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12.ATOMS Single Correct Answer Type 1. First Bohr radius of an atom with Z = 82is R. Radius of its third orbit is a) 9 R b) 6 R c) 3 R d) R 2. In the Bohr model of a hydrogen atom, the centripetal force is furnished by the coulomb attraction between the proton and the electron. If a is the radius of the ground state orbit, is the mass and is o m e charge on the electron and ε is the vacuum permittivity, the speed of the electron is o a) 0 b) e ε 0 a 0m c) e 4πε 0 a 0m d) 4πε 0 a 0m e 3. In Bohr’s model of hydrogen atom, which of the following pairs of quantities are quantized? a) Energy and linear momentum b) Linear and angular momentum c) Energy and angular momentum d) None of the above 4. Energy required for the electron excitation in Li from the first to the third Bohr orbit is 2+ a) 36.3 eV b) 108.8 eV c) 122.4 eV d) 12.1eV 5. The ratio of minimum wavelength of Lyman and Balmer series will be a) 10 b) 5 c) 0.25 d) 1.25 6. The ionisation potential of hydrogen atom is − 13. 6 eV. An electron in the ground state of a hydrogen atoms absorbs a photon of energy 12. 75 eV. How many different spectral line can one expect when the electron make a downward transition? a) 1 b) 4 c) 2 d) 6 7. A charged particle q is shot towards another charged particle Q which is fixed, with a speed v. It approaches Qupto a closest distance r and then returns. If q was given a speed 2v, the closest distance of approach would be a) r b) 2r c) r/2 d) r/4 8. Ionization potential of hydrogen atom is13.6 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) Two b) Three c) Four d) One 9. The first member of the Balmer’s series of the hydrogen has a wavelength λ, the wavelength of the second member of its series is a) 27 20 λ b) 20 27 λ c) 27 20 λ d) None of these 10. The ratio of areas of the electron orbits for the first excited state and the ground state for the hydrogen atom is a) 4:1 b) 16:1 c) 8:1 d) 2:1 Page| 1
11. The acceleration of electron in the first orbit of hydrogen atom is a) 4π 2m h 3 b) h 2 4π 2mr c) h 2 4π 2m 2 r 3 d) m 2 h 2 4π 2 r 3 12. Anα-particle of energy 5 MeV is scattered through 180°by a fixed uranium nucleus. The distance of the closest approach is of the order of a) 1Å b) 10 cm −10 c) 10 cm −12 d) 10 cm −15 13. In Raman effect, Stokes’ lines are spectral lines having a) Frequency greater than that of the original line b) Wavelength equal to that of the original line c) Wavelength less than that of the original line d) Wavelength greater than that of the original line 14. Suppose an electron is attracted towards the origin by a force , where is constant and is the distance k r k r of the electron from the origin. By applying Bohr model to this system, the radius of the nth orbital of the electron is found to be r and the kinetic energy of the electron to be Then which of the following is true? n T n . a) T n ∝ 1 n 2 , r n ∝ n 2 b) T n independentof n, r n ∝ n c) T n ∝ 1 n , r n ∝ n d) T n ∝ 1 n , r n ∝ n 2 15. What is the difference of angular momenta of an electron in two consecutive orbits in hydrogen atom? a) h 2 b) h π c) 2π h d) h 2π 16. The Kinetic energy of the electron in an orbit of radius r in hydrogen atom is (e =electronic charge) a) e 2 r 2 b) e 2 2r c) e 2 r d) e 2 2r 2 17. Imagine an atom made up of proton and a hypothetical particle of double the mass of electron, but having the same charge as that of electron. Apply the Bohr atom model and consider all possible transitions of this hypothetical particle to the first excited level. The longest wavelength photon that will be emitted has wavelength λ,(given in terms of Rydberg constantR for hydrogen atom) equal to a) 9 5R b) 36 5R c) 18 5R d) 4 R 18. If E and are the potential energy and kinetic energy of the electron in stationary orbit in the hydrogen P E K atom, the value of is E P E K a) 2 b) − 1 c) 1 d) − 2 19. Let the PE of hydrogen atom in the ground state be zero. Then its total energy in the first excited state will be a) 27.2 eV b) 23.8 eV c) 12.6 eV d) 10.2eV 20. An alpha nucleus of energy bombards a heavy nuclear target of charge . Then the distance of 1 2 mv 2 Ze closest approach for the alpha nucleus will be proportional to Page| 2
a) v 2 b) 1/m c) 1/v 4 d) 1/Ze 21. A photon collides with a stationary hydrogen atom in ground state inelastically. Energy of the colliding photon is 10.2 eV. After a time interval of the order of micro second another photon collides with same hydrogen atom inelastically with an energy of 15n eV. What will be observed by the detector? a) 2 photon of energy 10.2 eV. b) 2 photon of energy of 1.4eV. c) One photon of energy 10.2eV and an electron of energy 1.4eV d) One photon of energy 10.2eV and another photon of energy 1.4eV 22. Which state of triply ionised beryllium (Be ) has the same orbital radius as that of ground state of 3+ hydrogen? a) n = 3 b) n = 4 c) n = 1 d) n = 2 23. The energy of an electron in nth orbit of the hydrogen atom is given by E The energy required n = −13.6 n 2 eV to raise an electron from the first orbit to the second orbit will be a) 10.2 eV b) 12.1 eV c) 13.6 eV d) 3.4 eV 24. When a hydrogen atom is bombared, the atom is excited to then n = 4 state. The energy released, when the atom goes from n = 4 state to the ground state is a) 1.275 eV b) 12.75 eV c) 5 eV d) 8 eV 25. Energy E of a hydrogen atom with principal quantum number n is given by E = − .The energy of a 13.6 n 2 eV photon ejected when the electron jumps fromn =3 state to n = 2state of hydrogen , is approximately a) 1.5 eV b) 0.85eV c) 3.4eV d) 1.9eV 26. In the Bohr model of the hydrogen atom, let R, Vand E represent the radius of the orbit, the speed of electron and the total energy of the electron respectively. Which of the following quantities is proportional to quantum number n? a) R E b) E V c) RE d) VR 27. For ionising an excited hydrogen atom, the energy required (in eV) will be a) A little less than 13.6 b) 13.6 c) More than 13.6 d) 3.4 or less 28. In hydrogen atom, the electron is moving round the nucleus with velocity 2. 18 × 10 in an orbit of 6 ms −1 radius 0. 528 Å. The acceleration of the electron is a) 9 ×10 18 ms −2 b) 9 × 10 22 ms −2 c) 9 × 10 −22 ms −2 d) 9 × 10 12 ms −2 29. The angular momentum of electron in hydrogen atom is proportional to a) r b) 1/r c) r 2 d) 1/ r 30. For an electron in the second orbit of Bohr’s hydrogen atom, the moment of linear momentum is a) nπ b) 2πh c) 2h π d) h π 31. If the electron is a hydrogen atom jumps from an orbit with level n to an orbit with level the 1 = 3 n 1 = 2, emitted radiation has a wavelength given by Page| 3
a) λ = 36 5R b) λ = 5R 36 c) λ = 6 R d) λ = R 6 32. In a hydrogen atom, the electron moves around the nucleus in a circular orbit of radius 5 × 10 m. Its −11 time period is 1. 5 × 10 .The current associated with the electron motion is (charge of electron is −16 1. 6 × 10 ) −16 C a) 1.00 A b) 1. 066 × 10 −3A c) 1. 81 × 10 −3A d) 1. 66× 10 −3A 33. Let the potential energy of hydrogen atom in the ground state be regarded as zero. Then its potential energy in the first excited state will be a) 20.4eV b) 13.6eV c) 3.4eV d) 10.2eV 34. If the shortest wavelength in the Lyman series is 911.6 Å, the longest wavelength in the same series will be a) 1600 Å b) 2430Å c) 1215 Å d) ∞ 35. According to Bohr’s atomic model, the relation between principal quantum number(n) and radius of orbit( r) is a) r∝n 2 b) r∝ 1 n 2 c) r∝ 1 n d) r ∝ n 36. The atomic number and the mass number of an atom remains unchanged when it emits a) a photon b) a neutron c) β −particle d) An α − particle 37. The Rydberg constant R for hydrogen is a) R =− 1 4πε o ( ) 2π 2me 2 ch 2 b) R = 1 4πε o ( ) 2π 2me 2 ch 2 c) R = 1 4πε o ( ) 2 2π 2me 2 c 2 h 2 d) R = 1 4πε o ( ) 2 2π 2me 4 ch 3 38. For light of wavelength 5000Å, photon energy is nearly 2.5 eV. For X-rays of wavelength 1 Å, the photon energy will be close to a) [2. 5÷5000]eV b) [2. 5÷(5000) 2 ]eV c) [2. 5×5000]eV d) [2. 5×(5000) 2 ]eV 39. Which of the following transition in Balmer series for hydrogen will have longest wavelength? a) n=2 to n=1 b) n =6 to n=1 c) n =3 to n=2 d) n =6 to n=2 40. Ionization potential of hydrogen atom is 13.6 eV. Hydrogen atoms in the ground state are exicted by monochromatic radiation of photon energy 12.1 eV. The spectral lines emitted by hydrogen atom according to Bohr’s theory will be a) One b) Two c) Three d) Four 41. The ratio of the frequencies of the long wavelength limits of the Lyman and Balmer series of hydrogen is a) 27: 5 b) 5: 27 c) 4: 1 d) 1: 4 42. Hydrogen atom from excited state comes to the ground state by emitting a photon of wavelength λ. If R is the Rydberg constant, the principal quantum number n of the excited state is a) λR λR−1 b) λ λR−1 c) λR 2 λR−1 d) λR λ−1 Page| 4