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

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SUMMARY

This discussion focuses on the properties of muonic hydrogen, specifically the calculation of binding energy, the applicability of Rydberg formulas, and the determination of muon momentum. The binding energy for muonic hydrogen is calculated to be approximately 0.068 eV, derived from the relationship that binding energy scales inversely with mass. The Rydberg formula can be adapted for muonic hydrogen by substituting the electron mass with the muon mass, which is about 200 times heavier. This substitution leads to a binding energy that is 200 times smaller than that of ordinary hydrogen, prompting further contemplation on the relationship between mass, binding energy, and photon energy.

PREREQUISITES
  • Understanding of muonic hydrogen and its properties
  • Familiarity with the Rydberg formula and its applications
  • Knowledge of binding energy calculations in quantum mechanics
  • Basic principles of photon energy and momentum
NEXT STEPS
  • Research the derivation of binding energy for muonic hydrogen
  • Explore the adaptation of the Rydberg formula for different particles
  • Study the implications of mass on binding energy and photon energy
  • Investigate the differences between muonic hydrogen and ordinary hydrogen
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Physicists, researchers in quantum mechanics, and students studying atomic structure and particle physics will benefit from this discussion.

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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