CS (Main) 2015 PH Y S IC S Paper—II

Constants which may be needed
Velocity of light in vacuum 3 x 108(Ten Power Eight) 1
Mass of electron 9-11 x 10-31 kg
Charge of electron 1.602 x 10“19C
Specific charge of electron 1-76 x 1011 C kg"1
1 u s 1 a.m.u. 1*6605 x 10“27kg 931-5 MeV
Rest mass energy of electron (roec2)
0-5110 MeV
Permittivity in free space
8-8542 x lO C
Permeability of free space 47rx N
Gas constant 8-314 J mol-1 K"1
Boltzmann constant 1 *381 x 10-23 J 1
Planck constant 6-626 x 10"34 J s
1 -0546 x J s
Bohr magneton 9-274 X J T*1
Nuclear magneton 5 051 x J 1
fine structure constant 1/137-03599
Mass of proton 1-0072766 u 1-6726 xlO"27 kg
Mass of neutron 1 -0086652 u l-6749x
Mass of deuteron 2-013553 u
Mass of 4-001506 u
Mass of ‘£ c 12-000000 u
Mass of 1oV) 15-994915 u 91
Mass of Sr= 86 99999 u
Mass of He 4*002603 u

SECTION—A
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Q. Obtain an expression for the probability current for the plane wave <img src='./qimages/136-1a.jpg'> Interpret your result. 10

Q. Using dimensional analysis, explain why the angular momentum of a particle cannot be Y2(Lamda square)10

Q. Two successive lines in the rotational emission spectrum of HCI molecule appear at wave numbers 83.5 cm-1 and 104.1 c n r1. Calculate the position of the next line appearing at the higher wave number. 10

Q. Establish that
he 1240 eV.nm
1240 MeV. fm

The energy levels of a hydrogen atom are given by <img src='./qimages/136-1d-1.jpg'> where

<img src='./qimages/136-1d-ii.jpg'>
Show that R 1.097x107 m


Q. If L and M energy levels of platinum are approximately 78,12 and 3 keV, respectively, below the vacuum level, calculate the wavelengths of Ka and Kb lines. (a-alpha, b-beta) 10

Q. Solve the Schrfldinger equation for a particle in a three dimensional rectangular potential barrier. Explain the terms degenerate and non-degenerate states in this context. 30

Q. Write the time independent Schrodinger equation for a bouncing ball. 10

Q. Normalized wave function of a particle is given below

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Find the expectation value of position. 10

Q. What is Zeeman effect How can it be understood on the basis of quantum mechanics 25

Q. Obtain Zeeman splitting for sodium D-lines. 15

Q. Find the magnetic moment of an atom in 3P2 state, assuming that LS coupling holds for this case. 10

Q. Hydrogen molecule is diatomic. Obtain the rotational energy levels of this molecule. Write down the selection rules. Obtain the smallest energy required to excite the lowest rotational mode. 30

Q. The observed vibrational frequency of CO molecule is 6.42x1013 Hz. What is the effective force constant of the molecule 10

Q. A particle trapped in an infinitely deep square well of width a has a wave function <img src='./qimages/136-2c.jpg'> The walls are suddenly separated by infinite distance. Find the probability of the particle having momentum between p and p+dp. 10

SECTION—B

Q. Define Q of a reaction. Calculate the Q-value of the reaction

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Q. Show that any arbitrary rotation axis is not permitted in a crystal lattice. 10

Q. State the quantum numbers I2, Y and S for uds quarks and antiquarks Which combination of these leads to the formation of a proton and neutron 10


Q. Simplify the logical expression [AB BD) A B]C. 10

Q. Differentiate between and transistors. Give their device structure and biasing circuits when used as an amplifier. 10

Q. Describe grand unification theories (GUT). 20

Q. How many types of neutrinos exist How do they differ in their masses 15

Q. Write down the following decays in terms of quarks

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Q.7(a) Design a transistor based Colpitt oscillator which can oscillate at 9 MHz. Explain how the oscillations are created and sustained. 15

Q. Describe an operational amplifier based integrator. Using operational amplifier integrators, design a circuit to solve the following differential equation

src='./qimages/136-7b.jpg'>

Q. Draw the device structure of a p-n junction solar cell and explain how light energy is converted into electrical energy. Draw and explain its I-V characteristics. 15

Q. Find an expression for lattice specific heat of a solid, and its low and high temperature limits. What is Debye temperature 20

Q. Describe the motion of an electron in one dimensional periodic potential and show that it leads to formation of bands of allowed and forbidden states in the electron energy spectrum. How are the conductors, semiconductors and insulators discriminated on the
basis of band structure 20

Q. Distinguish between a superconductor and perfect conductor. Explain what is a Cooper pair. 10
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