C. S. (MAIN) EXAM, 2009

PHYSICS

Paper II

Time Allowed Three Hours Maximum Marks 300

INSTRUCTIONS

Each question is printed both in Hindi and in English. Answers must be written in the medium, specified in the Admission Certificate issued to you, which must be stated 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 Questions no. 1 and 5 which are compulsory, and any three of the remaining questions selecting at least one question from each Section.
The number of marks carried b y each
question is indicated at the end of the
question.

Symbols I notations carry usual meaning . Assu,ne suitable data if considered necessary and indicate the same clearly. Some constants are given at the end of questions.

SECTION A

1. Using dimensional analysis, explain why the angular momentum of a particle cannot be t2 . 10

Establish that he= 1240 eV. nm 1240 MeV. fm The energy levels of a hydrogen atom are given by En Ryd, where 1 Ryd hcR. Show that R 1·097 x 107 m-1. What exactly is R 10

Identify all the spin-half particles in the following list Antineutron;, Antiproton. Muon, Muon Neutrino, Neutral Ka.on, Neutral Sigrn.a;, Neutral Xi • Neutron, Photon, Positive Pion1 Positron, Proton, u-quark. 10

Find the ground state total orbital and total spin quantum numbers for nitrogen. Find the L and S values of the two "first excited states" of helium atom. 10

Explain fluorescence and phosphorescence 1n electronically excited molecules. 10
22SY2 level in H atom is 1058 MHz above the 22PY2 level. What is this known as Express the above frequency in cm-1. Calculate the energy difference between the above two levels in eV. 10

2. Show that the Pauli Spin Matrices obey the following relations Tr Tr det det The eigenvalues of crz and crx are the same. Write down the y-component of the spin angular momentum matrix corresponding to an antineutrino. 20

The quantulll mechanical probability distribution function of an electron in the ground state of the hydrogen atom is <img src='./qimages/47-2b.jpg'> deduce that N is proportional to b3 . Prove that the value of 40 k8T at T 300 K is nearly 1 e V. Hence determine the Fermi temperature of a metal whose Fermi energy is 9·4 eV. Show that the Fermi velocity is related to the Fermi energy of electrons through the relation <img src='./qimages/47-2b3.jpg'> 20
Show that the time-dependent part of all the solutions of the Schrodinger equation one-dimension has the structure <img src='./qimages/47-2c.jpg'> provided the potential is not an explicit function of time. 20

3. Consider a positron in a box. If the energy released is 60 eV when it jumps from the third excited state to the ground state, show that the width of the potential 1s nearly 0·3 nm. Prove that the most probable distance of an electron from the proton (in the hydrogen atom) is the Bohr radius of the hydrogen atom. Consider only the ground state. 20

Consider a particle in a three-dimensional box. Derive an expression for the density of states. 10

Show that dE /dp where 1s the density of states in the momentum space. Deduce that 1s proportional to p2 for a free non-relativistic particle. 10

What was the aim of Stern Gerlach experiment? Why were si1ver atoms chosen in.stead of electrons in the experiment What was the outcome of the experiment 20

4. DIscuss the vibrational spectra of a diatomic molecule treating it as a harmonic oscillator as well as an anharmonic oscillator and compare them. 20

Explain spin-orbit coupling of an atomic electron. Show that the 2p state in the H atom splits up into two substates due to spin-orbit coupling. Calculate the energy of· separation 1n eV, resulting fromthe spin-orbit coupling when the magnetic field experienced by the electron is 4 T. 20

Explain Born Oppenheimer approximation. Discuss the intensity distribution 1n the vibrational electronic spectra of a diatomic molecule on the basis of Franck Condon principle. 20


SECTION B

5. What are the field quanta of weak and electromagnetic interactions Show that weak interaction is a short range force while electromagnetic interaction is a long range one. 10

Write down the Yukawa potential and derive an expression for the mass of n-meson in terms of range of nuclear force. What part of the Nucleon Nucleon interaction is explained by this potential 10

Show that the reciprocal lattice of a hexagonal lattice is a hexagonal lattice with a rotation of axes. 10

A type-II superconducting material with superconducting transition temperature Tc is placed in a magnetic field. What is the material state (normal or superconducting or mixed) for T H H C2 T H H cl T Hc1 H H c2 T T C H H cl T H C2 where Hc1 and H c2 are the lower and upper critical fields for a type-II superconductor. 2x5=10

Verify that the circuit shown below IS an exclusive OR. <img src='./qimages/47-5e.jpg'> 10

Silicon is the most popular semiconductor material used for the fabrication of electronic devices and integrated circuits. Why Give at least five reasons. 10

6. What is the simplest two-nucleon bound system How does its study help in obtaining information about nuclear forces Indicate clearly how the non-central forces can be explained by the observed magnetic moment of this system. 20

At what energjes, do we anticipate the unification of strong and electroweak interactions What will happen to coupling constants of these interactions in this situation How does unification indicate the decay of proton and existence of leptoquark 20

Compare the methods of electron scattering and neutron scattering experiments to obtain information about nudear size.20


7. Which of the waves out of X-rays, de-Broglie waves due to e1ectrons or neutrons v11ill be suitable for crystal diffraction Justify your answer in term s of energies of these waves for 0· 1 nm. 15

Derive an expression for the specific heat of a solid on the basis of Debye's model. Show that it converges to Dulong and Petit's law at high temperatures. 25

What is Meissner effect Explain the conclusions drawn from the Meissner effect. 20

8. List the characteristics of an ideal OP-AMP Write the expression for the output voltage in terms of input voltages and resistance values. <img src='./qimages/47-8a.jpg'> 20

The resistance of silicon and germanium vanes with temperature. But these are not used normally as thermistors. Why Name at least two widely used m.aterials for making thermistors and give any five applications of thermistor.20

What do you understand by earl y effect in bipolar junction transistors What are its consequences Discuss briefly the adva ntage of using the BJT in the common collector configuration. 20

Constants which May be needed

Velocity of light in vacuum 3 x 108 ms- 1
Mass of electron (ni 9·11 x 10 -31 kg
Charge of electron 1·602 x 10??19 C
Specific charge of electron J 1·76 x 1011 C kg- 1
1 u 1 a.ni.u. 1·6605 x 10- 27 kg 931·5 MeV
Rest mass energy of electron (tnec2) 0·5110 MeV
Permittivity in free space
8·8542 x 10-12 c2 N-1 m-2
Permeability of fr ee space 4,r x 10-7 N A-2
Gas constant 8·314 J mol-1 K-1
Boltzmann constant 1·381 x 10- 23 J K-1
Planck constant 6·626 x 10-34 J s
1 ·0546 X 10-34 J S
Bohr magneton (µB 9·274 x 10-24 J y-1
Nuclear magneton (µN 5·051 x 10-27 J y-1
Fine structure constant l/137·03599
Mass of proton 1·0072766 u l ·6726 x 10- 27 kg
Mass of neutron l ·0086652 u
1· 6749 X 10- 27 kg
Mass of deuteron 2·013553 u
Mass of a-particle 4·001506 u
Mass of 12 C 12·000000 u 6
u
q;r s;.oll111-1 12-000000 u

Note English version of the Instructions is printed on the front cover of this question paper.