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
71. A plane electromagnetic wave has a maximum electric field of magnitude 2.98 x 10-6 V/m. Find the maximum magnetic field amplitude. ______T
72. In a plane radio wave the maximum value of the electric field component is 6.83 V/m. Calculate (a) the maximum value of the magnetic field component and (b) the wave intensity.
a. ______T
b. ______ W/m^2
73. The maximum electric field 10 m from a point light source is 1.6 V/m. What are (a) the maximum value of the magnetic field and (b) the average intensity of the light there? (c) What is the power of the source?
a. ______T
b. ______ W/m^2
c. ______units

51. The work function of tungsten is 4.50 eV. Calculate the speed of the fastest electrons ejected from a tungsten surface when light whose photon energy is 5.62 eV shines on the surface. (______Km/s)
52. The wavelength associated with the cutoff frequency for silver is 325 nm. Find the maximum kinetic energy of electrons ejected from a silver surface by ultraviolet light of wavelength 253 nm. (_______eV)
53. Light of wavelength 5.46 pm is directed onto a target containing free electrons. Find the wavelength of light scattered at 101° from the incident direction. The electron Compton wavelength is 2.43 x 10-12 m. (_______pm)
54. What (a) frequency, (b) photon energy, and (c) photon momentum magnitude are associated with x rays having wavelength 34.5 pm?
a. _______Hz
b. _______units
c. _______units
55. In an old-fashioned television set, electrons are accelerated through a potential difference of 24.1 kV. What is the de Broglie wavelength of such electrons? (Relativity is not needed.) (_______pm)
56. Singly charged sodium atoms are accelerated through a potential difference of 238 V. (a) What is the momentum acquired by such an ion? (b) What is its de Broglie wavelength (in pm)? The mass of a sodium ion is 3.819 x 10-26 kg.
a. _______units
b. _______pm
57. The wavelength of the yellow spectral emission line of sodium is 590 nm. At what kinetic energy would an electron have that wavelength as its de Broglie wavelength? _______microeV
58. What is the wavelength of (a) a photon with energy 9.0 eV (in nm), (b) an electron with energy 9.0 eV (in nm), (c) a photon of energy 9.0 GeV (in fm), and (d) an electron with energy 9.0 GeV (in fm)?
a. ______nm
b. _______nm
c. _______units
d. _______units
59. A particle of mass 3.1 x 10-27 kg has a potential energy of 7.5 x 10-15 J, independently of its position. If its energy is 12 x 10-15 J, what is its angular wave number? (_____units)
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? ______

31. Cancer cells are more vulnerable to x and gamma radiation than are healthy cells. In the past, the standard source for radiation therapy was radioactive 60Co, which decays, with a half-life of 5.27 y, into an excited nuclear state of 60Ni. That nickel isotope then immediately emits two gamma-ray photons, each with an approximate energy of 1.2 MeV. How many radioactive 60Co nuclei are present in a 7000 Ci source of the type used in hospitals? (Energetic particles from linear accelerators are now used in radiation therapy.) ______units
32. The half-life of a radioactive isotope is 120 d. How many days would it take for the decay rate of a sample of this isotope to fall to 0.58 of its initial rate? (______units)
33. A radioactive nuclide has a half-life of 24.1 y. What fraction of an initially pure sample of this nuclide will remain undecayed at the end of 78.8 y? _____
34. A certain radioactive nuclide decays with a disintegration constant of 0.0143 h-1. (a) Calculate the half-life (in terms of hours) of this nuclide. What fraction of a sample will remain at the end of (b) 4.64 half-lives and (c) 7.69 days?
a. ______units
b. ______
c. ______
35. Plutonium isotope 239Pu decays by alpha decay with a half-life of 24100 y. How many milligrams of helium are produced by an initially pure 13.5 g sample of 239Pu at the end of 19610 y? (Consider only the helium produced directly by the plutonium and not by any by-products of the decay process.) _____units
36. The cesium isotope 137Cs is present in the fallout from aboveground detonations of nuclear bombs. Because it decays with a slow (30.2 y) half-life into 137Ba, releasing considerable energy in the process, it is of environmental concern. The atomic masses of the Cs and Ba are 136.9071 and 136.9058 u, respectively; calculate the total energy released in such a decay. (_____MeV)
37. The isotope 238U decays to 206Pb with a half-life of 4.47 x 109 y. Although the decay occurs in many individual steps, the first step has by far the longest half-life; therefore, one can often consider the decay to go directly to lead. That is, 238U → 206Pb + various decay products A rock is found to contain 4.17 mg of 238U and 2.760 mg of 206Pb. Assume that the rock contained no lead at formation, so all the lead now present arose from the decay of uranium. How many atoms of (a) 238U and (b) 206Pb does the rock now contain? (c) How many atoms of 238U did the rock contain at formation? (d) What is the age of the rock?
a. _______
b. _______
c. _______
d. _______years
38. A radiation detector records 77 x 102 counts in 1.0 min. Assuming that the detector records all decays, what is the activity of the radiation source in (a) becquerels and (b) nanocuries?
a. _______units
b. _______units
39. A 83 kg person receives a whole-body radiation dose of 2.3 x 10-4 Gy, delivered by alpha particles for which the RBE factor is 12. Calculate (a) the absorbed energy (in terms of mJ) and (b) the dose equivalent.
a. _____MJ
b. _____units
40. During the Cold War, the Premier of the Soviet Union threatened the United States with 4.0 megaton 239Pu warheads. (Each would have yielded the equivalent of an explosion of 4.0 megatons of TNT, where 1 megaton of TNT releases 2.6 × 1028 MeV.) If the plutonium that actually fissioned had been 9.61% of the total mass of the plutonium in such a warhead, what was that total mass? (______kg)