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Line spectra and Bohr's model

  1. Apr 25, 2007 #1
    1. The problem statement, all variables and given/known data
    Is it possible to use electromagnetic radiation to ionize atoms. To do so, the atoms must absorb the radiation, the photons of which must have enough energy to remove an electron from an atom. What is the longest radiation wavelength (nm) that can be used to ionize the ground state hydrogen atom?



    2. Relevant equations
    Lyman Series:
    1/lambda = R {(1/nf^2) - (1/ni^2)}



    3. The attempt at a solution
    According to my notes, the lyman series consists of transitions TO the ground state (n=1) starting with the first excited state (n=2). What i am having trouble with here is that when they say "What is the longest wavelength that can be used to ionize the ground state hydrogen?" Are they asking what wavelength of radiation will cause hydrogen to go from n=1 to n=0? Should i be using the Balmer or Paschen series instead of the Lyman? I know how to work the math part of the problem but i am confused as to what values i should be using for n.
     
  2. jcsd
  3. Apr 25, 2007 #2

    Dick

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    If you are initially in the ground state, then to remove the electron you need to raise it past all of the bound states. You could sort of say you want to move it to n=infinity.
     
  4. Apr 25, 2007 #3

    Chi Meson

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    What you need to know is the energy defecit of the elctron in the ground state. Each level has a negative energy associated with it. In hydrogen, n=1 , the deficit is -13.6 eV. Guess how much energy the photon must have to free this electron?

    For the Lyman formula to work, you are going from energy level 1 to energy level "infinity," not to zero.

    edit: Dang. Beat again.
     
    Last edited: Apr 25, 2007
  5. Apr 25, 2007 #4
    how does this look?

    lambda = R [(1/infinity)-(1/1^2)]^-1
    lambda= 9.12x10^-8 meters or 91.2 nm
     
  6. Apr 25, 2007 #5

    Chi Meson

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    Nope. It's 91.3 nm:biggrin:
     
  7. Apr 25, 2007 #6
    got it right finally. thanks
     
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