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Electric Potential of Hydrogen-like ions

  1. Apr 12, 2008 #1
    1. The problem statement, all variables and given/known data
    Hydrogen-like ions consist of one electron and a nucleus of a charge Ze (Z - the number of protons in the nucleus and e - the charge of an electron). The Bohr model of a hydrogen-like ion states that the single electron can exist only in certain allowed orbits around the nucleus. The radius of each Bohr orbit is: r=(a*n^2)/Z, where a = 0.0529 nm (Bohr'r radius of a hydrogen atom for n=1), n = 1, 2, 3, .... - the number of an allowed orbit (excited level), and Z - the number of protons in the nucleus.

    Note: Express your answers in electron volts. Assume that potential energy PE = 0 at r = (infinity). For the hydrogen-like ion with Z = 3, that is Li+2 ion, determine the potential energy of the electron-nucleus system when the electron is in the

    (a) first allowed orbit, n = 1;
    (b) second allowed orbit, n = 2;
    (c) when the electron has escaped from the atom, r = (infinity).

    Determine the kinetic energy of the electron in the
    (d) first allowed orbit, n = 1;
    (e) second allowed orbit,

    2. Relevant equations
    r=(a*n^2)/Z
    V=kQ/r

    3. The attempt at a solution
    I try plugging in the data into the equations, but I cannot even start a or b.
     
  2. jcsd
  3. Apr 12, 2008 #2
    Show your work, we can't help you if we don't know where you went wrong.
     
  4. Apr 12, 2008 #3
    For a, I've tried doing the following:
    r=(a*n^2)/Z
    r=(0.0529*1^2)/3
    r=0.0176333333

    V=(kQ)/r
    V=(8.99e9*1.6e-19)/0.0176
    V=8.17272727e-8

    eV=V/1.6e-19
    eV=8.1727e-8/1.6e-19
    eV=510,793,750,000

    However, I do not think my attempt is correct at all.
     
  5. Apr 12, 2008 #4
    It's asking for the potential energy, not the potential.
     
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