Photoelectric effect and Rydberg's formula

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SUMMARY

The discussion centers on the application of Rydberg's formula to determine the energy of a gamma ray that ejects an electron during a 2s to 1s electronic transition in germanium. A peak energy of 134.2 keV is observed using a germanium detector, correlating with the x-ray emission. The Rydberg constant is specified as Rhc = 13.61 eV, which is essential for calculating the wavelength and subsequently the energy of the emitted gamma ray using the equation E = hc/lambda.

PREREQUISITES
  • Understanding of Rydberg's formula for spectral lines
  • Familiarity with the concepts of energy transitions in atoms
  • Knowledge of Planck's constant and the speed of light
  • Basic skills in solving equations related to energy and wavelength
NEXT STEPS
  • Study the derivation and applications of Rydberg's formula in various atomic models
  • Learn how to calculate energy transitions in hydrogenic atoms
  • Explore the principles of gamma ray emission and detection techniques
  • Investigate the relationship between energy, wavelength, and frequency in electromagnetic radiation
USEFUL FOR

Physicists, students studying quantum mechanics, and anyone interested in atomic transitions and gamma ray spectroscopy will benefit from this discussion.

iuchem16
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A peak in the energy spectrum is seen at 134.2 keV when using a germanium detector. In coincidence with this, an x-ray corresponding to the 2s to 1s electronic transition in germanium is detected. Find the energy (in keV) of the gamma ray that ejected the electron.

Use Rydberg's formula for spectral lines of hydrogenic atoms:

1/lambda = R Z2 ( ( 1/n12) - ( 1/n22) )

where R, the Rydberg constant, is such that Rhc = 13.61 eV
(c is the speed of light, h is Planck's constant).




not really sure where to begin, do I solve for the wavelength and use that in the energy equation E=hc/lambda??
 
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You might want to substitute the above equation into the equation for energy that you mentioned. Especiay since you are given R in terms of Rhc
 
nevermind..i got it...thanks!
 

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