SM_chapter42

SM_chapter42 - 42 Atomic Physics Note: In chapters 39, 40,...

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42 Atomic Physics CHAPTER OUTLINE 42.1 Atomic Spectra of Gases 42.2 Early Models of the Atom 42.3 Bohr’s Model of the Hydrogen Atom 42.4 The Quantum Model of the Hydrogen Atom 42.5 The Wave Functions of Hydrogen 42.6 Physical Interpretation of the Quantum Numbers 42.7 The Exclusion Principle and the Periodic Table 42.8 More on Atomic Spectra: Visible and X-ray 42.9 Spontaneous and Stimulated Transitions 42.10 Lasers ANSWERS TO QUESTIONS Q42.1 If an electron moved like a hockey puck, it could have any arbitrary frequency of revolution around an atomic nucleus. If it behaved like a charge in a radio antenna, it would radiate light with frequency equal to its own frequency of oscillation. Thus, the electron in hydrogen atoms would emit a continuous spectrum, electromagnetic waves of all frequencies smeared together. *Q42.2 (a) Yes, provided that the energy of the photon is precisely enough to put the electron into one of the allowed energy states. Strangely—more precisely non-classically—enough, if the energy of the photon is not sufF cient to put the electron into a particular excited energy level, the photon will not interact with the atom at all! (b) Yes, a photon of any energy greater than 13.6 eV will ionize the atom. Any “extra” energy will go into kinetic energy of the newly liberated electron. *Q42.3 Answer (a). The 10.5-eV bombarding energy does not match the 10.2-eV excitation energy required to lift the atom from state 1 to state 2. But the atom can be excited into state 2 and the bombarding particle can carry off the excess energy. *Q42.4 (i) b (ii) g ±rom Equations 42.7, 42.8 and 42.9, we have −= − = + − =+ E ke r r r KU ee e e 22 2 . Then KE = and UE e =− 2 . 489 Note : In chapters 39, 40, and 41 we used u to represent the speed of a particle with mass. In this chapter 42 and the remaining chapters we go back to using v for the symbol for speed.
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490 Chapter 42 *Q42.5 In E nn if = ( ) 13 6 11 22 .e V for E > 0 we have absorption and for E < 0 we have emission. (a) for n i = 2 and n f = 5, E = 286 V (absorption) (b) for n i = 5 and n f = 3, E =− 0 967 V (emission) (c) for n i = 7 and n f = 4, E 0 572 V (emission) (d) for n i = 4 and n f = 7, E = 0 572 V (absorption) (i) In order of energy change, the ranking is a > d > c > b (ii) E hc = λ so the ranking in order of decreasing wavelength of the associated photon is c = d > b > a. *Q42.6 (a) Yes. (b) No. The greatest frequency is that of the Lyman series limit. (c) Yes. We can imagine arbitrarily low photon energies for transitions between adjacent states with n large. Q42.7 Bohr modeled the electron as moving in a perfect circle, with zero uncertainty in its radial coordinate. Then its radial velocity is always zero with zero uncertainty. Bohr’s theory violates the uncertainty principle by making the uncertainty product ∆∆ rp r be zero, less than the minimum allowable h 2 .
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SM_chapter42 - 42 Atomic Physics Note: In chapters 39, 40,...

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