Title 24. Atomic Physics 2 - Hard.pdf ✅

1. The innermost orbit of the hydrogen atom has a diameter 1.06 Å. The diameter of tenth orbit is (a) 5.3 Å (b) 10.6 Å (c) 53 Å (d) 106 Å 2. Energy E of a hydrogen atom with principal quantum number n is given by eV n E 2 −13.6 = . The energy of a photon ejected when the electron jumps n = 3 state to n = 2 state of hydrogen is approximately (a) 1.9 Ev (b) 1.5 Ev (c) 0.85 Ev (d) 3.4 Ev 3. In the Bohr model of the hydrogen atom, let R, v and E represent the radius of the orbit, the speed of electron and the total energy of the electron respectively. Which of the following quantity is proportional to the quantum number n` (a) R/E (b) E/v (c) RE (d) Vr 4. In hydrogen atom, if the difference in the energy of the electron in n = 2 and n = 3 orbits is E, the ionization energy of hydrogen atom is (a) 13.2 E (b) 7.2 E (c) 5.6 E (d) 3.2 E 5. In Bohr model of hydrogen atom, the ratio of periods of revolution of an electron in n = 2 and n = 1 orbits is (a) 2 : 1 (b) 4 : 1 (c) 8 : 1 (d) 16 : 1 6. A double charged lithium atom is equivalent to hydrogen whose atomic number is 3. The wavelength of required radiation for emitting electron from first to third Bohr orbit in ++ Li will be (Ionisation energy of hydrogen atom is 13.6 eV) (a) 182.51 Å (b) 177.17 Å (c) 142.25 Å (d) 113.74 Å 7. The energy levels of a certain atom for 1st, 2nd and 3rd levels are E, 4E/3 and 2E respectively. A photon of wavelength  is emitted for a transition 3 → 1. What will be the wavelength of emissions for transition 2 → 1 (a)/3 (b) 4/3 (c) 3/4 (d) 3 8. Hydrogen atom emits blue light when it changes from n = 4 energy level to n = 2 level. Which colour of light would the atom emit when it changes from n = 5 level to n = 2 level (a) Red (b) Yellow (c) Green (d) Violet 9. The third line of Balmer series of an ion equivalent to hydrogen atom has wavelength of 108.5 nm. The ground state energy of an electron of this ion will be (a) 3.4 Ev (b) 13.6 eV (c) 54.4 Ev (d) 122.4 eV 10. Hydrogen atom in its ground state is excited by radiation of wavelength 975 Å. How many lines will be there in the emission spectrum (a) 2 (b) 4 (c) 6 (d) 8 11. A photon of energy 12.4 eV is completely absorbed by a hydrogen atom initially in the ground state so that it is excited. The quantum number of the excited state is (a) n =1 (b) n = 3 (c) n = 4 (d) n =  12. In an atom, the two electrons move round the nucleus in circular orbits of radii R and 4R. the ratio of the time taken by them to complete one revolution is (a) 1/4 (b) 4/1 (c) 8/1 (d) 1/8 13. A atomic power reactor furnace can deliver 300 MW. The energy released due to fission of each of uranium atom 238 U is 170 MeV. The number of uranium atoms fissioned per hour will be (a) 5  1015 (b) 10  1020 (c) 40  1021 (d) 30  1025 14. The ratio of ionization energy of Bohr’s hydrogen atom and Bohr’s hydrogen like Lithium atom is (a) 1:1 (b) 1:3 (c) 1: 9 (d) None of these 15. The ratio of minimum to maximum wavelengths of radiation that an electron causes in a Bohr’s hydrogen atom is (a) 1⁄2 (b) Zero (c) 3/4 (d) 27/32 16. An electron in Bohr’s hydrogen atom has an energy of –3.4 eV. The angular momentum of the electron is (a) h/ (b) h/2 (c) nh/2 (n is an integer) (d) 2h/ 17. According to Bohr correspondence principle when quantum number is very large – (a) Frequency of revolution of electron in an orbit is equal to the frequency of photon emitted when electron jumps from that orbit to next lower orbit (b) Classical physics approaches quantum physics (c) Wavelength of electron De Broglie wavelength does not depend on kinetic energy of electron (d) Energy of electrons are not quantized 18. In a transition to a state of excitation energy 10.19ev, a hydrogen atom emits a 4890Ao photon. The Binding energy of the initial state is - (a) 1.51 ev (b) 3.4 ev (c) 0.54 ev (d) 0.87 ev 19. According to Bohr model, magnetic field at centre (at the nucleus) of a hydrogen atom due to motion of electron in the n th orbit is proportional to - (a) 1/n3 (b) 1/n5 (c) n5 (d) n3 20. The shortest wavelength of the Braqkett series of a hydrogen like atom (atomic number = Z) is the same as the shortest wavelength of the Balmar series of hydrogen atom. The value of Z is –
(a) 2 (b) 3 (c) 4 (d) 6 21. A hydrogen atom in ground state absorbs 10.2 eV of energy. The orbital angular momentum of the electron is increased by - (a) 1.05 × 10–34Js (b) 2.11 × 10–34Js (c) 3.16 × 10–34Js (d) 4.22 × 10–34Js 22. When hydrogen like atom in excited state make a transition from excited state to ground state, most energetic photons have energy Emax = 52.224 eV and least energetic photons haveenergyEmin = 1.224 eV. Find the atomic number – (a) 4 (b) 6 (c) 2 (d) 8 23. According to Bohr correspondence principle when quantum number is very large – (a) Frequency of revolution of electron on an orbit is equal to the frequency of photon emitted when electron jumps from that orbit to next lower orbit (b) Classical physics approaches quantum physics (c) Wavelength of electron De-Broglie wavelength does not depend on kinetic energy of electron (d) Energy of electrons are not quantized 24. The Bohr radius of an atom of nuclear charge Z is of order – (a) Zmc  (b) mc Z (c) Z mc (d) Zc m 25. The shortest wavelength of the Brackett series of a hydrogen like atom (atomic number = Z) is the same as the shortest wavelength of the Balmar series of hydrogen atom. The value of Z is: (a) 2 (b) 3 (c) 4 (d) 6 26. A hydrogen atom is in an excited state of principle quantum number n. It emits a photon of wavelength  when returns to the ground state. The value of n is - (a) R(R −1) (b) R 1 R  −  (c) R ( R 1)   − (d) (R –1) 27. A hydrogen atom is in 5th excited state. When the electron jumps to ground state, the velocity of recoiling hydrogen atom is - (a) 1.1 m/s (b) 4.2 m/s (c) 8.4 m/s (d) 11.2 m/s 28. Imagine an atom made of a nucleus of charge (Ze) and a hypothetical particle of same mass but double the charge of the electron. Apply the Bohr atom model and consider all possible transitions of this hypothetical particle to the ground state. The longest wavelength of photon that will be emitted has wavelength  (Given in terms of Rydberg constant R of hydrogen atom) equal to – (a) 4Z R 1 2 (b) 3Z R 1 2 (c) 3Z R 4 2 (d) Z R 4 2 29. The speed of an electron in the orbit of hydrogen atom in the ground state is - (a) c (b) c/10 (c) c/2 (d) c/137 30. The difference in the angular momentum associated with the electron in the two successive orbits of the hydrogen atom is - (a) h (b) h/2 (c) h/2  (d) 2h 31. The angular momentum of an electron in a hydrogen atom is proportional to - (a) 1/ r (b) 1/r (c) r (d) r 2 32. Which of the following transitions in a hydrogen atom emits photons of the highest frequency ? (a) n = 1 to n = 2 (b) n = 2 to n = 1 (c) n = 2 to n = 6 (d) n = 6 to n = 2 33. The ratio of areas within the electron orbits for first excited to the ground state for hydrogen atom is – (a) 2 : 1 (b) 4 : 1 (c) 8 : 1 (d) 16 : 1 34. The Bohr radius of an atom of nuclear charge Z is of order – (a) Zmc  (b) mc Z (c) Z mc (d) Zc m 35. In Hydrogen-atom what type of radiation is expected to be associated with energy transitions down to n = 3 energy level ? (a) Infrared (b) Ultraviolet (c) X-rays (d) Gamma rays 36. In Bohr model of H-atom - (a) The radius of nth orbit is proportional to n2 (b) The velocity of nth orbit is proportional to 1/n3 (c) Angular momentum is directly proportional to principal quantum number n2 (d) None of these 37. The longest wavelength present in the Balmer series of hydrogen, corresponding to H line is – (a) 656 nm (b) 565 nm (c) 400 nm (d) 700 nm 38. In Bohr Model, when an electron revolves around the nucleus in an orbit - (a) It radiates energy (b) It absorbs energy (c) Its total mechanical energy is conserved (d) Its angular momentum changes continuously
39. The radius of hydrogen atom in its ground state is 5.3 × 10–11 m. After collision with an electron it is found to have a radius of 21.2 × 10–11 m. What is the principal quantum number n of the final state of the atom ? (a) n = 4 (b) n = 2 (c) n = 16 (d) n = 3 40. When the hydrogen atom emits a photon in going from n = 5 to n= 1 state, its recoil speed is nearly - (a) 10–4 m/s (b) 2 × 10–2 m/s (c) 4 m/s (d) 8 × 102 m/s 41. Ionization potential of hydrogen atom is 13.6 eV. Hydrogen atoms in the ground state are excited by monochromatic radiation of photon energy 12.1 eV. According to Bohr's theory, the spectral lines emitted by hydrogen will be - (a) One (b) Two (c) Three (d) Four 42. The ground state energy of hydrogen atom is – 13.6 eV. What is the potential energy of the electron in this state ? (a) – 27.2 Ev (b) – 13.6 eV (c) + 13.6 eV (d) 0 eV 43. The series limit wavelength of the Lyman series for hydrogen atom is given by - (a) 16/R (b) 9/R (c) 4/R (d) 1/R 44. Rydberg constant for positronium atom is - (a) 456Å 1 (b) 912Å 1 (c) 1824Å 1 (d) 2736Å 1 45. The ratio of the areas within the electron orbits for the first excited state to the ground state for the hydrogen atom is - (a) 2 : 1 (b) 4 : 1 (c) 8 : 1 (d) 16 : 1 46. The ratio of the speed of the electron in the first Bohr orbit of hydrogen and the speed of light is equal to - (where e, h and c have their usual meanings) (a) 2hc/e2 (b) e2 /20hc (c) e2 h/2c (d) None 47. Which of the following statements is true of hydrogen atom? (a) Angular momentum  n 1 (b) Linear momentum  n 1 (c) Radius  n 1 (d) Energy  n 1 48. If the series limit wavelength of the Lyman series for hydrogen atom is 912 Å, then the series limit wavelength for the Balmer series for the hydrogen atom is - (a) 912 Å (b) 912 × 2 Å (c) 912 × 4 Å (d) 2 912 Å 49. The radius of hydrogen atom in its ground state is 5.3 × 10–11 m. After collision with an electron it is found to have a radius of 21.2 × 10–11 m. What is the principal quantum number n of the final state of the atom? (a) n = 4 (b) n = 2 (c) n = 16 (d) n = 3 50. The radius of hydrogen atom, when it is in its second exicted state, becomes - (a) Double (b) Half (c) Four times (d) Nine times 51. The speed of an electron in the orbit of the hydrogen atom in the ground state is - (a) c (b) 10 c (c) 121 c (d) 137 c 52. The energy of an electron in an excited hydrogen atom is –3.4 eV. The angular momentum of the electron according to Bohr's theory is - (a) h/2 (b) h/ (c) 3h/2 (d) 2h/ 53. If 13.6 eV energy is required to ionize the hydrogen atom, then the energy required to remove an electron from n = 2 is - (a) 10.2 eV (b) 0 (c) 3.4 eV (d) 6.8 eV 54. Hydrogen atom emits blue light when it changes from n = 4 energy level to n = 2 level. Which colour of light would the atom emit when it changes from n = 5 level to n = 2 level ? (a) Red (b) Yellow (c) Green (d) Violet 55. The energy levels of a certain atom for 1st, 2nd and 3rd levels are E, 4E/3 and 2E respectively. A photon of wavelength  is emitted for a transition 3 → 1. What will be the wavelength of emission for transition 2 → 1 ? (a) /3 (b) 4/3 (c) 3/4 (d) 3 56. In a hypothetical Bohr hydrogen atom, the mass of the electron is doubled. The energy E0 and radius r0 of the first orbit will be (a0 is the Bohr radius) - (a) E0 = –27.2 eV; r0 = a0 (b) E0 = –13.6 eV; r0 = a0/2 (c) E0 = –27.2 eV; r0 = a0/2 (d) E0 = –13.6 eV; r0 = a0 57. How much energy an electron in the hydrogen atom in ground state should absorb so that its angular momentum changes by        h - (a) 12.1 eV (b) 10.2 eV (c) 12.75 eV (d) 13.05 eV 58. Photons of energy 12.1 eV can excite hydrogen atoms. Find the maximum wavelength of the radiations emitted when electrons drop back to ground state -
(a) 6563 Å (b) 1026 Å (c) 1215 Å (d) 9567 Å 59. As the electron in Bohr orbit of hydrogen atom passes from state n = 2 to n = 1, the KE (K) and PE (U) change as - (a) K two fold and U also two fold (b) Both K and U four fold (c) K four fold and U two fold (d) K two fold and U four fold 60. In Bohr's model, the atomic radius of the first orbit is r0. Then the radius of third orbit is - (a) 9 r0 (b) r0 (c) 9r0 (d) 3r0 61. The ground state energy of H-atom is 13.6 eV. The energy needed to ionise H-atom from its second excited state is - (a) 1.51 eV (b) 3.4 eV (c) 13.6 eV (d) 12.1 eV 62. The ratio of the areas within the electron orbits for the first excited state to the ground state for the hydrogen atom is - (a) 2 : 1 (b) 4 : 1 (c) 8 : 1 (d) 16 : 1 63. The velocity of an electron in the first orbit of H atoms is v. The velocity of an electron in the 2nd orbit of He+ is (a) 2v (b) v (c) v/2 (d) v/4 64. When a hydrogen atom is raised from the ground state to an excited state - (a) Both kinetic energy (KE) and potential energy (PE) increase (b) Both KE and PE decrease (c) PE increases, KE decreases (d) PE decreases, KE increases 65. The velocity of an electron in the nth orbit of H atom is given by - (a) n c (b) nc (c) 137 1 n c (d) 137 n c 66. The ratio between kinetic energy and total energy of the electron of hydrogen atom, according to Bohr's model, is - (a) 1 : –1 (b)1 : 1 (c)1 : 2 (d)2 : 1 67. Two alpha-particles with equal energies are fired towards the nucleus of a gold atom. Which diagram could represent their paths (in the plane of the paper ? Gold nucleus A Gold nucleus B Gold nucleus C Gold nucleus D (a) A (b) B (c) C (d) D 68. The radius of the Bohr orbit in the ground state of hydrogen atom is 0.5 Å The radius of the orbit of the electron in the third excited state of He+ will be - (a) 8 Å (b) 4 Å (c) 0.5 Å` (d) 0.25 Å 69. The force acting on the electron in a hydrogen atom depends on the principal quantum number as - (a) F  n 2 (b)F  2 n 1 (c) F  n 4 (d)F  4 n 1 70. The potential energy of an electron in the fifth orbit of hydrogen atom is - (a) 0.54 eV (b)– 0.54 eV (c) 1.08 eV (d)– 1.08 eV 71. Let An be the area enclosed by the nth orbit in a hydrogen atom. The graph of ln(An/A1) against ln(n) - (a) Will not pass through the origin (b) Will be a straight line with slope 4 (c) Will be a monotonically increasing non-linear curve (d) Will be a circle 72. The Bohr radius of the hydrogen atom in the ground state is 0.529 A. What is the Bohr radius of the hydrogen atom in first excited state ? (a) 0.529 Å (b) 1.058 Å (c) 2.116 Å (d) 0.2645 Å 73. Hydrogen atom is excited from n = 1 to n = 3. The energy that must be absorbed is - (a) 12.09eV (b) 10.2eV (c) 13.6eV (d) – 12.09eV 74. The potential energy of the orbital electron in the ground state of hydrogen atom is –E. What is the kinetic energy ? (a) 4E (b) 2E (c) E/2 (d) E/4 75. What will be the angular momentum of an electron, if energy of this electron in H-atom is –1.5eV (in J sec) ? (a) 1.05 × 10–34 (b) 2.1 × 10–34 (c) 3.15 × 10–34 (d) –2.1 × 10–34 76. When the electron of hydrogen atom comes from infinity into the first orbit, then the value of wave number        1 is - (a) 109700 cm–1 (b) 1097 cm–1 (c) 109 cm–1 (d) None of these