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Text book mistake?

  1. Feb 10, 2010 #1
    This is a question from a chem text book but it seems relevant to electrodynamics/quantum mechanics. The energy to ionize a hydrogen atom in its ground state is given by:

    En = -Rhc / n2

    Ei = Rhc (because the electron is being taken to infinity) = 1312kJ/mol

    The book claims that to ionize a He+ ion (which has 2 protons in its nucleus) would require 4 times the amount of energy. However the potential energy of two charges separated by distance r is given by

    P.E. = kq1q2/r

    Since the charge of an electron is the same in both cases (the H atom and the He ion) and the nuclear charge is doubled in the case of the He+ ion- shouldn't the P.E. at infinity (therefore ionization energy) also double? (not quadruple as the book claims!)
  2. jcsd
  3. Feb 10, 2010 #2

    Doc Al

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    Staff: Mentor

    The book is correct. To a rough approximation, the energy depends on the square of the number of protons.
  4. Feb 10, 2010 #3
    Thanks for your reply. Why does it depend on the square of the number of protons? Doesn't that contradict the equation below?

    P.E. = kq1q2/r
  5. Feb 10, 2010 #4

    Physics Monkey

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    Hi p.tryon,

    You may find it useful to think about how the effective value of [tex] r[/tex] in your equation depends on the number of protons.
  6. Feb 10, 2010 #5

    Doc Al

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    Staff: Mentor

    No, there's no contradiction. In the Bohr model of the atom, realize that r is inversely proportional to Z (the number of protons) so the total energy ends up being proportional to Z². (You might want to review how energy levels are derived in the Bohr model, which is admittedly only an approximation for multi-electron atoms. But it's OK for this purpose with helium, since there are only two electrons.)
  7. Feb 10, 2010 #6
    Hello! Wow I see thank you! That makes sense
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