Wavelength, emission spectrum, electron transitions

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SUMMARY

The wavelength of the emission spectrum line for the He+ ion during the transition from n = 3 to n = 1 is calculated using a modified Rydberg equation. The initial calculation yielded 102.6 nm, which is incorrect; the correct wavelength is 25.6 nm. This discrepancy arises because the Rydberg constant for He+ differs from that of hydrogen due to its +2 charge, necessitating the use of a specific formula for multi-electron ions.

PREREQUISITES
  • Understanding of the Rydberg equation for hydrogen and its modifications for multi-electron ions.
  • Knowledge of electron transitions and energy levels in atomic physics.
  • Familiarity with the concept of emission spectra and their significance in spectroscopy.
  • Basic mathematical skills for manipulating equations and performing calculations.
NEXT STEPS
  • Research the modified Rydberg constant for He+ ions and its derivation.
  • Study the Lyman series and its application to hydrogen-like ions.
  • Explore the principles of atomic emission spectra and their applications in spectroscopy.
  • Learn about electron transitions in multi-electron atoms and their impact on spectral lines.
USEFUL FOR

Students in physics or chemistry, educators teaching atomic structure, and anyone interested in the principles of spectroscopy and atomic transitions.

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Homework Statement



Determine the wavelength (in nm, to one decimal place) of the line in the emission spectrum of the He+ ion produced by a transition from n = 3 to n = 1.

Homework Equations


I used the Rydberg equation for this, although I'm not sure it is the correct one to use.
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The Attempt at a Solution


Plugging in n1=1 and n2=3, I get an answer of 102.6nm. A search on wikipedia for the Lyman series also shows that transition from n=3 to n=1 is 102.6nm.

The solution given, however, is 25.6nm. Obviously I am not understanding the question. Help would be appreciated.
 
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The Rydberg constant will be different for He+ than for hydrogen because He+ has more protons in its nucleus.
 
The equation you used is for Hydrogen. The He ion has a charge of +2, so the Rydberg constant is modified. Go back and look up the equation for how this Rydberg constant is derived.
 

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