1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    mfb

    User Avatar
    2016 Award

    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

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    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

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted