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J.B.A.S. College for Women Autonomous Chennai

Mid Semester Examinations January 2011

Code: FVIC11 Relativity and Quantum Mechanics Marks: 75

Section A (Answer ALL questions) 20 Marks

I. Fill in the Blanks:- Marks: 4x1

1. The shortening or contraction in length of an object along the direction of motion is called _________

2. The de Broglie wavelength of a molecule of thermal energy KT is given by _________

3. The uncertainty relation for energy and time is _________4. Two photons approach each other. The relative speed between them is _________

II. Choose the right answer:- Marks: 4x1

5. Which of these quantities is invariant under special theory of relativity? a) Mass b)Momentum c) Timed) Acceleration

6. A spaceship of length 100m takes 4 s to pass an observer on earth. Its velocity relative to the earth is:a) C b) 0.02C c) 0.0233C d) 0.5C7. The Hamiltonian for a free particle is: a) H =-h^2/2m ^2 + V(r) b) H = -h^2/2m ^2 c) V(r) d) A

8. Operator form of time dependent Schrodingers Equation is: a) H =E b) H = 1 c) HA = AH d) H =A

III. Match the Following:- Marks: 4x1

9. Vp

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Answer in one or two sentences:- Marks: 4x1

17. Define inertial and non-inertial frame of reference?

18. State the complementarity principle?

19. Show that 1amu is equal to 931 MeV

20. Define phase velocity and group velocity?

Section B Marks: 5x7

VI. Answer any FIVE questions

21. Deduce the formula for relativistic variation of mass with velocity. Explain its significance.

22. Describe Davisson and Germer experiment for study of electron diffraction? What are the results ofthe experiment?

23. Explain the principle and working of an electron microscope.

24. a) Distinguish between mass-energy equivalence and the principle of equivalence. b) Explaingravitational red-shift on the basis of general theory of relativity.

25. a) State and explain Heisenbergs uncertainty principle. b) Show that there is no existence for freeelectrons in the nucleus of an atom?

26. a) Deduce the time independent Schrdinger equation. b) Give the significance of the wave function.

27. a) State the postulates of the quantum mechanics. b) Prove that:

(x p p x) = i

28.Write a note on

Section C

Answer any THREE questions Marks: 3x15

28. a) State and explain the basic postulates of special theory of relativity. b) Derive the Lorentz space-time transformation equations.

29. a) Show that (E/C) - p is invariant. b) The rest mass of a proton is 2000 times the rest mass of anelectron. Calculate the speed at which the electron should move so that its mass is equal to the rest massof the proton.

30. a) Describe Michelson-Morley experiment and explain the significance of negative result. b) At whatspeed should a clock be moved so that it may appear to lose one minute in each hour?

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31. a) Obtain the time dependent Schrdinger equation for a particle. b) Deduce operators for momentumand energy.

32. a) Does the concept of Bohr orbit violate Heisenbergs uncertainty principle. b) Derive a relationshipbetween phase velocity and group velocity.

BEST OF LUCK!!!