General Formula for atomic emission spectra

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SUMMARY

A general Rydberg-like formula does not exist for predicting the emission spectrum wavelengths of any atom due to the complexity of non-trivial quantum many-body systems. Unlike hydrogen, which is a two-body system allowing for exact integration, other atoms require numerical calculations of their wave functions, accounting for electron-electron and electron-nucleus interactions. While approximate or fitted formulas may be developed for specific atoms, their effectiveness can vary significantly based on the application.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with atomic structure and electron configurations
  • Knowledge of wave functions and their calculations
  • Basic grasp of the Rydberg formula and its applications
NEXT STEPS
  • Research numerical methods for calculating wave functions in quantum systems
  • Explore the Rydberg formula and its limitations in multi-electron atoms
  • Study electron-electron and electron-nucleus interactions in quantum mechanics
  • Investigate approximate models for atomic transitions in complex atoms
USEFUL FOR

Physicists, quantum chemists, and students studying atomic physics who are interested in the complexities of atomic emission spectra and the limitations of existing formulas.

rayclan
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hi everyone!

does a general Rydberg-like formula exist to predict the emission spectrum wavelengths of any atom?

if not, why?
 
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No. Apart from hydrogen, atoms are non-trivial quantum many-body systems. Calculating their properties requires an actual numerical calculation of their wave functions, taking all the electron-electron and electron-nucleus interactions into account. Of course, one could maybe get an approximate or fitted formula for transitions of some atoms, which might or might not work well enough for a given application.

It is really just luck that there is a simple formula for hydrogen. It works because the H system is a two-body system (nucleus and one electron, nothing else) and such systems can be integrated exactly.
 

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