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Given the ionization energy, find the number of protons

  1. Sep 10, 2011 #1
    1. The problem statement, all variables and given/known data

    A hydrogen like system has ionization energy of 11808 kJ/mol. Find the number of protons in the nucleus.


    2. Relevant equations

    Not sure.

    Should I use the formula En = E1/n2?

    3. The attempt at a solution

    The ionization energy of H is 1312 kJ/mol. The ionization energy of the system is 11808 kJ/mol. Since this is hydrogen like system, it has only one electron in its outer shell and so the effects of electron repulsion can be ruled out. If I try to use the above formula, I am not getting the answer. Or should I use the complicated formula for total energy of the system and then try to find z from it?
     
  2. jcsd
  3. Sep 10, 2011 #2

    kuruman

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    Not quite. Try En=-Z2E1/n2.
     
  4. Sep 10, 2011 #3
  5. Sep 10, 2011 #4
    Thanks, but how do I find Z ?

    En = 11808
    E1 = 1312
    Z = ?
    n = ? (Is it the number of electrons in the outer shell? In that case it would be 1)

    What to do with the negative sign ?
     
  6. Sep 10, 2011 #5
    @ Spinnor: Thanks for the link. I posted before viewing your post.

    Guess n = 1 and then it works out (at least I think so)

    En = E1 * Z2/n2

    11808/1312 = Z2

    Z = 3, which incidentally is the right answer.

    Is my working correct?
     
  7. Sep 10, 2011 #6

    kuruman

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    Z is the number of protons in the nucleus of this atom and n is the lowest energy level from which you remove an electron when you ionize it. In this case n = 1. Do nothing with the negative sign. It just means that you need to add energy to the atom in order to ionize it, i.e. end up with a nucleus and an electron separate from one another.
     
  8. Sep 10, 2011 #7

    kuruman

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    That is correct.
     
  9. Sep 10, 2011 #8
    Thank You, kuruman.
     
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