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Chapter 7: Quantum Mechanics in Three Dimensions and the Hydrogen Atom

Expert-verified
Modern Physics
Pages: 231 - 288
Modern Physics

Modern Physics

Book edition 2nd Edition
Author(s) Randy Harris
Pages 633 pages
ISBN 9780805303087

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83 Questions for Chapter 7: Quantum Mechanics in Three Dimensions and the Hydrogen Atom

  1. A gas can be too cold to absorb Balmer series lines. Is this also true for the Panchen series? (See Figure 7.5.) for the Lyman series? Explain.

    Found on Page 278

  2. What are the dimensions of the spherical harmonics Θl,ml(θ)Φml(ϕ)given in Table 7.3? What are the dimensions of theRn,l(r)given in Table 7.4, and why? What are the dimensions ofP(r), and why?

    Found on Page 278

  3. Question: Explain to your friend. who has just learned about simple one-dimensional standing waves on a string fixed at its ends, why hydrogen's electron has only certain energies, and why, for some of those energies, the electron can still be in different states?

    Found on Page 278

  4. Question: A particle is trapped in a spherical infinite well. The potential energy is 0for r < a and infinite for r > a . Which, if any, quantization conditions would you expect it to share with hydrogen, and why?

    Found on Page 278

  5. Taking then=3states as representative, explain the relationship between the complexity numbers of nodes and antinodes-of hydrogen's standing waves in the radial direction and their complexity in the angular direction at a given value of n. Is it a direct or inverse relationship, and why?

    Found on Page 278

  6. At heart, momentum conservation is related to the universe being "translationally invariant," meaning that it is the same if you shift your coordinates to the right or left. Angular momentum relates to rotational invariance. Use these ideas to explain at least some of the differences between the physical properties quantized in the cubic three-dimensional box versus the hydrogen atom.

    Found on Page 278

  7. (a) For one-dimensional particle in a box, what is the meaning of n? Specifically, what does knowing n tell us? (b) What is the meaning of n for a hydrogen atom? (c) For a hydrogen atom. What is the meaning of landml?

    Found on Page 279

  8. Can the transition 2s→1s in the hydrogen atom occur by electric dipole radiation? The lifetime of the 2 s is known to be unusual. Is it unusually short or long?

    Found on Page 279

  9. If the constantCxinequation(7-5)were positive, the general mathematical solution would be

    Found on Page 279

  10. For the cubic 3D infinite well wave function

    Found on Page 279

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