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Macroscopic quantum model

  1. Oct 9, 2007 #1
    [SOLVED] Macroscopic quantum model

    I'm supposed to calculate the quantum number of a macroscopic system (The earth and a satellite).

    I should assume that the satellite is moving in a circular motion around earth, and that it fulfills the same quantization conditions as the Bohr model of the Hydrogen atom.

    So far, I started by calculating the total energy of the system, but using a gravitational potential instead of the Coulomb potential, which gives me a total energy of:


    Then, by using the centripetal force and the gravitational force (to find an equilibrium between the two), I got:


    Substituting this into the energy expression gives:


    The total energy then becomes:


    ... After this, I'm stuck. As far as I can see (using the book that I have in this course), Bohr postulated that the emitted radiation from the hydrogen atom has a frequency which is given by:


    ... Where [tex]E_{n}[/tex] is given by:


    My thought was that the total energy expression which I calculated must be for a specific value of n, so what I tried was to set my expression equal to [tex]E_{n}[/tex] and then calculate the quantum number n from this relationship. This yielded:


    ...However, I'm not even sure that this is a reasonable approach. What especially bothers me is the Rydberg Constant. Can I use a standardized value on this, or do I have to recalculate it so that it too depends on a gravitational force?

    I'm really stuck on this one (I think)... Any help is truly appreciated!
  2. jcsd
  3. Oct 9, 2007 #2


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    Bohr used the quantization condition that the angular momentum of the "orbitting" electron be an integer multiple of [itex]\hbar [/itex]. I imagine you are expected to apply the same condition to the orbitting satellite.
  4. Oct 9, 2007 #3
    Well, that sure reduced the calculations a lot :P
    Thanks for the help!
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