Babu Banarasi Das National Institute of Technology & Management, Lucknow Department of Physics 1. Short Answer Type Questions: a) Why wave nature of matter is not observed in our daily life? b) What are de Broglie’s matter waves? c) What is the physical significance of wave function? d) Define eigen values and eigen wave functions. e) Why is uncertainty principle valid for microscopic particles and not for macroscopic particles? 2. Describe Davisson and Germer’s experiment to show the existence of matter waves. 3. Calculate the de Broglie wavelength associated with a proton moving with a velocity equal to 1/20th of the velocity of light. 4. Calculate the de Broglie wavelength of neutron of energy 12.8 MeV. Given h= 6.62x1034 J.sec, m=9.1x10-31 kg. 5. Show that the de Broglie wavelength for a material particle of rest mass m0 and charge q, accelerated from rest through a potential difference of V volts relativistically is given by h 2m0 qV 1 qV 2m0 c 2 6. Can a photon and an electron of the same momentum have the same wavelength? Compare their wavelengths if the two have the same energy. 7. Calculate the kinetic energy needed by an electron to be confined in hydrogen atom of radius 0.5Å. 8. State Heisenberg’s uncertainty principle. Show that electron cannot exist inside nucleus. 9. Calculate the de Broglie wavelength of an α-particle accelerated through a potential difference of 2000V. 10. What is the minimum uncertainty in the frequency of a photon whose life time is about 10-8 sec. 11. Deduce a relation between phase velocity and group velocity in a medium where wave velocity is frequency dependent.What happens if the wave velocity is independent of frequency. 12. Derive time-dependent Schrodinger wave equation. Give its physical significance. 13. Derive the expression of wave function and energy eigen values of particlein one dimensional infinitely deep potential well. 14. Find the probability that a particle trapped in a box L wide can be found between 0.45L and 0.55L for the ground and first excited state. 15. A particle is moving in one dimensional potential box (of infinite height) of width 25Å. Calculate the probability of finding the particle within an interval of 5Å at the center of the box when it is in the state of least energy.
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