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SM_PDF_chapter29

# SM_PDF_chapter29 - Atomic Physics CHAPTER OUTLINE 29.1 29.2...

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797 Atomic Physics CHAPTER OUTLINE 29.1 Early Structural Models of the Atom 29.2 The Hydrogen Atom Revisited 29.3 The Wave Functions for Hydrogen 29.4 Physical Interpretation of the Quantum Numbers 29.5 The Exclusion Principle and the Periodic Table 29.6 More on Atomic Spectra: Visible and X-Ray 29.7 Context Connection Atoms in Space ANSWERS TO QUESTIONS Q29.1 Bohr modeled the electron as moving in a perfect circle, with zero uncertainity 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 ∆ ∆ r p r be zero, less than the minimum allowable h 2 . Q29.2 Fundamentally, three quantum numbers describe an orbital wave function because we live in three- dimensional space. They arise mathematically from boundary conditions on the wave function, expressed as a product of a function of r , a function of θ , and a function of φ . Q29.3 Bohr’s theory pictures the electron as moving in a flat circle like a classical particle described by F ma = . Schrödinger’s theory pictures the electron as a cloud of probability amplitude in the three-dimensional space around the hydrogen nucleus, with its motion described by a wave equation. In the Bohr model, the ground-state angular momentum is 1 h ; in the Schrödinger model the ground-state angular momentum is zero. Both models predict that the electron’s energy is limited to discrete energy levels, given by 13 606 2 . eV n with n = 1 2 3 , , . Q29.4 The term electron cloud refers to the unpredictable location of an electron around an atomic nucleus. It is a cloud of probability amplitude. An electron in an s subshell has a spherically symmetric probability distribution. Electrons in p , d , and f subshells have directionality to their distribution. The shape of these electron clouds influences how atoms form molecules and chemical compounds. Q29.5 The direction of the magnetic moment due to an orbiting charge is given by the right hand rule, but assumes a positive charge. Since the electron is negatively charged, its magnetic moment is in the opposite direction to its angular momentum. Q29.6 The deflecting force on an atom with a magnetic moment is proportional to the gradient of the magnetic field. Thus, atoms with oppositely directed magnetic moments would be deflected in opposite directions in an inhomogeneous magnetic field. Q29.7 Practically speaking, no. Ions have a net charge and the magnetic force q r r v B × e j would deflect the beam, making it difficult to separate the atoms with different orientations of magnetic moments.

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798 Atomic Physics Q29.8 The Stern-Gerlach experiment with hydrogen atoms shows that the component of an electron’s spin angular momentum along an applied magnetic field can have only one of two allowed values. So does electron spin resonance on atoms with one unpaired electron.
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