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Homework Help: Bohr model question - transition between first excited state and ground state

  1. May 18, 2012 #1
    1. The problem statement, all variables and given/known data

    In a hydrogenlike ion with atomic number Z, the energies of the allowed states are given by

    E(n) = (-13.6eV) (Z^2/n^2)

    What is the wavelength asociated with the transition between first excited state and ground state of hydrogen-like helium? (He+)

    2. Relevant equations

    E(n) = (-13.6eV) (Z^2/n^2)
    E = hf = hc/Lambda

    3. The attempt at a solution

    Hydrogen like helium is He+ which has 2 protons and 1 electron. Atomic number Z is 2.
    So I'd sub in 2 for Z (4 for Z^2), but I don't know what to choose n as.
    I assume n=1 for ground state and n=2 for first excited state.
    An idea I had was to do it twice - sub in n=1 and complete the equation, sub in n=2 and complete the equation, and... take them away?
    I'm not sure :(

    Thanks very much.
  2. jcsd
  3. May 18, 2012 #2
    n is the principle quantum number, which goes like, n = 1 for ground state, 2 for 1st excited state, 3 for 2nd excited state and so on, so your assumption is correct. Now you'll have the energies for both the ground and first excited states. So, doing the second step you suggested would be correct, too. You need the difference in their energy states, after all.
  4. May 18, 2012 #3
    Yes, calculate the difference between E(n=1) and E(n=2). That is the energy of the photon. Then find the wavelength that corresponds to that energy.
  5. May 18, 2012 #4
    Thanks both, I understand :)

    One question though, does it give me the (energy) answer in ev? I assume it does since ev is the unit of the -13.6.
    And then, do I need to convert both to Joules, then take them away, and then find corresponding wavelength?

    Thanks again.
  6. May 18, 2012 #5
    Z and n are just plain numbers, without any units, and 13.6 is in eV, so yep. :wink:

    This depends on which kind of values you are using for the equation [itex]E = hc/\lambda[/itex], i.e the unit of c and h. The answer units for [itex]\lambda[/itex] will vary accordingly. Just make sure all the variables, E, h, c have the same type of units, or you'll have to convert them. Its usually a good idea to stick to SI units, though.
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