# Radius of bound states (Bohr)

1. Oct 25, 2007

### Ewok

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

Hi I'm having difficulty in understanding how to calculate the radius for certain situations.

for example, I have a question that asks me to calculate the radius and binding energy of muonic hydrogen.

2. Relevant equations

3. The attempt at a solution
my first instincts were to use and re-arrange the following formula
(Me v^2)/r = (e^2)/(4pi(r^2) epsilon)

re-arranging this to make r the focus and simply multiplying the electron mass by 207 to make it the muon mass.

I don't think this is correct however - seems a bit of a flaky way of doing it.

I do also have equations for the expectation values - which I presume to be the expected values for the location of the muon (and hence possibly the radius), but I'm unsure of how to apply these to the question.

I also have to apply this to other situations other than a straight hydrogen atom, so any advice would be appreciated.

Thanks

2. Oct 25, 2007

### javierR

For "hydrogenic" atoms, you can look at how the mass of the electron came into the Bohr radius estimation, and replace with the muon...but you might notice that the analysis used the fact that the mass of the electron is much less than the proton's, so the orbital motion could be approximated by a fixed center and an electron in circular motion. Since a muon is a much heavier version of an electron, it is better to describe the muon and proton as orbiting about each other, and you use a "reduced mass".