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Angular momentum of this classical electron?

  1. Aug 16, 2012 #1
    1. The problem statement, all variables and given/known data
    a classical electron moves in a circle of radius 0.5mm with velocity 20ms-1
    what is the value of the quantum number L which gives a quantised angular momentum close to the angular momentum of this classical electron?


    2. Relevant equations

    L=r * p

    3. The attempt at a solution

    L=r*p
    500e-6 * 20=0.010
     
  2. jcsd
  3. Aug 16, 2012 #2
    You need to throw in the equation for quantum angular momentum.
     
  4. Aug 16, 2012 #3
    is it L=[itex]\sqrt{l(l+1)hbar}[/itex]
     
  5. Aug 16, 2012 #4
    is it possible to find the value of the quantum number "l" (azimuthal quantum number)?
     
  6. Aug 16, 2012 #5
    Check the dimensions in that formula.
     
  7. Aug 16, 2012 #6
    do i have to presume that n=1 before i continue the calculation, because there is no mention of principal quantum number in the question?
     
  8. Aug 16, 2012 #7
    The description says "classical electron". So I guess you should use Bohr's model here. What is the angular momentum in Bohr's model?
     
  9. Aug 16, 2012 #8
    the lowest value for n is 1, this gives the smallest orbital radius 0.0529nm(bohr radius)
    L=r*p=mvr m=9.1e-31, v=20m/s r=0.5nm
    mvr=nhbar

    L=n h/2pi=nhbar
     
  10. Aug 16, 2012 #9
    I think you should use the latter formula to determine n that gives the closest match of L to that of the classical electron.
     
  11. Aug 16, 2012 #10
    can you explain that again please
     
  12. Aug 16, 2012 #11
    You can compute the angular momentum from the radius and velocity given.

    You have the formula for the angular momentum in Bohr's model. What n gives the closest fit between the two?

    You could also consider the other formula, involving the square root of l(l + 1). For large n, and correspondingly large l, what can be said about the results given by these two equations?
     
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