* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Atomic Physics
Quantum state wikipedia , lookup
EPR paradox wikipedia , lookup
James Franck wikipedia , lookup
History of quantum field theory wikipedia , lookup
Chemical bond wikipedia , lookup
Canonical quantization wikipedia , lookup
Renormalization group wikipedia , lookup
Renormalization wikipedia , lookup
Bohr–Einstein debates wikipedia , lookup
Symmetry in quantum mechanics wikipedia , lookup
Relativistic quantum mechanics wikipedia , lookup
X-ray photoelectron spectroscopy wikipedia , lookup
Matter wave wikipedia , lookup
Auger electron spectroscopy wikipedia , lookup
Rutherford backscattering spectrometry wikipedia , lookup
Tight binding wikipedia , lookup
X-ray fluorescence wikipedia , lookup
Particle in a box wikipedia , lookup
Wave–particle duality wikipedia , lookup
Quantum electrodynamics wikipedia , lookup
Ferromagnetism wikipedia , lookup
Atomic orbital wikipedia , lookup
Theoretical and experimental justification for the Schrödinger equation wikipedia , lookup
Electron configuration wikipedia , lookup
Atomic Physics Multiple Choice 1. An energy of 13.6 eV is needed to ionize an electron from the ground state of a hydrogen atom. What wavelength is needed if a photon accomplishes this task? a. b. c. d. e. 2. What value of wavelength is associated with the Lyman series for n = 2? (RH = 1.097 × 107 m–1) a. b. c. d. e. 3. 8.2 × 106 m 1.2 × 10–7 m 2.7 × 106 m 3.6 × 10–7 m 8.8 × 10–7 m What wavelength (in µm) is associated with the Paschen series for n = 4? (RH = 1.097 × 107 m–1) a. b. c. d. e. 4. 60 nm 80 nm 70 nm 90 nm 40 nm 320 530 2.7 1.9 0.5 Light is emitted by hydrogen atoms in the visible range for a hydrogen atom. Its wavelength is 656 nm. What value of n is associated with the light? (RH = 1.097 × 107 m–1) a. b. c. d. e. 5 2 4 3 6 345 5. An electron in a hydrogen atom makes a transition from the n = 4 to the n = 3 energy state. Determine the energy (in eV) of the emitted photon. a. b. c. d. e. 6. An electron in a hydrogen atom makes a transition from the n = 3 to the n = 1 energy state. Determine the wavelength of the emitted photon (in nm). a. b. c. d. e. 7. 3 × 10–24 2 × 10–24 1 × 10–24 4 × 10–24 3 × 10–15 How fast is the electron moving in the first Bohr orbit? a. b. c. d. e. 9. 1006 209 306 103 821 A hydrogen atom is in its first excited state (n = 2). The linear momentum of the electron is (in kg · m/s) a. b. c. d. e. 8. 0.54 0.66 0.85 1.51 10.2 3.3 × 106 m/s 2.2 × 106 m/s 4.4 × 106 m/s 5.5 × 106 m/s 5.5 × 1015 m/s An electron is moving at a speed of 2.1 × 106 m/s in the first Bohr orbit. Determine its de Broglie wavelength. a. b. c. d. e. 0.3 × 10–10 m 1.7 × 10–10 m 0.5 × 10–10 m 3.5 × 10–10 m 1.5 × 10–10 m Atomic Physics 10. Suppose Bohr had chosen the potential energy of the electron in the hydrogen atom to be V = 0 when the electron is in the orbit with n = 1. He could do this by a. b. c. d. e. 11. c. d. 1 to ∞ 2 to ∞ 3 to ∞ any real number 1 to 10 The allowed values of l for the n = 3 shell in a Li2+ ion are a. b. c. d. e. 14. the ground state angular momentum was L = 1 h. the frequency of the radiation emitted when an electron “jumps” from one allowed orbit to another was hf = Ei - Ef. the potential energy function for the hydrogen atom was given by V(r) = –ke2/r. the energy of the ground state of the hydrogen atom was En = –13.6 eV. The allowed values of n for the Li2+ ion are a. b. c. d. e. 13. choosing n = 1 for the orbit where the kinetic energy of the electron is zero. adding a constant 13.6 eV to the potential energy for all values of n. adding a constant 27.2 eV to the potential energy for all values of n. subtracting a constant 13.6 eV from the potential energy for all values of n. subtracting a constant 27.2 eV from the potential energy for all values of n. One of the main problems with the Bohr model of the hydrogen atom when compared with the results of the methods of quantum mechanics used to describe atoms, was that the Bohr model predicted a. b. 12. 347 1, 2 0, 1 0, 1, 2 0, 1, 2, 3 1, 2, 3 In the subshell of the Li2+ ion with orbital quantum number l, the allowed values of the magnetic quantum number ml are a. b. c. d. e. –l to l –(l + 1) to (l + l) –(l + 2) to (l + 2) –(l + 3) to (l + 3) 0 to n – 1 15. In a shell of the hydrogen atom with n = 3, the permitted values of the orbital magnetic quantum number ml are a. b. c. d. e. 16. The K, L, M symbols represent values of the quantum number a. b. c. d. e. 17. ms n ml l mj The number of states in the He+ ion corresponding to the principle quantum number n = 5 are a. b. c. d. e. 19. n l ml ms mj The s, p, d, f, symbols represent values of the quantum number a. b. c. d. e. 18. –1, 0, 1 2, 1, 0 2, 1, 0, –1, –2 0 3, 2, 1, 0, –1, –2, –3 18 25 50 9 11 The energy needed to remove an electron from the first excited state of a Li2+ ion is a. b. c. d. e. 53 eV 31 eV 92 eV 122 eV 61 eV Atomic Physics 20. Of the following states, 5s, 3p, 4f, 5p, 4g, 3d, and 2p, the one which is NOT allowed is a. b. c. d. e. 21. 13.6 eV 54.4 eV 112.4 eV 92.9 eV 27.2 eV A Li2+ ion undergoes a transition from the n = 4 to the n = 3 state. The energy of the emitted photon is a. b. c. d. e. 24. n = 2 to n = 1 n = 3 to n = 2 n = 3 to n = 1 n = 1 to n = 3 n = 4 to n = 1 The energy needed to change a He+ ion in the ground state into a He2+ ion is a. b. c. d. e. 23. 3p 4f 3d 4g 2p For the following allowed transitions, which photon would have the largest wavelength when an electron “jumps” from one energy level, characterized by the quantum number n, to another? a. b. c. d. e. 22. 349 4.5 eV 10.2 eV 5.95 eV 2.6 eV 0.66 eV 2 The probability density for the 1s state is given by Ψ1s . The probability of finding the particle somewhere in space is a. b. c. d. e. ∫ ∫ ∫ ∫ ∫ 2 Ψ1s 4πr2dr 2 Ψ1s dr 2 Ψ1s r dr 2 Ψ1s r2dr 2 Ψ1s r3dr 25. If P(r) is the radial probability density function for an electron in the ground state of a hydrogen atom, the most probable value for r can be found from a. b. dP/dt dP/dr c. ∫ rP(r)4πr dr ∫ rP(r)dr d. e. 26. 2 d2P/dr2 The radial portion of the de Broglie wavefunction for an electron in the ground ( ) 12 state of the hydrogen atom is Ψ1s(r) = 1 πa03 exp(− r a0 ) where a0 is the Bohr radius. The probability of finding the electron is a. b. c. d. e. 27. (π (π (π (π ) ∫ exp(− 2r a )4πr dr a ) ∫ exp(− 2r a )4πr dr a ) ∫ exp(− 2r a )dr a ) ∫ exp(− 2r a )dr a03 2 0 3 12 0 0 3 12 0 0 3 12 0 0 2 1 d 1 3 exp(− 2r a0 ) 3 dr πa0 πa0 12 0 e− r a 1/2 The probability density of a particle at a distance r from the nucleus is essentially the a. b. c. d. e. probability of finding the particle within a small volume about r. probability per unit area of finding the particle within a unit area centered on r. probability per unit length of finding the particle within a unit length of r. probability per unit volume of finding the particle within a small volume about r. ∫ 2 Ψ 2 4πr2dr 0 28. Of the following states of the hydrogen atom, 1s, 2p, 3d, 4f, 4s, which answer lists all the states that are not spherically symmetrical? a. b. c. d. e. 1s, 4s 3d, 4f 2p, 3d, 4f 2p, 3d, 4s, 4f 1s, 4s, 4f Atomic Physics 29. A hydrogen atom in the 4f state has a total angular momentum (in terms of h) of magnitude a. b. c. d. e. 30. orbital angular momentum quantization energy quantization space quantization magnetic orbital quantization that particles behave like waves The magnitude of the spin angular momentum for an electron is equal to a. b. c. d. e. 33. L can never be perpendicular to B. L can be aligned parallel to B. L must be perpendicular to B. L can never be aligned parallel to B. In 1921, Stern and Gerlach performed an experiment that first demonstrated a. b. c. d. e. 32. 2 3 3 6 3 12 Which of the following statements is true? a. b. c. d. 31. 351 3h 3 h 2 h/2 ±h/2 3 h 4 When using the Pauli Exclusion Principle, we assume the particle’s spin angular momentum is of magnitude a. b. c. d. e. 1 h 2 3 h 2 h ±h 1 − h 2 34. What angle does the orbital angular momentum make with the z axis of a hydrogen atom in the state n = 3, l = 2, ml = –1? a. b. c. d. e. 35. The total angular momentum for a 3P3/2 electron is a. b. c. d. e. 36. b. c. d. e. no two electrons in the same atom can have the same set of quantum numbers. there is an inherent uncertainty in the position and momentum of a particle. when an atom has orbitals of equal energy, the maximum number of electrons will have unpaired spins. when an atom has orbitals of equal energy, the maximum number of electrons will be paired spins. no two atoms can have the same set of quantum numbers. Forbidden transitions and selection rules suggest that a. b. c. d. e. 38. 15 h 2 3 h 2 3 h 2 3h 3h The Pauli Exclusion Principle states a. 37. –66° 66° 24° 114° 73° a photon has linear momentum. a photon has energy. a photon has angular momentum. a photon has parity. a photon has mass. Characteristic x-rays can be produced by bombarding targets with electrons. These x-rays occur when a. b. c. d. electrons from higher shells fill the vacant lower shell electrons fill the vacant valence shell photons are emitted with energies on the order of 103 eV photons are emitted with wavelengths on the order of 103 nm Atomic Physics 39. The ground state configuration of chlorine (Z = 17) is a. b. c. d. e. 40. 353 1s2 2s2 2p5 3s2 3p6 1s2 2s2 2p6 3s2 3p5 1s2 2s2 2p6 3s2 3p4 3d1 1s2 2s2 2p6 3s2 3p5 4s1 1s2 2s2 2p6 3s1 3p7 Rubidium (Z = 37) and potassium (Z = 19) are similar to sodium in that they have a. b. c. d. e. five p three p two s one d one s electron(s) in the outermost shell. 41. When electrons fill a subshell in which the orbitals have equal energy, the order in which the orbitals are filled is such that a. b. c. d. e. 42. a minimum number of electrons has unpaired spins. a minimum number of electrons has intrinsic angular momentum. a maximum number of electrons has unpaired spins. a maximum number of electrons first fills the next energy level. the maximum number of electrons has the same set of quantum numbers. In a completely filled atomic shell, a. b. c. d. e. the intrinsic spin of the electrons does not produce a resultant magnetic moment. the orbital motion of the electrons does not produce a resultant magnetic moment. the electrons do not contribute to paramagnetic or ferromagnetic effects. all of the above are correct. none of the above are correct. 43. Which of the following, in which n and m have integer values, is a correct formula for a wavelength emitted by a hydrogen atom? a. b. c. d. e. 44. λ = R H (m 2 − n2 ) 1 = RH m 2 − 2 n 1 1 = RH 2 − m 2 λ n 1 1 1 = RH − λ m n 1 1 1 = RH 2 − 2 λ n m 1 λ In the Bohr model of the hydrogen atom, the total energy of the electron-proton system is a. b. c. d. e. 45. 1 kee2 2r k e2 − e r 0. k e2 + e r k e2 + e 2r − . . . . In terms of a0, where a0 = 0.0529nm , the radii of the allowed orbits in the Bohr model of the hydrogen atom are given by rn = c. d. 1 a0 . n2 a0 . n na0 . na0 . e. n2a0 . a. b. Atomic Physics 46. Quantum physics agrees with the classical physics limit when a. b. c. d. e. 47. 355 the total angular momentum is a small multiple of h . the total energy is a small multiple of the energy in the lowest quantized state. the difference in energy between adjacent quantized levels becomes vanishingly small. all electron spins are paired so that L = 0 . there is a vacancy in an inner level in the atom. The number of electrons in the n = 4 , l = 2 subshell in strontium ( Z = 38) is _____ the number of electrons in the n = 4 , l = 2 subshell in barium ( Z = 56). 2 a. b. c. d. 38 times 56 38 times 56 equal to 56 times 38 2 e. 48. In an atom that has an electron in a sub-shell for which l = 4 , with respect to the magnetic field vector B the magnetic moment vector µ of the electron is allowed to be oriented in a. b. c. d. e. 49. 56 times 38 any direction. l discrete directions l − 1 discrete directions. l + 1 discrete directions. 2l + 1 discrete directions. In an allowed electron transition in a hydrogen atom, a. b. c. d. e. ∆l = 0;m l = 0,±1 . ∆l = 0,±1;m l = ±1. ∆l = 0,±1;m l = 0,±1 . ∆l = ±1;m l = 0,±1. ∆l = ±1;m l = ±1. 50. What is the difference in frequency for spectral lines emitted by hydrogen for transitions from the n=16 level to the n=2 level and transitions from the n=15 level to the n=2 level? ( R H = 1.097 × 10−7 m -1 .) a. b. c. d. e. 51. What is the difference in wavelength for spectral lines emitted by hydrogen for transitions from the n=16 level to the n=2 level and transitions from the n=15 level to the n=2 level? ( R H = 1.097 × 10−7 m -1 .) a. b. c. d. e. 52. 53. 54. 5.65 × 10−13 Hz 31 Hz 1.77 × 1012 Hz 2.55 × 1016 Hz 1.02 × 1017 Hz 1.0 × 10−10 m 2.0 × 10−10 m 4.1 × 10 −10 m 8.1 × 10 −10 m 1.6 × 10−9 m All quantum states forming a shell have the same a. b. c. principal quantum number n. orbital quantum number l . orbital magnetic quantum number m l . d. e. n, l and m l n and l only. All quantum states forming a sub-shell have the same a. b. c. principal quantum number n. orbital quantum number l . orbital magnetic quantum number m l . d. e. n, l and m l n and l only. Adam and Eve are contemplating the beauty of the hydrogen atom. Adam claims that the quantum states with a given value of the principal quantum number n can have any value of the orbital quantum number l . Eve says that the Snake told her that a state with a given value of l could have any value of n. Which one, if either, is correct, and why? a. b. c. d. e. Adam, because the man is always right. Adam because n ≤ l − 1 . Eve, because n ≤ l − 1 . Eve, because l ≤ n − 1 . Neither, because Adam is wrong and the Snake told a subtle lie. Atomic Physics 55. 357 Zeke says that the magnitude of the orbital angular momentum in the hydrogen atom has the value L = lh . Ruth says that the maximum magnitude of the projection of the angular momentum along the direction of a constant magnetic r field vector B is l( l + 1) h . Which one, if either, is correct, and why? a. b. c. d. e. Ruth, because the maximum value of L is l( l + 1) h . Ruth, because the orbital angular momentum always lines up with a r magnetic field so that L has its maximum value along the field. r Zeke, because the maximum magnitude of L is L = lh . Zeke, because the orbital angular momentum always lines up with a r magnetic field so that L has its maximum value along the field. r Neither, because they have interchanged the maximum magnitude of L , l( l + 1) h , and lh , its maximum projection along a magnetic field direction. 56. Aline says that the magnetic moment of an atom originates in the orbital angular momentum of the electron. Bevis says that it comes from the electron spin. Which one, if either, is correct, and why? a. b. c. d. e. 57. Aline, because only atoms, not electrons, can have angular momentum. Bevis, because only atoms, not electrons, can have angular momentum. Neither, because electron spin and orbital angular momentum always cancel exactly. Neither, because the magnetic moment of an atom comes only from the spin of the nucleus. Both, because both the orbital angular momentum and the spins of the electrons contribute to the magnetic moment of an atom. A headwaiter at a restaurant decides to apply the exclusion principle to the seating of patrons. He will treat tables as sub-shells, and will only seat patrons if the number of the people to be seated adds up to a complete sub-shell. Of the numbers below, the number he would not be willing to seat at one table is a. b. c. d. e. 2. 4. 6. 10. 14. Open-Ended Problems 58. Suppose a beam of electrons is incident on a collection of hydrogen atoms, all of which are in the lowest energy state (n = 1). What is the minimum energy the electrons can have if they are to excite the hydrogen atoms into the n = 2 state? 59. The energy difference between the upper and lower levels in a certain laser is 1.9593 eV. What is the wavelength of the light emitted by the laser? 60. A hydrogen atom emits a photon of wavelength 657.7 nm. From what energy state to what lower energy state did the electron jump? Atomic Physics 359 Chapter 42 Atomic Physics 1. d 29. a 2. b 30. d 3. d 4. d 5. b 6. d 7. c 8. b 9. d 10. c 11. a 12. a 13. c 14. a 15. c 16. a 17. d 18. c 19. b 20. d 21. b 22. b 23. c 24. a 25. b 26. a 27. d 28. c Atomic Physics 31. c 32. b 33. b 34. d 35. a 36. a 37. c 38. a 39. b 40. e 41. c 42. d 43. e 44. a 45. e 46. c 47. c 48. e 49. d 50. c 51. d 52. a 53. e 54. e 55. e 56. e 57. b 58. 10.2 eV 59. 634 nm 60. n = 3 to n = 2 361