Questions about Muonic Hydrogen: Binding Energy, Rydberg Formulas & Momentum

[Myslius]

I have a few questions about muonic hydrogen:
How to calculate the binding energy?
Is there Rydberg formula analog for muonic hydrogen?
Is there a way to calculate muon momentum (similar like the electron has, 2.730 e-22 kg m/s)?

 

[jtbell]

Find a formula for whatever quantity you're interested in, that contains the electron mass (for ordinary hydrogen). For example, Rydberg's constant can be written in terms of the electron mass and other constants. Replace the electron mass with the muon mass.

 

[Myslius]

Muon is approximately 200 heavier than electron. If I replace electron mass with muon mass I get that binding energy is 200 smaller (13.6 eV / 200). That doesn't make any sense to me. How come 200 times heavier muon, who is 200 closer can have 200 smaller binding energy? That does look similar to strong force.

 

[Vanadium 50]

If I replace electron mass with muon mass I get that binding energy is 200 smaller

Try it and see.

 

[Myslius]

if m is 200 times bigger, wavelength is 200 smaller, so the binding energy is 200 smaller too. Lyman limit for electron-hydrogen atom is 91.2 nm, which corresponds to 13.6eV. Binding energy from Rydberg formula is 13.6 eV / 200

 

[jtbell]

if m is 200 times bigger, wavelength is 200 smaller,

Correct.

so the binding energy is 200 smaller too.

Incorrect. Hint: what is the energy of a photon proportional to, in general?

 

[Myslius]

Ah yes, 13.6 eV * 200. I need to contemplate the answer.