sigma z if a and b are
the vectors in 3-dimensional space,
prove the identity
<img src='./qimages/1053-1c.jpg'> 10
Discuss the fine structure of hydrogen atom spectrum.
Draw the compound doublet spectrum arising as a result of
transitions between 2 P and 2 D levels. 10 What do you mean by 'term symbols'? Obtain term symbols
for the following set of values of S and L 10 L 2 L L 1
(f)Estimate the size of the hydrogen atom and the ground-state
energy from the uncertainty principle. 10

2.(a)Solve the Schrodinger equation for a
particle of mass m in an infinite
rectangular well defined by the potential infinity x>L
Obtain the normalized eigenfunctions
and the corresponding eigenvalues. 25
Calculate (deltax)2 ,where deltax 15 The normalized wave function for the
electron in the ground state of the
hydrogen atom is given by
<img src='./qimages/1053-2c.jpg'>

where ao is the radius of the first Bohr
orbit. Calculate and 20
3.(a) Show that 2S 1/2 2P 1/2 and 2P 3/2 levels of
sodium spectrum are split in the ratio
of due to anomalous Zeeman
effect. 30 On the basis of three principal moments
of inertia IA,IB and Ic each about Y
and Z axes respectively,how can you
classify molecules? 30 Treating a diatomic molecule as a
simple harmonic oscillator, obtain
its vibrational energy levels. 20

(ii) The observed vibrational frequency of the CO molecule
is 6·42 X 10 13 Hz. What is the effective
force constant of this molecule?
(Mass of carbon atom =12u and mass of oxygen atom l6u, where
u is atomic mass unit) 10
(b)(i).Discuss pure rotational spectra of
linear molecule. 25 What is Lamb shift? 5

Section-B
5.(a) Show that nucleus is a quantum system. 10 Derive Bragg diffraction condition in vectorial form
using incident and diffracted wave vectors
and reciprocal lattice vector. 10

(c)Find the total kinetic energy of electron and antielectron
neutrino emitted in beta decay of free neutron.


(The neutron-proton mass difference is
1.30MeV and mass of electron is 0.51MeV) 10

(d)An electron beam of 4keV is diffracted through
a Bragg angle of 16° for the first
maxima.If the energy is increased to 16keV,find the
corresponding Bragg angle for diffraction. 10 Explain conservation of baryon number. Comment on
stability of proton. 10 Simplify the logical expression
AB AB bar ABC
using a Karnaugh map. 10
What is the importance of study of deuteron?
Obtain the solution of Schrodinger equation for ground
state of deuteron and show that deuteron is a loosely bound
system. 25
(ii) What do you mean by 'non-central forces'? 5
What are chain reactions? What do you mean by
critical size of the core in which chain reaction takes
place? What is critical mass? 20
(ii)235 U yields two fragments Qf A=95 and A =140. Obtain the
energy distribution of the fission products.
Assume that the two fragments are ejected with equal
and opposite momentum. 10
7.(a) Find an expression for lattice specific heat solids, and
its low and high temperature limits. What is
Debye-temperature? 20 Explain the origin of energy band formation in solids.
Show that in nearly free electron approximation,
the energy band gap is where VG is Fourier transform
of periodic potential seen by the valence electrons. 20

(c)Describe the characteristic properties of a superconductor.
Derive London equation for a superconductor
and hence explain Meissner effect. 20

8.(a)Distinguish between intrinsic and extrinsic semiconductors.
Show that in a semiconductor, the product of concentrations
of the two types of charge carriers is constant
at a given temperature. 30

(b)Simplify the logical expression
<img src='./qimages/1053-8b.jpg'>
and draw the logical circuit to implement it 15
Draw the common-base amplifier circuit, using an
transistor and briefly discuss its working. 15