Understanding Muonium Energy Levels and Relativistic Velocities

In summary: What would be the result if you had two muons that were not bound to one another?In summary, two muons that are not bound to one another would have extremely high velocities relative to other objects in the vicinity.
  • #1
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? :yuck:
 
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  • #2
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? :yuck:

Compare the the reduced mass of an electron in muonium to the reduced mass of an electron in hydrogen.
 
  • #3
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?
 
  • #4
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?
 
  • #6


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?
 

1. What is Muonium and why is it important in terms of energy levels?

Muonium is an exotic atom consisting of a positively charged muon and an electron. It is important in terms of energy levels because it allows for the study of quantum mechanics and the fundamental forces of nature.

2. How are Muonium energy levels determined and what factors affect them?

Muonium energy levels are determined through spectroscopy experiments, where the energy levels can be measured by observing the absorption or emission of light. The factors that affect Muonium energy levels include the mass of the muon, the strength of the electromagnetic force, and the external magnetic field.

3. What is the significance of the 1S-2S transition in Muonium energy levels?

The 1S-2S transition in Muonium energy levels is significant because it is the most accurately measured energy transition in an atom, with a precision of one part in a trillion. This makes it a valuable tool for testing the predictions of quantum electrodynamics.

4. How do Muonium energy levels compare to those of hydrogen?

The energy levels of Muonium are very similar to those of hydrogen, as both atoms have one electron and are affected by the same fundamental forces. However, Muonium has a lower mass due to the presence of the muon, which can lead to small differences in the energy levels.

5. How do scientists use Muonium energy levels to study the properties of matter?

Scientists use Muonium energy levels to study the properties of matter by comparing the energy levels of Muonium to those of other atoms and molecules. This allows them to make precise measurements and test theories about the fundamental forces of nature and the behavior of matter at the atomic level.

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