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60. An electron in a one-dimensional infinite potential well of length *L* has ground-state energy *E*1. The length is changed to *L*‘ so that the new ground-state energy is *E*1′ = 0.660*E*1. What is the ratio *L*‘/*L*? ______

61. The ground-state energy of an electron trapped in a one-dimensional infinite potential well is 3.0 eV. What will this quantity be if the width of the potential well is multiplied by 7? _______eV

62. What must be the width (in nm) of a one-dimensional infinite potential well if an electron trapped in it in the *n* = 1 state is to have an energy of 6.1 eV? _______nm

63. An electron is trapped in a one-dimensional infinite potential well. For what **(a)** higher quantum number and **(b)** lower quantum number is the corresponding energy difference equal to the energy difference 7*E*43 between the levels *n*4 and *n*3? **(c)** Can a pair of adjacent levels have an energy difference equal to 2*E*43? If no, then enter 0. If yes, then enter 1.

a. _______units

b. _______units

c. _______units

64. An electron is trapped in a one-dimensional infinite potential well that is 330 pm wide; the electron is in its ground state. What is the probability that you can detect the electron in an interval of width δ*x* = 5.0 pm centered at *x* = 310 pm? (*Hint*: The interval δ*x* is so narrow that you can take the probability density to be constant within it.) (_____units)

65. What is the ratio of wavelength #4 of the Balmer series to wavelength #4 of the Lyman series? (______units)

66. An atom (not a hydrogen atom) absorbs a photon whose associated wavelength is 235 nm and immediately emits a photon whose associated wavelength is 590 nm. How much net energy (in terms of eV) is absorbed by the atom in this process? (______eV)

67. What are the **(a)** energy (in eV), **(b)** magnitude of the momentum, and **(c)** wavelength (in nm) of the photon emitted when a hydrogen atom undergoes a transition from a state with *n* = 5 to a state with *n* = 3?

a. _______nm

b. _______units

c. ______nm

68. An atom (not a hydrogen atom) absorbs a photon whose associated frequency is 6.9 x 1014 Hz. By what amount does the energy (in terms of eV) of the atom increase? (_____eV)

69. What is the intensity of a traveling plane electromagnetic wave if *Bm* is 1.1 x 10-5 T?_____ W/m^2

70. Assume (unrealistically) that a TV station acts as a point source broadcasting isotropically at 1.2 MW. What is the intensity of the transmitted signal reaching a nearby star that is 18 ly away. (An alien civilization at that distance might be able to watch *X Files*.) A light-year (ly) is the distance light travels in one year. _______ W/m^2

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