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!

Homework Help: Muonic atom energy

  1. Sep 26, 2008 #1
    1. The problem statement, all variables and given/known data
    A muon is captured by a deuteron to form a muonic atom. Find the energy of the ground state and the first excited state.
    find the wavelength when the transition occurs

    2. Relevant equations
    E[tex]_{n}[/tex] = [tex]\frac{-13.6Z^{2}}{n^{2}}[/tex]

    [tex]\frac{1}{\lambda}[/tex] = R{[tex]\frac{1}{n_{f}^{2}}[/tex]-[tex]\frac{1}{n_{i}^{2}}[/tex]}

    3. The attempt at a solution
    I'm not sure what the n's are for each state. I think [tex]n_{f}[/tex] or ground state = 1 but don't know where to go from here
    Last edited: Sep 26, 2008
  2. jcsd
  3. Sep 26, 2008 #2
    Those equations would be right if you were just talking about the hydrogen atom. All you'd have to do would be to plug the right numbers in. Z=1, n=1 in the ground state... and what number would you give one energy level above the ground state n=1?

    Unfortunately, it's slightly more complicated than that. Where does the number 13.6 come from? And how is this system different from a hydrogen atom?
  4. Sep 26, 2008 #3
    the deuteron is the hydrogen atom, it's [tex]^{2}H[/tex] and the 13.6 is [tex]\frac{ke^{2}}{2a_{o}}[/tex].

    we're not sure how to utilize the equations though. like what is the first excited state? is ground state n=1? how is [tex]n_{i}[/tex] found? once that is found the wavelength should be easy but we're just not sure how determine the excited state, is it n = 2? tough to tell n could = 2,3,4....[tex]\infty[/tex]
  5. Sep 27, 2008 #4
    Yes, the ground state is n=1 like I said above, and n=2 is the first excited state.
    The term you used for the bohr radius is only applicable for the hydrogen atom- a bound state of a proton (or deuteron) and an electron. It's a slight approximation because the reduced mass of the system is very nearly the mass of the electron. This approximation is actually slightly more accurate for a deuteron + electron than for a proton + electron.. But what's the mass of the muon???
    Similarly, you can't use the Rydberg formula for anything other than a common or garden hydrogen atom. Find a version of your first equation that includes a correction for the reduced mass of the system, and convert the difference between the two energy levels to a wavelength.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook