Hypothetical atom + Rydberg equation

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SUMMARY

The discussion centers on calculating photon wavelengths and energies for a hypothetical atom using the Rydberg equation. The energy levels provided are E4 at -1.0 x 10-19 J, E3 at -5.0 x 10-19 J, E2 at -10 x 10-19 J, and E1 at -15 x 10-19 J. The Rydberg formula, modified for hydrogen-like ions, is essential for these calculations, specifically incorporating the atomic number (Z). Participants seek guidance on applying this equation to determine photon wavelengths and energies for electron transitions.

PREREQUISITES
  • Understanding of the Rydberg equation for hydrogen-like atoms
  • Knowledge of energy level transitions in atomic physics
  • Familiarity with the concept of photon emission and absorption
  • Basic skills in unit conversion, particularly between joules and nanometers
NEXT STEPS
  • Research the modified Rydberg equation for hydrogen-like ions, including the atomic number (Z)
  • Learn how to calculate photon energy using the equation E = hν
  • Study the principles of electron transitions and their implications in spectroscopy
  • Explore examples of energy level calculations for various hydrogen-like ions
USEFUL FOR

Students in physics, particularly those studying atomic structure and quantum mechanics, as well as educators looking for practical examples of the Rydberg equation in action.

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Homework Statement



Consider the following energy levels of a hypothetical atom.
E4 -1.0 10-19 J

E3 -5.0 10-19 J

E2 -10 10-19 J

E1 -15 10-19 J
(a) What is the wavelength of the photon needed to excite an electron from E1 to E4?
_______nm
(b) What is the energy (in joules) a photon must have in order to excite an electron from E2 to E3?
_______J
(c) When an electron drops from the E3 level to the E1 level, the atom is said to undergo emission. Calculate the wavelength of the photon emitted in this process.
_______nm

Homework Equations



1/lambda= R(1/n^2-1/n^2)

The Attempt at a Solution


I have no idea where to start other than that equation... I did the ones that involved hydrogen but I'm stuck on these on... can you point me in the right direction?
 
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This is an almost good equation. Problem is, as written it holds only for a hydrogen atom, while this is an "hydrogen-like" ion. There is a slightly modified version of the formula that includes Z (atomic number) and holds in this case.
 

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