1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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 ..
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Quantum Physics Problem Date
Mach-Zehnder Interferometer interpretation Feb 7, 2018
Atoms and quantum physics problem Apr 19, 2013
Quantum Physics help/Electron trap problem Dec 5, 2011
Quantum physics problem Jun 15, 2009
Quantum Physics Problem May 1, 2005