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First Bohr Radius - Quantum and Atomic Model

  1. Nov 21, 2012 #1
    1. The problem statement, all variables and given/known data

    Suppose an electron was bound to a proton, as in the hydrogen atom, but by the gravitational force rather than by the electric force. What would be the radius of the first Bohr orbit?

    2. Relevant equations

    r = h^2 / 4∏^2*mke^2

    3. The attempt at a solution

    I'm not sure how to manipulate the above equation to account for gravitational force. Should I start by looking at that fact

    F = ma
    kZe^2/r^2 = mv^2/r
     
  2. jcsd
  3. Nov 21, 2012 #2

    ehild

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    Replace the electric force by the gravitational one. What is the force of gravity between two masses? (It is the mass of the proton and the mass of the electron now).

    ehild
     
  4. Nov 21, 2012 #3
    Ah, so F = km1m2/r^2 ?

    Which means...

    F = ma
    km1m2/r^2 = mv^2/r
     
  5. Nov 21, 2012 #4

    ehild

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    "k" must be the gravitational constant, usually denoted by G.
    So what do you get for r?

    ehild
     
  6. Nov 24, 2012 #5
    r = Gmm/mv^2

    The question I now have is which mass will cancel as I have a mass in the numerator and denominator...
     
  7. Nov 25, 2012 #6

    ehild

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    Which particle orbits around the other?

    ehild
     
  8. Nov 25, 2012 #7
    The electrons orbit around the protons so does this mean the electron mass will cancel out?
     
  9. Nov 25, 2012 #8

    ehild

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    It needs the centripetal force, so the term mv^2/r refers to the
    electron.


    ehild
     
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