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Homework Help: Quantum Physics Problem

  1. May 1, 2010 #1
    1. The problem statement, all variables and given/known data

    A particle of charge q and a mass m, moving with a constant speed v, perpendicular to a constant magnetic field B, follows a circular path. If in this case the angular momentum about the center of this circle is quantized so that [tex]mvr_n = 2nh[/tex], determine the allowed radii for the particle in terms of n, h, q, and B for n = 1,2,3,....

    2. Relevant equations

    [tex]F = qvBsin\vartheta [/tex]

    3. The attempt at a solution

    As far as I can tell, this has something to do with relating magnetism to the quantum level. It is easy enough to calculate the radius at a given energy level by solving for [tex]r_n[/tex]. But I do not understand how to relate the charge and the B field to the situation. The best I can come up with is the formula provided... I feel like there is some way it ties into the problem. Help greatly appreciated.
     
  2. jcsd
  3. May 1, 2010 #2

    kuruman

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    Use the relevant equation you have provided to write Newton's Second Law, F = ma. What is the acceleration for circular motion?
     
  4. May 2, 2010 #3
    [tex]\frac{mv^2}{r_n} = qVB sin \vartheta [/tex]

    [tex]sin \vartheta = 0[/tex] as the angle of the particle with the B field is 90 degrees.

    So, simplifying I get,

    [tex]r_n = \frac{mv}{qB} [/tex]

    How do I tie in this equation with the above?
     
    Last edited: May 2, 2010
  5. May 2, 2010 #4
    try to use your original equation mvr = 2nh again in the last equation to get red of mv ..
     
  6. May 2, 2010 #5
    I think I see it now.

    [tex]mv = \frac{2nh}{r_n}[/tex]

    Subbing mv into equation from above [tex]r_n = \frac{mv}{qB} [/tex]

    I get

    [tex]r_n = \frac{2nh}{r_nqB}[/tex]

    A bit more simplification yields [tex]r_n = \sqrt{\frac{2nh}{qB}}[/tex]

    Is that correct?
     
  7. May 2, 2010 #6
    well, it seems correct to me since you achieved what is required in the question which was asking to write r in terms of n, h, q, and B ..
     
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