Exam Details
| Subject | physics | |
| Paper | paper 2 | |
| Exam / Course | indian forest service | |
| Department | ||
| Organization | union public service commission | |
| Position | ||
| Exam Date | 2003 | |
| City, State | central government, |
Question Paper
PHYSICS
PAPER· II
SECTION A
1. Answer any four of the following:
Define angular momentum. Express it in the operator form and show that LxLy LyLx ihL2
A photon and an electron have energy 15 keV each. Which of them will have a longer
wavelength
Write down the Schrodinger equation in three dimensions for a free electron and solve it for electrons confined to a cube of edge L and hence obtain an expression for the density of states.
State Franck-Condon principle and discuss its applications in molecular spectroscopy.(10)
If the magnetic moment of proton is '2.793new N.calculale, giving necessary steps, the radio
frequency at which nuclear magnetic resonance occurs in water kept in a unifom1 magnetic
field of 2.4T.
2 Consider a one-dimensional square well potential,as shown below, which is attractive.<br><br> <img src='./qimages/1412-2a.jpg'> potential is Vo in the region x to x and zero elsewhere A stream of particles of mass M and energy E is directed from the left, Set up time-independent Schrodinger equation and obtain an expression for the transmission ratio from region I to 11.
Write the Schrodinger equation for a free particle confined in a cube of edge L. Determine the energy eigenvalues. Show that for a single value of energy different quantum slates are possible. Explain the term degeneracy
3 Set up the time-independent Schrodinger equation for an electron moving in a Coulomb field, <img src='./qimages/1412-3a.jpg'> ,in polar coordinates. Solve solve radial equation to get the energy eigenvalues
What is Zeeman effect? How it can be understood on a quantum mechanical basis Obtain
an expression for the energy splitting
4. Write the wave function for the ground state of the hydrogen molecule under the molecular orbital approximation. Estimate the energy of the electron In the ground state of H2+moleculeion.(20)
Derive the combined vibration-rotation spectrum of a diatomic molecule. What are P and R branches
SECTION B
5. Answer any four of the following:
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.
A star converts all its hydrogen to helium. achieving 100"/o helium composition. II then converts the helium to carbon via the reaction.<br><br> <img src='./qimages/1412-5b.jpg'> The mass of the star is 5.0 x 1012 kg and it generates energy at the rate of 5 x 10 30 W How long will it take to convert all helium to carbon at this rate
Indicate the interactions in which 1he following conservation laws are obeyed or violated:(10)
Hypercharge
Charge conjugation
lsotopic spin
Calculate the number of nearest neighbours and the packing fraction for an fcc lattice,(10)
Explain the operation of the following circuit as a gate. Draw the truth table and find the
operation carried out by this gale<br><br> <img src='./qimages/1412-5e.jpg'>
6 What are magic numbers? Discuss the shall structure of a nucleus How this model is able to
explain various properties of nuclei? Discuss the limitations of this model
What is internal conversion Describe an experiment to determine internal conversion
coefficients.
What is Moasbauer effect? Describe an experimental arrangement employed for, the study of
nuclear resonance scattering. Mention some applications of this phenomenon.(I5)
7 (a)Discuss various symmetry elements of a crystal lattice Explain why five- fold rotation
symetry is not observed.
Consider the motion of electrons in a periodic potential of a crystal lat1ice. 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?(20)
Distinguish between a superconductor and a perfect Conductor Explain what is a Cooper pair.(10)
8. Explain the working principle of a phase shift oscillator. Obtain au expression for the
frequency of oscillations.(IS)
Describe the constructional details of a MOSFET. Draw the drain current-drain voltage characteristics.
A common emitter amplifier using transistor is shown below<br><br> <img src='./qimages/1412-8c.jpg'> Calculate the output signal for an input signal of 1 mV. Explain the functions of 50 newF capacitor across 3kom resistor in the emitter circuit and the resistors 930 kom and 250 kom
PAPER· II
SECTION A
1. Answer any four of the following:
Define angular momentum. Express it in the operator form and show that LxLy LyLx ihL2
A photon and an electron have energy 15 keV each. Which of them will have a longer
wavelength
Write down the Schrodinger equation in three dimensions for a free electron and solve it for electrons confined to a cube of edge L and hence obtain an expression for the density of states.
State Franck-Condon principle and discuss its applications in molecular spectroscopy.(10)
If the magnetic moment of proton is '2.793new N.calculale, giving necessary steps, the radio
frequency at which nuclear magnetic resonance occurs in water kept in a unifom1 magnetic
field of 2.4T.
2 Consider a one-dimensional square well potential,as shown below, which is attractive.<br><br> <img src='./qimages/1412-2a.jpg'> potential is Vo in the region x to x and zero elsewhere A stream of particles of mass M and energy E is directed from the left, Set up time-independent Schrodinger equation and obtain an expression for the transmission ratio from region I to 11.
Write the Schrodinger equation for a free particle confined in a cube of edge L. Determine the energy eigenvalues. Show that for a single value of energy different quantum slates are possible. Explain the term degeneracy
3 Set up the time-independent Schrodinger equation for an electron moving in a Coulomb field, <img src='./qimages/1412-3a.jpg'> ,in polar coordinates. Solve solve radial equation to get the energy eigenvalues
What is Zeeman effect? How it can be understood on a quantum mechanical basis Obtain
an expression for the energy splitting
4. Write the wave function for the ground state of the hydrogen molecule under the molecular orbital approximation. Estimate the energy of the electron In the ground state of H2+moleculeion.(20)
Derive the combined vibration-rotation spectrum of a diatomic molecule. What are P and R branches
SECTION B
5. Answer any four of the following:
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.
A star converts all its hydrogen to helium. achieving 100"/o helium composition. II then converts the helium to carbon via the reaction.<br><br> <img src='./qimages/1412-5b.jpg'> The mass of the star is 5.0 x 1012 kg and it generates energy at the rate of 5 x 10 30 W How long will it take to convert all helium to carbon at this rate
Indicate the interactions in which 1he following conservation laws are obeyed or violated:(10)
Hypercharge
Charge conjugation
lsotopic spin
Calculate the number of nearest neighbours and the packing fraction for an fcc lattice,(10)
Explain the operation of the following circuit as a gate. Draw the truth table and find the
operation carried out by this gale<br><br> <img src='./qimages/1412-5e.jpg'>
6 What are magic numbers? Discuss the shall structure of a nucleus How this model is able to
explain various properties of nuclei? Discuss the limitations of this model
What is internal conversion Describe an experiment to determine internal conversion
coefficients.
What is Moasbauer effect? Describe an experimental arrangement employed for, the study of
nuclear resonance scattering. Mention some applications of this phenomenon.(I5)
7 (a)Discuss various symmetry elements of a crystal lattice Explain why five- fold rotation
symetry is not observed.
Consider the motion of electrons in a periodic potential of a crystal lat1ice. 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?(20)
Distinguish between a superconductor and a perfect Conductor Explain what is a Cooper pair.(10)
8. Explain the working principle of a phase shift oscillator. Obtain au expression for the
frequency of oscillations.(IS)
Describe the constructional details of a MOSFET. Draw the drain current-drain voltage characteristics.
A common emitter amplifier using transistor is shown below<br><br> <img src='./qimages/1412-8c.jpg'> Calculate the output signal for an input signal of 1 mV. Explain the functions of 50 newF capacitor across 3kom resistor in the emitter circuit and the resistors 930 kom and 250 kom