Emission Spectral Lines & the Rydberg Formula

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SUMMARY

The discussion centers on calculating the shortest wavelength of the Lyman series for a triply-ionized beryllium atom (Be3+) using Rydberg's Formula. The user correctly identifies the parameters: Rydberg's Constant (R) as 1.097 x 107 m-1, atomic number (Z) as 4, and the principal quantum numbers n1 as 1 and n2 as 2. The calculated wavelength is approximately 7.596 nm, but the user encounters an error when submitting this value, realizing that the correct approach requires maximizing n2 for the shortest wavelength.

PREREQUISITES
  • Understanding of Rydberg's Formula for spectral lines
  • Knowledge of quantum numbers and their significance in atomic physics
  • Familiarity with the concept of ionization states in atoms
  • Basic proficiency in unit conversion, particularly between meters and nanometers
NEXT STEPS
  • Review the derivation and applications of Rydberg's Formula in different ionization states
  • Study the Lyman series and its significance in hydrogen-like atoms
  • Explore the implications of quantum mechanics on atomic transitions
  • Learn about the calculation of wavelengths for other elements using Rydberg's Formula
USEFUL FOR

Students and educators in physics, particularly those focusing on atomic structure and spectral analysis, as well as researchers working with ionized atoms and their spectral emissions.

ObliviousSage
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FIGURED IT OUT, PLEASE DISREGARD

Homework Statement



Find the shortest wavelength of the Lyman series for a triply-ionized beryllium atom (Be3+). Express your answer in nanometers using four significant digits.

Homework Equations



Rydberg's Formula: 1/\lambda=RZ2(1/n12 - 1/n22)

The Attempt at a Solution



For the Lyman series, n1 is 1.
Since we want the shortest wavelength, we want the smallest n2, which would be 2.
Beryllium's atomic number (Z) is 4.
Rydberg's Constant (R) is 1.097*107.

Thus 1/n12 is 1, and 1/n22 is 1/4, and their difference is 3/4.

3/4 * 1.097*107 * 42 = 131640000

The wavelength is one over that, or approximately 7.59647523549*10-9m.

In nanometers, to 4 significant digits, that's 7.596nm, yet the website insists that's incorrect (I also tried 7.597nm). What am I doing wrong?
 
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This always happens, as soon as I finish typing up my question I figure out what I was doing wrong. >_<

I need n2 as large as possible to get the smallest wavelength.
 

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