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Chapter 4: Waves and Particles II: Matter Behaving as Waves

Expert-verified
Modern Physics
Pages: 97 - 140
Modern Physics

Modern Physics

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

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65 Questions for Chapter 4: Waves and Particles II: Matter Behaving as Waves

  1. Question: Starting with the assumption that a general wave function may be treated as an algebraic sum of sinusoidal functions of various wave numbers, explain concisely why there is an uncertainty principle.

    Found on Page 133

  2. 10A beam of electrons strikes a barrier with two narrow but equal-width slits. A screen is located beyond the barrier. And electrons are detected as they strike the screen. The "center" of the screen is the point equidistant from the slits. When either slit alone is open,electrons arrive per second in a very small region at the center of the screen. When both slits are open, how many electrons will arrive per second in the same region at the center of the screen?

    Found on Page 134

  3. Question: Analyzing crystal diffraction is intimately tied to the various different geometries in which the atoms can be arranged in three dimensions and upon their differing effectiveness in reflecting waves. To grasp some of the considerations without too much trouble, consider the simple square arrangement of identical atoms shown in the figure. In diagram (a), waves are incident at angle with the crystal face and are detected at the same angle with the atomic plane. In diagram (b), the crystal has been rotated 450 counterclockwise, and waves are now incident upon planes comprising different sets of atoms. If in the orientation of diagram (b), constructive interference is noted only at an angle, θ=40°at what angle(s) will constructive interference be found in the orientation of diagram (a)? (Note: The spacing between atoms is the same in each diagram.)

    Found on Page 134

  4. The setup depicted in Figure4.6is used in a diffraction experiment using X-rays of0.26 nmwavelength. Constructive interference is noticed at angles of23.0oand,51.4obut none between. What is the spacingdof atomic planes?

    Found on Page 134

  5. A beam of electrons strikes a crystal at an angleθwith the atomic planes, reflects of many atomic planes below the surface, and then passes into a detector also making angleθwith the atomic planes. (a) If the minimumθgiving constructive interference is.35° What is the ratioλ/d, Where is the spacing between atomic planes? (b) At what other angles, if any, would constructive interference occur?

    Found on Page 134

  6. How slow would an electron have to be traveling for its wavelength to be at least1 μm?

    Found on Page 134

  7. A brag diffraction experiment is conducted using a beam of electrons accelerated through a1.0 kVpotential difference. (a) If the spacing between atomic planes in the crystal is0.1nm, at what angles with respect to the planes will diffraction maximum be observed? (b) If a beam ofX-rays products diffraction maxima at the same angles as the electron beam, what is theX-ray photon energy?

    Found on Page 134

  8. Determine the Compton wavelength of the electron, defined to be the wavelength it would have if its momentum weremec.

    Found on Page 134

  9. A particle is “thermal” if it is in equilibrium with its surroundings – its average kinetic energy would be32kBT. Show that the wavelength of a thermal particle is given by

    Found on Page 134

  10. The average kinetic energy of a particle at temperatureTis32kBT. (a) What is the wavelength of a room-temperature (22°C)electron? (b) Of a room-temperature proton? (c) In what circumstances should each behave as a wave?

    Found on Page 134

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