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Probablity density of 1s in hydrogen atom

  1. Feb 12, 2010 #1
    I have two asks
    first ask :
    In plot of probablity density of 1s electron of hydrogen atom
    when r=0 where electron exist ?
    is inside nucleus?! how happen this

    second ask
    what is the reduis of electron ri? and what reduis of nucleos RI is ? in Hamltonain operator
    i mean the defination of r for (electron) and R for( nucleus)
  2. jcsd
  3. Feb 12, 2010 #2
    Here is (I think) an estimate for the probability of the electron in a 1s hydrogen orbit being inside the proton (hydrogen nucleus).

    The probability of the electon being "inside the proton" according to perturbation theory is (using Dirac notation)

    P = <Re(r) l Rp(r) l Re(r)>

    where Re(r) is the 1s electron radial wave function and Rp(r) is the proton radial charge distribution.

    Using Re(r=0) = 2/a03/2

    where a0 = Bohr radius and proton radius = Rp

    we get

    P = [STRIKE][4/a03][4 πRp3/3][/STRIKE] = [4/a03][Rp3/3]

    Note that the probability is unitless. For muonic atoms, where a muon has replaced the electron in the 1s orbit, the muon in high-Z muonic atoms spends much of its time inside the nucleus.

    Bob S
    Last edited: Feb 12, 2010
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