Quantum Physics

Answers to Quick Quizzes, Odd-Numbered Conceptual Questions and Problems A.29light will generally increase the size of the current, butwill not change the energy of the individual electronsthat are ejected. Thus, the stopping potential remainsconstant.11. Wave theory predicts that the photoelectric effect shouldoccur at any frequency, provided that the light intensity ishigh enough. However, as seen in photoelectric experiments,the light must have sufficiently high frequency forthe effect to occur.13. (a) Electrons are emitted only if the photon frequency isgreater than the cutoff frequency.15. No. Suppose that the incident light frequency at whichyou first observed the photoelectric effect is above the cutofffrequency of the first metal, but less than the cutofffrequency of the second metal. In that case, the photoelectriceffect would not be observed at all in the secondmetal.17. The frequency of the scattered photon must decrease,because some of its energy is transferred to the electron.PROBLEMS1. (a) 3 000 K (b) 20 000 K3. 500 nm5. (a) 2.49 10 5 eV (b) 2.49 eV (c) 249 eV7. 2.27 10 30 photons/s9. (a) 2.3 10 31 (b) E/E 4.3 10 3211. (a) 2.24 eV (b) 555 nm (c) 5.41 10 14 Hz13. 234 nm15. 148 days, incompatible with observation17. 4.8 10 14 Hz, 2.0 eV19. 1.2 10 2 V and 1.2 10 7 V, respectively21. 41.4 kV23. 0.078 nm25. 0.281 nm27. 1.78 eV, 9.47 10 28 kg m/s29. 70°31. 1.18 10 23 kg m/s, 478 eV33. (a) 1.2 eV (b) 6.5 10 5 m/s35. (a) 1.46 km/s (b) 7.28 10 11 m37. (a) 10 2 MeV (b) No. With kinetic energy much largerthan the magnitude of the negative potential energy, theelectron would immediately escape.39. 3.58 10 13 m41. (a) 15 keV (b) 1.2 10 2 keV43. 10 6 m/s45. 116 m/s47. 5 200 K; clearly, a firefly is not at that temperature, sothis cannot be blackbody radiation.49. 18.2°51. 1.36 eV53. 2.00 eV55. (a) 0.022 0c (b) 0.999 2c57. (b) 3.72 km/s59. (b) 5.19 10 16 m61. (a) 0.263 kg (b) 1.81 W(c) 0.015 3°C/s 0.919°C/min (d) 9.89 m(e) 2.01 10 20 J (f) 8.98 10 19 photon/sChapter 28QUICK QUIZZES1. (b)2. (a)3. (a) 5 (b) 9 (c) 254. (d)CONCEPTUAL QUESTIONS1. If the energy of the hydrogen atom were proportional to n(or any power of n), then the energy would become infiniteas n grew to infinity. But the energy of the atom is inverselyproportional to n 2 . Thus, as n grows to infinity, the energyof the atom approaches a value that is above the groundstate by a finite amount, namely, the ionization energy13.6 eV. As the electron falls from one bound state to another,its energy loss is always less than the ionization energy.The energy and frequency of any emitted photon are finite.3. The characteristic x-rays originate from transitions withinthe atoms of the target, such as an electron from the Lshell making a transition to a vacancy in the K shell. The vacancyis caused when an accelerated electron in the x-raytube supplies energy to the K shell electron to eject it fromthe atom. If the energy of the bombarding electrons wereto be increased, the K shell electron will be ejected fromthe atom with more remaining kinetic energy. But the energydifference between the K and L shell has not changed,so the emitted x-ray has exactly the same wavelength.5. A continuous spectrum without characteristic x-rays is possible.At a low accelerating potential difference for theelectron, the electron may not have enough energy toeject an electron from a target atom. As a result, there willbe no characteristic x-rays. The change in speed of theelectron as it enters the target will result in the continuousspectrum.7. The hologram is an interference pattern between lightscattered from the object and the reference beam. If anythingmoves by a distance comparable to the wavelengthof the light (or more), the pattern will wash out. Theeffect is just like making the slits vibrate in Young’s experiment,to make the interference fringes vibrate wildly sothat a photograph of the screen displays only the averageintensity everywhere.9. If the Pauli exclusion principle were not valid, theelements and their chemical behavior would be grosslydifferent, because every electron would end up in the lowestenergy level of the atom. All matter would thereforebe nearly alike in its chemistry and composition, since theshell structures of each element would be identical. Mostmaterials would have a much higher density, and the spectraof atoms and molecules would be very simple, resultingin the existence of less color in the world.11. The three elements have similar electronic configurations,with filled inner shells plus a single electron in an sorbital. Since atoms typically interact through their unfilledouter shells, and since the outer shells of theseatoms are similar, the chemical interactions of the threeatoms are also similar.13. Each of the eight electrons must have at least one quantumnumber different from each of the others. They candiffer (in m s ) by being spin-up or spin-down. They can differ(in ) in angular momentum and in the general shapeof the wave function. Those electrons with 1 can differ(in m ) in orientation of angular momentum.15. Stimulated emission is the reason laser light is coherentand tends to travel in a well-defined parallel beam. Whena photon passing by an excited atom stimulates that atomto emit a photon, the emitted photon is in phase with the