civils mains 2013 PHYSICS (Paper II)

Time Allowed: Three Hours

Maximum Marks: 250

QUESTION PAPER SPECIFIC INSTRUCTIONS

Please read each of the following instructions carefully before attempting questions.
There are EIGHT questions divided into two SECTIONS and printed both in HINDI and in ENGLISH.
Candidate has to attempt FIVE questions in all.
Question No. 1 and 5 are compulsory and out of the remaining, 1HREE are to be attempted choosing at least ONE from each section.
The number of marks carried by a question! part is indicated against it.
Answers must be written in the medium authorized in the Admission certificate which must be stated clearly on the cover of this Question-cum-Answer booklet in the space provided. No marks will be given for answers written in medium other than the authorized one.
Assume suitable data, if considered necessary, and indicate the same clearly.
Unless and otherwise indicated, symbols and notations carry their usual standard meaning. Any page or portion of the page left blank in the answer book must be clearly struck off. Attempts of questions shall be counted in chronological order. Unless struck off, attempt of a question shall be counted even if attempted partly.

Constants which may be needed
Velocity of light in vacuum X 108 ms-I
Mass of electron 9·11 x 10-31 kg
Charge of electron =1·602 x 10-19 C
Specific charge of electron 1·76 X 1011 C kg-I 1 u 1 a.m.u. 1·6605 x 10-27 kg 931·5 MeV
Rest mass energy of electron (IIleC2) 0·5110 MeV
Permittivity in free space 8·8542 x 10-12 C2N-lm-2
Permeability of free space Guo) =410 x 10-7N A-2
Gas constant =8·314 J mol-1K-l
Boltzmann constant 1·381 x 10-23 J K-l
Planck constant 6·626 x 10-34 J s I ·0546 X 10-34 J s
Bohr magneton =9·274 x 10-24 J
Nuclear magneton =5·051 X 10-27 J
Fine structure constant 137·03599
Mass of proton 1·0072766 u 1·6726 x 10-27 kg
Mass of neutron (MJ =1·0086652 u ·6749 X 10-27 kg
Mass of deuteron 2·013553 u
Mass of a-particle =4·001506 u

Mass of12 6C =12·00000o u

Massof16 80= 15·994915u

Mass of 87 38 Sr=86·99999 u

Mass of 4 2He =4·002603 u

SECTION

In a series of experiments on the detennination of the mass of elementary particle, the results showed a variation of ± 20 where electron mass. Estimate the lifetime of the particle.

Using the definition L r x p of the orbital angular momentum operator,evaluate[Lx,Ly].

(c)The normalized wave function for the electron in the ground state of the hydrogen atom is given by <img src='./qimages/195-1c.jpg'> where ao is the radius of the first Bohr orbit. Calculate the probability of finding the electron within a distance roof the proton in the ground state. 10

(d)How are electrons distributed in the various sub-shells for n Give the quantum numbers for the electrons in the second shell. 10

(e)What do you understand by H-one interstellar clouds and their importance to understand the universe. 10

<img src='./qimages/195-2a.jpg'>
Consider a beam of particles incident on a one-dimensional step function potential with energy E>Voas shown in the above figure. Solve the Schrodinger equation and obtain expressions for the reflection and transmission coefficients. 30
What are the limits of the reflection coefficient for E Va and E oo? 10
Discuss the cases 0 E Vo and E O. 10

3. With proper selection rules, construct the energy level diagram and allowed transitions for ESR spectrum of hydrogen atom. 30

Why are Raman active vibrations and infrared vibrations in CO2 molecule complementary to each other? 10

In a Raman spectrum of a linear triatomic molecule, the fIrst three lines are 4·86, 8·14 and 11·36 em-I. Calculate the rotational constant, B and the moment of inertia of the molecule. (Given h 6·626xlO-27J.s, C 3·0xlOlO cm/sec.) 10


4. (a)The term symbol for atomic states are quoted as 3pZ and zDs12. What are the values of Sand 10

(b)Discuss the [me structure of sodium D line. Draw D1 and Dz lines due to the transitions between zp and Zs levels. 25

(c)Show that the velocity of electron in the first orbit of hydrogen atom is C where C is the velocity of light. (Given electronic charge 1·602xlO-19C Planck Constant 6·63xlO-34 I.s, permittivity 8·85xlO-1Z C2lN-1m-Z) 15

SECTION

5. Calculate the Q-value oUhe reaction: <img src='./qimages/195-5a.jpg'>

Write down the nucleonic configuration of, 7Li, 1Ze, 170 and 27Al 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 basis of shell model ?10

State the quantum numbers Iz, Yand S for the u d s quarks and antiquarks. Which combination of these leads to the formation of proton and neutron? 10

<img src='./qimages/195-5d.jpg'> A crystal plane is shown m the above figure. Find its Miller indices and interplanar spacing. 10

(e)Draw and explain the collector characteristics of a bipolar junction transistor in common emitter configuration. Using the plot, explain how the transistor can be used as an ON-OFF switch. 10

6. Explain parity violation in {3-decay. Describe how parity violation was experimentally detected in the decay of 60Co. Mention any other decay process in which the parity violation has been demonstrated. 20

What is the role of neutrino in the weak interaction of radioactive nuclides? Explain the experimental detection of neutrino. 15
In the following reactions indicate with an explanation, whether they proceed by strong, electromagnetic or weak interaction or they are forbidden <img src='./qimages/195-6c.jpg'>

7. (a)Starting with the expression for the density of states for electrons in a band, show that the Fermi energy of an intrinsic semiconductor is at the middle of the band gap. Use these results to estimate the electron density at 300 K (Assuming Eg eV and the rest masses of electron and hole as Ille and 20 .

perfect conductor and a superconductor with Tc 10 K are subjected to the following conditions cooled under applied magnetic field to 4 K cooled to 4 K and then magnetic field is applied with schematic diagrams, explain path of magnetic field lines in all these situations. 15

(c)Show that the London equation <img src='./qimages/195-7c.jpg'> <br><br>leads to the Meissner effect.

<img src='./qimages/195-8a.jpg'> Explain how the circuit shown above can be a source of oscillations. Use this circuit to construct a transistor oscillator and explain its working. What is the frequency of oscillations of this circuit? 25

Construct a digital circuit to add three bits Band C and provide their sum and carry as outputs. Show appropriate Boolean expressions and truth table to justify the outputs. 25