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Hydrogen atom: potential well and orbit radii

  1. Feb 22, 2014 #1
    Hello,

    I happened to open up an old book by Sah, and in it he says:

    "it is evident that the electron orbit radius is half the well radius at the energy level [itex]E_n[/itex]"

    The orbit radius is [itex]r_n=\frac{4*\pi*ε_0*\hbar^2*n^2}{mq^2}[/itex] and the potential well [itex]V(r_n)=\frac{-q^4*m}{(4*\pi*ε_0)^2*\hbar^2*n^2}[/itex]

    Of course the orbit radius has to be confined in the well, but it's not obvious to me why it should be exactly half the well radius? This isn't something I recall seeing before either.

    Thanks
     
  2. jcsd
  3. Feb 22, 2014 #2

    jtbell

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    Staff: Mentor

    What does "well radius" even mean in this context? I've never seen anyone talk of the "radius" or "width" of a 1/r potential well; it extends from r = 0 to r = ∞.
     
  4. Feb 22, 2014 #3
    He's speaking of the width of the potential well due to the nucleus at the specific energy levels [itex]E_n[/itex]. So that apparently [itex]r_1[/itex] of the electron is half of the width of the potential well itself at [itex]E_1[/itex], or the well would be twice the Bohr radius.

    Attached diagram he uses where he has drawn the orbit radius to be half that of the well. When I just add it to the post it is far too small to be useful.
     

    Attached Files:

    Last edited: Feb 22, 2014
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