An electron in a one-dimensional infinite potential

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An electron in a one-dimensional infinite potential

60. An electron in a one-dimensional infinite potential well of length L has ground-state energy E1. The length is changed to L‘ so that the new ground-state energy is E1′ = 0.660E1. 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 7E43 between the levels n4 and n3? (c) Can a pair of adjacent levels have an energy difference equal to 2E43? 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 δx = 5.0 pm centered at x = 310 pm? (Hint: The interval δx 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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