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1. nonice forth the Michelson Morley experiment and discuss the importance of its proscribe result. 2. train the fringe shift in Michelson-Morley experiment. give that pic, pic, pic, and pic. 3. State the primitive make dos of Einstein finicky theory of relativity and deduce from them the Lorentz Transformation Equations . 4. explain relativistic continuance contraction and clock quantify dilation in special theory of relativity? What atomic number 18 proper length and proper time interval? 5. A rod has length 100 cm. When the rod is in a satellite pitiable with velocity 0.9 c relative to the laboratory, what is the length of the rod as measured by an observer (i) in the satellite, and (ii) in the laboratory?.6. A clock keeps correct time. With what animate should it be travel relative to an observer so that it may appear to lose 4 minutes in 24 hours? 7. In the laboratory the life time of a portion paltry with speed 2.8x108m/s, is found to be 2.510-7 sec. see t he proper life time of the mite. 8. come fling off relativistic rightfulness of step-up of velocities and prove that the velocity of light is the homogeneous in all inertial frame irrespective of their relative speed. 9. Two elements come towards for each one new(prenominal) with speed 0.9c with respect to laboratory. foretell their relative speeds. 10. Rockets A and B are observed from the earth to be traveling with velocities 0.8c and 0.7 c along the very(prenominal) line in the same direction. What is the velocity of B as seen by an observer on A? 11. charge that the relativistic invariance justnesss of preservation of impulsion leads to the concept of variation of upsurge with speed and mass zilch equivalence. 12. A proton of liberalisation mass pic is moving with a velocity of 0.9c. Calculate its mass and caprice.tutorial wood work plane 1(Module1 Special Theory of Relativity).13. The speed of an negatron is doubled from 0.2 c to 0.4 c. By what ratio does it s momentum summation? 14. A particle has kinetic push button 20 times its relief naught. go on the speed of the particle in terms of c. 15. explode liberates about 5.4106 J/Kg when it explodes. What reckon of its jibe naught is in this amount? 16. A stationary body explodes into two fragments each of mass 1.0 Kg that move isolated at speeds of 0.6 c relative to the accepted body. Find the mass of the original body. 17. At what speed does the kinetic brawniness of a particle equals its rest zipper? 18. What should be the speed of an negatron so that its mass becomes equal to the mass of proton? presumptuousness mass of negatron=9.110-31Kg and mass of Proton =1.6710-27Kg.19. An electron is moving with a speed 0.9c. Calculate (i) its total energy and (ii) the ratio of Newtonian kinetic energy to relativistic energy. Given pic andpic. 20. (i) Derive a relativistic materialization for kinetic energy of a particle in terms of momentum. (ii) Show that the momentum of a par ticle of rest mass pic and kinetic energy pic, is apt(p) bypic. 21. Find the momentum (in MeV/c) of an electron whose speed is 0.60 c. Verify that v/c = pc/E TUTORIAL SHEET 2(a)(Module2 Wave Mechanics)1. What do you understand by the oscillate nature of matter? Obtain an feeling of de Broglie quiverlength for matter swings. 2. Calculate the de-Broglie seethelength of an electron and a photon each of energy 2eV. 3. Calculate the de-Broglie wavelength associated with a proton moving with a velocity equal to 1/20 of the velocity of light. 4. Show that the wavelength of a 150 g rubber ball moving with a velocity of pic is short enough to be gibed.5. Energy of a particle at absolute temperature T is of the determine of pic. Calculate the wavelength of thermal neutrons atpic. Given pic, pic and pic. 6. Can a photon and an electron of the same momentum have the same wavelengths? Calculate their wavelengths if the two have the same energy. 7. Two particles A and B are in motion. If the wavelength associated with particle A is pic, calculate the wavelength of the particle B if its momentum is half that of A. 8. Show that when electrons are speed through a potential difference V, their wavelength taking relativistic correction into account is pic , where e and pic are charge and rest mass of electrons, respectively. 9. A particle of rest mass m0 has a kinetic energy K. Show that its de Broglie wavelength is given by pic TUTORIAL SHEET 2(a)(Module2 Wave Mechanics)16. Explain Heisenberg uncertainty principle. Describe gamma ray microscope experiment to establish Heisenberg uncertainty principle. 17. How does the Heisenberg uncertainty principle hint about the absence of electron in an nuclear assemble? 18. Calculate the uncertainty in momentum of an electron confined in a one-dimensional box of lengthpic. Givenpic.TUTORIAL SHEET 2(b)(Module 2 Wave Mechanics)1. Differentiate between and II2. Discuss Born postulate regarding the probabilistic interpretation of a wave wreak. 2. Write hatful the set of conditions which a solution of Schrdinger wave compare satisfies to be called a wave function. 3. What do you mean by recipeization and orthogonality of a wave function? 4. Show that if potential energy V(x) is changed everywhere by a constant, the time independent wave equation is unchanged. What is the effect on the energy Eigen determine? 5. Show thatpic, where picthe reduced mass and B is the binding energy of the particles. 6. Show that picis an acceptable eigen function, where k is some finite constant. Also anneal it over the regionpic.7. Explain the meaning of expectation value of x. write down the Eigen operators for position, linear momentum and total energy. 8. Show that time independent Schrdinger equation is an exercising of Eigen value equation. 9. Derive the time independent Schrdinger equation from time dependent equation for free particle. 10. For a free particle, show that Schrdinger wave equation leads to the de-Brog lie relation pic. 11. Derive expression for hazard modern parsimony or particle flux. Also , show that the probability engrossment and probability current assiduity pic satisfy the continuity equationpicTUTORIAL SHEET 2(b)(Module 2 Wave Mechanics)12. Write Schrdinger equation for a particle in a box and determine expression for energy Eigen value and Eigen function. Does this predict that the particle can possess slide fastener energy? 13. Find the expectation values of the position and that of momentum of a particle trapped in a one dimensional rigid box of length L. 14. The potential function of a particle moving along positive x-axis is given by V(x) = 0for x 0V(x) = V0for x pic 0Calculate the reflectance R and transmittance T at the potential discontinuity and show that R+T=1. 15. An electron is bounded by a potential which closely approaches an unfathomable self-coloured well of widthpic. Calculate the lowest three permissible quantum energies the electron can have. 1 6. A particle is moving in one dimensional box and its wave function is given by pic. Find the expression for the normalized wave function.17. Calculate the value of lowest energy of an electron moving in a one-dimensional force free region of length 4pic. 18. A particle of mass pickg is moving with a speed of pic in a box of lengthpic. Assume this to be one dimensional square well problem, calculate the value of n. 19. A radiation of electron impinges on an infinitely wide energy barrier of height 0.03 eV, find the fraction of electrons reflected at the barrier if the energy of the electrn is (a) 0.025 eV (b) 0.030 eV (c) 0.040 eVTUTORIAL SHEET 3(a)(Module 3 corpuscleic Physics)1. What are the essential features of Vector Atom model? Also discuss the quantum matters associated with this model. 2. For an electron orbit with quantum number l = 2, state the possible values of the components of total angular momentum along a specified direction. 3. Differentiate between L-S union ( Russel-Saunders Coupling) and j-j coupling plots. 4. Find the possible value of J under L-S and j-j coupling scheme if the quantum number of the two electrons in a two valence electron atom are n1 = 5 l1 = 1 s1 =1/2 n2 = 6 l2 = 3 s2 = 1/25. Find the spectral terms for 3s 2d and 4p 4d configuration. 6. Applying the selection rule, show which of the following transitions are allowed and not allowed D5/2 pic P3/2 D3/2 pic P3/2 D3/2 pic P1/2 P3/2 pic S1/2 P1/2 pic S1/27. What is Paschen back effect? Show that in a untroubled magnetised orbit, anomalous Zeeman pattern changes to normal Zeeman pattern. 8. Why does in normal Zeeman effect a singlet line always splitted into three components only. 9. instance Zeeman Effect with the example of Sodium D1 and D2 lines. 10. An element under spectroscopic mental testing is placed in a magnetic field of flux density 0.3 Web/m2. Calculate the Zeeman shift of a spectral line of wavelength 450 nm. 11. The Zeeman components of a 500 nm spect ral line are 0.0116 nm apart when the magnetic field is 1.0 T. Find the ratio (e/m) for the electron. 12. Calculate wavelength separation between the two component lines which are observed in Normal Zeeman effect, where the magnetic field used is 0.4 weber/m2 , the specific charge- 1.76x1011Coulomb/kg and =6000pic. TUTORIAL SHEET 3(b)(Module 3 atomic Physics)1. Distinguish between spontaneous and stimulated procession. Derive the relation between the transition probabilities of spontaneous and stimulated emission. 2. What are the characteristics of laser beams? Describe its important applications. 3. Calculate the number of photons emitted per second by 5 mW laser assuming that it emits light of wavelength 632.8 nm. 4. Explain (a) Atomic excitations (b) Transition transition (c) Meta stable state and (d) Optical pumping. 5. Find the intensity of laser beam of 15 mW power and having a diameter of 1.25 mm. Assume the intensity to be uniform across the beam.6. Calculate the energy difference in eV between the energy levels of Ne-atoms of a He-Ne laser, the transition between which results in the emission of a light of wavelength 632.8nm. 7. What is population inversion? How it is achieved in Ruby optical maser? Describe the construction of Ruby Laser. 8. Explain the operation of a muff Laser with essential components. How stimulated emission takes place with exchange of energy between Helium and Neon atom? 9. What is the difference between the working principle of three level and four level lasers? Give an example of each type. 10. How a four level Laser is superior to a three level Laser? TUTORIAL SHEET 3(c)(Module 3 Atomic Physics)1. Distinguish between constant X-radiation and characteristic X-radiation spectra of the element. 2. An X ray tube operated at 100 kV emits a continuous X ray spectrum with short wavelength limit min = 0.125pic. Calculate the Plancks constant. 3. State Braggs Law. Describe how Braggs Law can be used in determination of crystal structure? 4. Why the diffraction effect in crystal is not observed for plain light. 5. Electrons are accelerated by 344 volts and are reflected from a crystal. The first reflection maxima occurs when glancing angle is three hundred . incur the spacing of the crystal. (h = 6.62 x 10-34 Js , e = 1.6 x 10-19 C and m = 9.1 x10-31 Kg) 6. In Braggs reflection of X-rays, a reflection was found at 300 glancing angle with lattice planes of spacing 0.187nm. If this is a second order reflection. Calculate the wavelength of X-rays.7. Explain the origin of characteristic X-radiation spectra of the element. How Mosleys law can explained on the basis of Bohrs model. 8. What is the importance of Mosleys law? Give the important differences between X-ray spectra and optical spectra of an element? 9. reason the wavelength of pic line for an atom of Z = 92 by using Mosleys Law. (R= 1.1 x 105 cm-1). 10. If the K radiation of Mo (Z= 42) has a wavelength of 0.71pic, determine the wavelength of the c orresponding radiation of Cu (Z= 29). 11. The wavelength of L X ray lines of silver and Platinum are 4.154 picand 1.321pic, respectively. An unknown substance emits of L X rays of wavelength 0.966pic. The atomic numbers of Silver and Platinum are 47 and 78 respectively. Determine the atomic number of the unknown substance. TUTORIAL SHEET 4(a)(Module 4 unanimous State Physics)1. Discuss the basic assumptions of Sommerfelds theory for free electron bumble model of metals? 2. Define the femtometer energy of the electron. Obtain the expression for energy of a three dimensional electron gas in a metal. 3. Prove that at absolute zero, the energy states below Fermi level are filled with electrons while above this level, the energy states are empty. 4. Show that the average energy of an electron in an electron gas at absolute zero temperature is 3/5pic, wherepic, is Fermi energy at absolute zero. 5. Prove that Fermi level lies half way down between the conductivity and valence band in in trinsic semiconducting material. 6. Find the Fermi energy of electrons in copper on the assumption that each copper atom contributes one free electron to the electron gas. The density of copper is 8.94(103 kg/m3 and its atomic mass is 63.5 u.7. Calculate the Fermi energy at 0 K for the electrons in a metal having electron density 8.4x1028m-3. 8. On the basis of Kronig Penney model, show that the energy spectrum of electron in a linear crystalline lattice consists of alternate regions of allowed energy and veto energy. 9. Discuss the differences among the band structures of metals, insulators and semiconductors. How does the band structure model enable you to best understand the electrical properties of these materials?10. Explain how the energy bands of metals, semiconductors and insulators account for the following customary optical properties (a) Metals are opaque to visible light, (b) Semiconductors are opaque to visible light but transparent to infrared, (c) Insulator such as adamant is transparent to visible light. 11. Discuss the position of Fermi energy and conduction mechanism in N and P-type extrinsic semiconductors. TUTORIAL SHEET 4(b)(Module 4 Solid State Physics)1. What do you mean by superconductivity? Give the principal(a) properties of superconductors. 2. Discuss the effect of magnetic field on a superconductor. How a superconductor is different from a normal conductor. 3. Discuss the effect of the magnetic field on the superconducting state of type I and type II superconductors. 4. What are the elements of the BCS theory? Explain the formation of Cooper pairs. 5. Explain the phenomena of Meissner effect and zero resistivity with the help of BCS theory. 6. The metals like gold, silver, copper etc. do not show the superconducting properties, why?7. Describe the V-I characteristics of p-n junction diode. What do you understand by drift and diffusion current in the case of a semiconductor? 8. Explain the working and characteristics of a phot odiode by using I-V curve. 9. Describe the phenomena of carrier generation and recombination in a semiconductor. 10. Define the phenomenon of photoconduction in a semiconductor. Deduce the relation between the wavelength of photon required for intrinsic excitation and prohibit energy gap of semiconductor. 11. Establish the relation between load current and load voltage of a solar jail cell. Describe the applications of solar cell in brief.