De-Broglie's explanation on Bohr's Angluar Momentum quantization?

  1. Apr 18, 2013 #1
    In order to understand about De-Broglie's explanation on Bohr's second postulate,concept of standing waves should be understood.
    But condition of λ for a given value of length(string) L is given by L=nλ/s where n =1,2,3 etc.
    But for a string whose ends are connected together and its shape is like a ring and let the radius of ring be r. Then standing waves condition is given by
    Circumference = nλ/2
    2∏r = nλ/2.

    But this isn't right.
    it should be 2∏r=nλ

    I am missing something.Please correct me.
     
  2. jcsd
  3. Apr 18, 2013 #2

    sophiecentaur

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    A standing wave can exist if there is one half wavelength around the circumference - in the same way that it can exist in a half wavelength string. It's the equivalent of two waves travelling in opposite directions around the circumference. Only one node is necessary.
     
  4. Apr 18, 2013 #3

    Philip Wood

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    If there were a rope around the circumference, we'd need a whole number of wavelengths in order for the wave pattern to join up properly, without discontinuities. An odd number of half wavelengths won't do - try drawing it.

    Note that this 'rope picture' is nothing like the 'proper' wave function picture, at least not for small values of the principal quantum number, n. Interestingly, for large n, and ell = m = n-1 it gives a remarkably good picture.
     
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