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

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Discussion Overview

The discussion revolves around muonic hydrogen, specifically focusing on the calculation of binding energy, the existence of a Rydberg formula analog for muonic hydrogen, and the calculation of muon momentum. The scope includes theoretical aspects and mathematical reasoning related to these concepts.

Discussion Character

  • Exploratory
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • Participants inquire about how to calculate the binding energy of muonic hydrogen.
  • There is a suggestion to find a formula for quantities of interest that incorporates the electron mass and to replace it with the muon mass.
  • One participant expresses confusion over the idea that a muon, which is approximately 200 times heavier than an electron, would lead to a binding energy that is 200 times smaller, questioning the logic behind this relationship.
  • Another participant attempts to clarify that if the mass is 200 times larger, the wavelength would be 200 times smaller, suggesting that this would also imply a smaller binding energy.
  • There is a correction offered regarding the relationship between mass and binding energy, prompting further contemplation on the energy of a photon.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the implications of the muon mass on binding energy, with some arguing for a direct proportionality while others challenge this reasoning. The discussion remains unresolved regarding the correct interpretation of these relationships.

Contextual Notes

Participants express uncertainty about the assumptions underlying the calculations and the relationships between mass, wavelength, and binding energy. There are unresolved mathematical steps in the reasoning presented.

Myslius
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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)?
 
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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.
 
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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.
 
Last edited:
Myslius said:
If I replace electron mass with muon mass I get that binding energy is 200 smaller

Try it and see.
 
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
 
Last edited:
Myslius said:
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?
 
Ah yes, 13.6 eV * 200. I need to contemplate the answer.
 

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