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!

The allowed radii and energies of positronium

Tags:
  1. May 3, 2015 #1

    squelch

    User Avatar
    Gold Member

    1. The problem statement, all variables and given/known data

    Positronium is a hydrogen-like atom consisting of a proton and an electron revolving around each other. Find the allowed radii and energies of the system.

    2. Relevant equations

    See solution attempt.

    3. The attempt at a solution

    The allowed radii of the positron/electron system are given by [itex]r = \frac{{4{n^2}\pi {\varepsilon _0}{\hbar ^2}}}{{\mu {e^2}}}[/itex] where [itex]\mu = \frac{{{m_{positron}}{m_e}}}{{{m_{positron}} + {m_e}}}[/itex] and n={1,2,3,...}

    The allowed energies of the positron/electron system are given by [itex]{E_n} = - \frac{{\mu {e^4}}}{{2{n^2}{{(4\pi {\varepsilon _0})}^2}{\hbar ^2}}}[/itex]

    It just seemed suspiciously simple. Is this all they're really asking me to state? I mean, other than calculating it all out and leaving it as a function of n times a constant.
     
  2. jcsd
  3. May 3, 2015 #2

    squelch

    User Avatar
    Gold Member

    Just in case that was what I needed to do, I calculated the following allowable radii and energies, using the reduced mass:

    [tex]\begin{array}{l}
    {r_n} = {n^2}(1.05835 \times {10^{ - 10}} m)\\
    {E_n} = \frac{1}{{{n^2}}}( - 6.8032eV)
    \end{array}[/tex]
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: The allowed radii and energies of positronium
  1. Earth Radii? (Replies: 15)

  2. Help with Positronium (Replies: 1)

  3. Positronium Decay (Replies: 1)

Loading...