Positronium emitted wavelengths

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SUMMARY

The discussion focuses on calculating the emitted wavelengths of positronium and their comparison to hydrogen atom emissions. The user correctly applies the concept of reduced mass, using the formula (M/m+M)Rinf=Rm to model the electron's orbit around the positron. By integrating this new value of Rm with the Balmer formula, the user concludes that the emitted wavelengths of positronium would be double those of hydrogen, assuming an infinitely heavy nucleus. This approach confirms the theoretical understanding of positronium's spectral lines.

PREREQUISITES
  • Understanding of quantum mechanics and atomic structure
  • Familiarity with the concept of reduced mass in two-body systems
  • Knowledge of the Balmer formula for hydrogen spectral lines
  • Basic grasp of positronium as a bound state of an electron and positron
NEXT STEPS
  • Study the derivation of the reduced mass formula in quantum mechanics
  • Explore the Balmer series and its applications in spectroscopy
  • Research the properties and behavior of positronium in quantum physics
  • Investigate the implications of comparing spectral lines of different atomic systems
USEFUL FOR

Students and researchers in quantum physics, physicists studying atomic interactions, and anyone interested in the spectral analysis of exotic atoms like positronium.

stefan.t1990
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Hey everyone so I'm having some trouble figuring out how to approach this question. I don't need a step by step solution just an idea of how I should approach the question and maybe some specifics on how to apply needed concepts such as reduced mass. Thank you.

"Assuming positronium were a normal atom, show that the wavelengths of the emitted lines would be double those emitted by a hydrogen atom ( assuming an infinitely heavy nucleus)."
 
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I used reduced mass to model the electron as orbiting the nucleus(positron). I used the formula: (M/m+M)Rinf=Rm, and then used the new value of Rm along with the Balmer formula to obtain emitted wavelengths. Can somebody confirm this is correct?
 

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