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**Unformatted text preview: **Chapter 34 Wave-Particle Duality and Quantum Physics Conceptual Problems *1 • Determine the Concept The Young double-slit experiment, the diffraction of light by a small aperture, and the J.J. Thomson cathode-ray experiment all demonstrated the wave nature of electromagnetic radiation. Only the photoelectric effect requires an explanation based on the quantization of electromagnetic radiation. ( ) correct. is c 2 •• Determine the Concept Since the power radiated by a source is the energy radiated per unit area and per unit time, it is directly proportional to the energy. The energy radiated varies inversely with the wavelength ( λ hc E = ); i.e., the longer the wavelength, the less energy is associated with the electromagnetic radiation. ( ) correct. is b 3 • ( a ) True ( b ) False. The work function of a metal is a property of the metal and is independent of the frequency of the incident light. ( c ) True ( d ) True 4 • Determine the Concept In the photoelectric effect, the number of electrons emitted per second is a function of the light intensity, proportional to the light intensity, independent of the work function of the emitting surface and independent of the frequency of the light. ( ) correct. is b *5 • Determine the Concept The threshold wavelength for emission of photoelectrons is related to the work function of a metal through t λ φ hc = . Hence φ λ hc = t and ( ) correct. is a 1083 Chapter 34 1084 6 •• Determine the Concept In order for electrons to be emitted hc / λ must be greater than φ . Evidently, hc / λ 1 < φ , but hc / λ 2 > φ . 7 • ( a ) True ( b ) True ( c ) True ( d ) False. Electrons are too small to be resolved by an electron microscope. 8 • Determine the Concept If the de Broglie wavelengths of an electron and a proton are equal, their momenta must be equal. Since m p > m e , v p < v e . Response ( c ) is correct. 9 • Picture the Problem The kinetic energy of a particle can be expressed, in terms of its momentum, as m p K 2 2 = . We can use the equality of the kinetic energies and the fact that m e < m p to determine the relative sizes of their de Broglie wavelengths. Express the equality of the kinetic energies of the proton and electron in terms of their momenta and masses: e 2 e p 2 p 2 2 m p m p = Use the de Broglie relation for the wavelength of matter waves to obtain: 2 e e 2 2 p p 2 2 2 λ λ m h m h = or 2 e e 2 p p λ λ m m = Since m e < m p : 2 e 2 p λ λ < and p e λ λ > and ( ) correct. is c 10 • Determine the Concept Yes. < x > can equal a value for which P ( x ) is zero. An example is the asymmetric well for all even numbered states. Wave-Particle Duality and Quantum Physics 1085 *11 • Determine the Concept In the photoelectric effect, an electron absorbs the energy of a single photon. Therefore, K max = hf − φ , independently of the number of photons incident on the surface. However, the number of photons incident on the surface determines the number of electrons that are emitted. number of electrons that are emitted....

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