Understanding Muonium Energy Levels and Relativistic Velocities

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Homework Help Overview

The discussion revolves around the energy levels of muonium, an atom composed of a proton and a muon, and how these levels compare to those of hydrogen. Participants explore the implications of the muon's greater mass and its effect on energy levels and velocities, particularly in relation to relativistic effects.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants examine the concept of reduced mass in muonium versus hydrogen and its impact on energy levels. Questions arise regarding the relationship between the mass of the muon and the energy required to maintain its orbit. There is also inquiry into the de Broglie wavelength and velocities of muons compared to electrons, as well as considerations of relativistic speeds.

Discussion Status

The discussion is active, with participants raising questions and exploring various interpretations of the concepts involved. Some have provided references to external resources for further clarification, while others are contemplating the implications of mass on energy levels and velocities.

Contextual Notes

Participants are considering the effects of mass on energy levels and velocities, with specific attention to relativistic speeds. There is an acknowledgment of the need to visualize these concepts, particularly in relation to the heavier muon compared to the electron.

physgirl
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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?
 
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physgirl said:
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?

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

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