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!

Average Separation of Proton

  1. Nov 3, 2013 #1
    Average Separation of Muon and Proton

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

    A muon is a particle with a mass of 206.7 me where me is the electron mass, and with the same charge as an electron. It can be captured in "orbit" by a proton to form a muonic hydrogen atom.
    a. Find the average separation <r> of proton and muon in the ground state of the system (in meters).

    b. Determine the minimum and maximum bound state transition energies to the ground state of the system, in eV.

    2. Relevant equations

    normal hydrogen atom

    Y00 = √(1/4pi)
    Y01 = √(3/(4pi)cos(θ)
    Y1±1 = √(3/(8pi))sinθe^(±iθ)

    3. The attempt at a solution

    a. For the electron, the average separation would be ∫R10rR10r2dr
    Now for the muon, is it simply a plug-in of the Bohr radius a = 4∏ε0[STRIKE]h[/STRIKE]/(206.7*m*e2)?

    b. I'm actually not sure how to approach this. Would it be something like doing <Y01|H|Y00>? I could be totally off.

    Thanks for any input.
    Last edited: Nov 3, 2013
  2. jcsd
  3. Nov 3, 2013 #2


    User Avatar
    2017 Award

    Staff: Mentor

    (a) is similar to the electron problem, and the distance just scales as the Bohr radius, indeed.
    (b) what are the energy levels of the muon?

    You don't need any wavefunctions here.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted