# Muonium energy levels

A muonium is an atom consisting of a proton and a muon. A muon has the same charge as an electron but about 200x the mass of an electron. Conceptually, how does it make sense that the energy of the first orbit of a muonium is more negative than that of a hydrogen? :yuck:

George Jones
Staff Emeritus
Gold Member
A muonium is an atom consisting of a proton and a muon. A muon has the same charge as an electron but about 200x the mass of an electron. Conceptually, how does it make sense that the energy of the first orbit of a muonium is more negative than that of a hydrogen? :yuck:

Compare the the reduced mass of an electron in muonium to the reduced mass of an electron in hydrogen.

Doc Al
Mentor
How does the expression for energy level of the hydrogen atom depend on the mass of the electron? How would you modify it for muonium?

Reduced mass for muonium is much greater than reduced mass for hydrogen...

And expression for energy level that I used was: E=-Rhc/n^2... but R depends directly on reduced mass, so the greater the reduced mass,the greater the R, and therefore the more negative the E...

But I guess I'm wondering how I can picture this in my head. Is it that since muons are heavier than electrons, the proton has to pull on the muon with greater energy to keep it orbiting there and therefore it has more energy? Can I think of it in those terms?

so does this mean the de broglie wavelength is 1/200th of that of an electron?

and the velocity is approx 14 times higher than that of an electron - and if so are we anywhere near relativistic speeds yet?

If two positive muons were bound to one negative muon in the same manner as a h2+ ion (basically an electron cloud separating two protons) what would the result be? would the velocities be relativistic?