Physics 10: Additional HW 7 Problems


In addition to the problems from the book: 26.E.3, 26.E.4, 26.E.10, 26.E.14, 26.E.38, 26.P.4, 31.E.4, 31.E.9, the following four problems are a part of the required homework.

  1. Your cell phone likely operates at a frequency of around 1.1 GHz (1.1×109 Hz). Convert this to a wavelength, and take a quarter of that to arrive at the ideal size for a cell phone antenna. What is the antenna size you get? Draw this length on the page (hint: if it is hard to draw, you've done something wrong).
  2. If you want to see individual atoms with visible light, you may be disappointed. In order to resolve something like an atom, the effective wavelength of the probing source must be smaller than the scale of the atom. Visible light has a wavelength around 550 nm (nanometers). Atoms are typically about a tenth of a nanometer in scale. So it won't work. All we can hope to do with visible light is resolve large blobs of atoms. About how many atoms across would the smallest blob resolvable to visible light be? Any smaller than this and a visible-light microscope is of no use.
  3. To see things smaller than the wavelength of light, we often use electrons as the probe (electron microscope), which via particle-wave duality have an effective wavelength (called de Broglie wavelength) that is λ = h/p, where h = 6.63×10-34 J·s is Planck's constant, and p = mv is the particle momentum. If the mass of an electron is m = 9×10-31 kg, how fast must it be traveling to probe a size scale of an atom (10-10 meters)? Make sure the units work out. The speed works out to be quite significant (more than 1% the speed of light!). You can imagine this is a disruptive way to probe small scales—in fact, it's too disruptive to really work: we use other means to see the atomic scale.
  4. Explain why the Heisenberg uncertainty principle is not a matter of sloppy measurements, but relates to a fundamental limit to how well one can simultaneously know a particle's position and momentum (velocity). (Note: this is not entirely unrelated to the previous problem.)

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