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Electron probabiltiy density

  1. Feb 17, 2012 #1
    Ok im a noob in quantum mechanics so plz keep the level down for me to understand.
    My text gives a graph of probability density(ψ^2) of 1s orbital agaisnt distance r -
    The graph is maximum near the nucleus and then decreases - i always thought electron has max probability at the bohr's radius but the graph seemsto show max near the nucleus. IS it correct.

    Searching at many places i have actually found two graphs - one which shows maximum at nucleus and then it decreases and
    other which shows zero at nucleus and then increases upto a point and then decreases

    Are both different ? Which is correct?
  2. jcsd
  3. Feb 17, 2012 #2

    Jano L.

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    Gold Member

    Hello jd12345,
    in fact both graphs are correct:

    1) The graph of the function with the maximum at the proton gives the probability that the electron is inside small ball-like region of volume [itex]\Delta V[/itex] of physical space located in a distance [itex]r[/itex] divided by that volume: [itex]f_1(r) = \frac{\Delta p}{\Delta V} [/itex].

    2) The graph with the maximum around the Bohr radius gives the probability that the electron is inside a shell of radius [itex]r[/itex] divided by the thickness of the shell: [itex]f_1(r) =\frac{\Delta p}{\Delta r}.[/itex]

    It turns out that for the first psi - function of the hydrogen atom,

    f_1(r) = Ce^{-2r/a_{\mathrm{B}}}

    f_2(r) = 4\pi r^2 f_1(r) = C4\pi r^2 e^{-2r/a_{\mathrm{B}}}.

    where [itex]C[/itex] is a normalization constant and [itex]a_{\mathrm{B}}[/itex] is the Bohr radius.
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