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Homework Help: Transition of Calcium Hydrogen-like Ion

  1. Apr 16, 2013 #1
    1. The problem statement, all variables and given/known data

    A hydrogen‑like ion of calcium emits a photon with energy E = 756 eV. What transition was involved?

    2. Relevant equations

    The energy equation: E=Z^2*E_R*(1/n^2-1/n'^2)

    3. The attempt at a solution

    First, Z=20 for a calcium ion, and E_R is the Rydberg energy 13.6 eV. Then I plugged everything in assuming that the electron which emits the photon goes back to the ground state, i.e. n=1.

    However, I get n' ≈ 1.07, which does not seem sensible to me.

    Any ideas or suggestions, please? Much appreciated.

    Note: How do you write down the equations in a neat format on the forums? I'm a newbie so please go easy on me!
  2. jcsd
  3. Apr 16, 2013 #2


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    Staff: Mentor

    If your result is wrong, one of the assumptions is wrong. In this case, the electron does not go back to the ground state.

    Formula formatting -> LaTeX
  4. Apr 16, 2013 #3
    Thank you for the formula formatting guidelines!

    In that case, how do I deduce the transition involved? Because otherwise the problem doesn't state much, unless I'm missing another given assumption.
  5. Apr 16, 2013 #4
    Attempt at the problem

    Ok so I separated the transition term of the equation ##E=Z^2E_R(\frac{1}{n^2}-\frac{1}{n'^2})##: $$\frac{E}{Z^2E_R}=\frac{1}{n^2}-\frac{1}{n'^2}$$

    and knowing that the right hand side's value, I started plugging in values for n for which $$\frac{1}{n'^2}= \frac{1}{n^2}-\frac{E}{Z^2E_R}$$ will still be come out positive.

    I tried for a transition back to the n=2 state and got a close approximation to an integer value n'=9.

    Could someone please check this for me?
  6. Apr 16, 2013 #5


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    Did you consider the square for n'?
    I get a different result with smaller numbers.
  7. Apr 16, 2013 #6
    I did.

    If I consider a transition back to the ground state, I get n' to be some non-integer close to 1, which does not make sense.

    What was your result?
  8. Apr 16, 2013 #7


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    n=2 is right, it fits perfectly to n'=3 and not to 9.
  9. Apr 16, 2013 #8
    Yes, you are right about that! That was my mistake.

    The transition is from n=3 to n'=2. Guess for this problem they wanted you make a reasonable guess.
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