Title QM DPP Sheet 04.pdf ✅

1 North Delhi : 56-58, First Floor, Mall Road, G.T.B. Nagar (Near Metro Gate No. 3), Delhi-09, Ph: 011-41420035 South Delhi : 28-A/11, Jia Sarai, Near-IIT Metro Station, New Delhi-16, Ph : 011-26851008, 26861009 IIT JAM PHYSICS 2024 (Online Batch) Section: MODERN PHYSICS (Quantum Mechanics) Chapter: WAVE PARTICLE DUALITY Daily Practice Problem (DPP) Sheet 4 PART I: Multiple Choice Questions (MCQ) 1. The de-broglie wavelength for (i) a proton of kinetic energy 70 MeV, (ii) a 10 gm ball moving at 900m/s are approximately (a) 15 34 10 m,10 m   (b) 10 30 10 m,10 m   (c) 20 34 10 m,10 m   (d) 15 30 10 m,10 m   2. The speed of an electron, whose de-broglie wavelength is equal to Compton wavelength is (a) 2 c (b) c (c) 2 c (d) 3 c 3. The relation between wave number and angular frequency for a given wave is 2 3  k  k . The wave number for which phase velocity equal to group velocity (a)   (b)   (c) 2   (d) 2   4. The phase velocity of ocean waves is 2 g  , where g is the gravitational acceleration of gravity. The group velocity of the ocean waves is (a) 3 2 2 g  (b) 5 2 2 g  (c) 1 2 2 g  (d) 2 g  5. In a certain medium, the dispersion relation is given by,   2 2 2 2   c k 1k . The relation between phase velocity and group velocity will be (a)   2 2 1 2 p g v v  c  k (b)   2 2 1 p g v v  c k (c)   2 2 2 1 p g v v  c  k (d)   2 2 2 1 2 p g v v  c   k 6. The phase velocity of ripples on a liquid surface is 2 S  , where S is the surface tension and  is the density of the liquid. The group velocity of the ripples is (a) 1 2 2  S  (b) 3 2 2  S  (c) 3 2 4  S  (d) 5 2 4  S 
2 North Delhi : 56-58, First Floor, Mall Road, G.T.B. Nagar (Near Metro Gate No. 3), Delhi-09, Ph: 011-41420035 South Delhi : 28-A/11, Jia Sarai, Near-IIT Metro Station, New Delhi-16, Ph : 011-26851008, 26861009 7. A particle having rest mass ‘m0 ’ and charge ‘q’ is accelerated through a potential difference ‘V’. Taking relativistic correction into account, the de-broglie wavelength associated with the particlecan be expressed as (a) 0 2 0 2 1 2 rel h qV qVm m c          (b) 0 2 0 2 1 2 rel h qV qVm m c          (c) 0 2 0 1 2 rel h qV qVm m c          (d) 0 2 0 1 2 rel h qV qVm m c          8. The phase velocity of the de-broglie waves asscocitaed with a particle of rest mass ‘m0 ’ and wavelength ‘λ’ is (a) 2 0 1 hc c m         (b) 2 0 1 hc c m        (c) 2 0 1 m c c h        (d) 2 0 1 m c c h         9. The ratio of the De Broglie wavelength to the Compton Wavelength of a particle, is (a) 1 c v  (b) 2 2 1 c v  (c) c v (d) v c 10. The de Broglie wavelength of particles of mass m with average momentum p at a temperature T in three dimensions is given by (a) B h 2mk T   (b) B h 3mk T   (c) B h mk T   (d) B h 2 mk T   11. The angular frequency  of deep water waves varies as the inverse square root of the wavelength , i.e.,       1/ . Which of the following is the relation between its group velocity g v and p v ? (a)  / 2 g p v v (b) v v g p  (c)  2 g p v v (d) v v g p   . 12. Phase velocity and group velocity for a wave will be identical (a) If the phase velocity is independent of wavelength. (b) If the phase velocity is dependent on wavelength. (c) If the group velocity is dependent on wavelength. (d) If the group velocity is dependent on refractive index of the medium. 13. The dispersion relation for a certain type of excitation is given by a   Ak , where A and a > 0 are constants. For these excitations, the group velocity is less than the phase velocity when (a) a =1 (b) a  2 (c) a < 1 (d) a  2 14. The de Broglie wavelength of photoelectron associated with its maximum kinetic energy when ejected from a metal surface (work function = W) by an incident light of wavelength  is (a) 2 e h hc m W         (b) 2 / e h m hc  (c) 2 e h m W (d) 2 e h hc m W        
3 North Delhi : 56-58, First Floor, Mall Road, G.T.B. Nagar (Near Metro Gate No. 3), Delhi-09, Ph: 011-41420035 South Delhi : 28-A/11, Jia Sarai, Near-IIT Metro Station, New Delhi-16, Ph : 011-26851008, 26861009 15. A particle moving with kinetic energy equal to its rest energy has a de Broglie wavelength of 0 . If the kinetic energy doubles, its new de Broglie wavelength will be (a) 1 3  (b) 3 8  (c) 1 2 2  (d) 3 16  PART II: Numerical Answer Type (NAT) Questions 16. The phase velocity of the de-broglie waves of electron having kinetic energy 500 keV is ____________ c. [Your answer should be upto TWO DECIMAL PLACES] 17. In a certain electron microscope, electrons having energy 40 keV is used. The de-broglie wavelength of electrons is ____________________ pm. [Your answer should be upto TWO DECIMAL PLACES] 18. The De Broglie wavelength of electron having kinetic energy 1 MeV is ____________________ fm. [Your answer should be AN INTEGER] 19. A free electron in a metal has average kinetic energy of 3 2 kT at high temperature. The temperature at which the average De-Broglie wavelength of the electron will be 0.5 nm, is _______________________ K. [Your answer should be AN INTEGER] PART III: Multiple Select Questions (MSQ) 20. An electron has a de-broglie wavelength 2 pm. Then which of the following statement is/are TRUE? (a) The kinetic energy of the electron will be 292 KeV. (b) The energy of the electron will be 850 KeV. (c) The phase velocity of the de-broglie wave of the electron will be 1.21c (d) The group velocity of the de-broglie wave of the electron will be 0.77c Answer Key PART I: Multiple Choice Questions (MCQ) 1. (a) 2. (c) 3. (a) 4. (c) 5. (a) 6. (b) 7. (a) 8. (d) 9. (b) 10. (b) 11. (a) 12. (a) 13. (c) 14. (d) 15. (b) PART II: Numerical Answer Type (NAT) Questions 16. (1.11 to 1.19) 17. (5.85 to 6.15) 18. (870 to 880) 19. (46600 to 46630) PART III: Multiple Select Questions (MSQ) 20. (a,d)