Balmer's Equation: Simpler Calculation of Hydrogen Wavelengths

  • Context: Undergrad 
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SUMMARY

The discussion focuses on a simplified calculation of hydrogen wavelengths using Balmer's constant, specifically B=91.126705, derived from the original Balmer series value of 364.50682. The formula presented is Wavelength = BN²(n²/(n²-N²)), where N represents the series (N=1 for Lyman, N=2 for Balmer). This method allows for easier calculations of hydrogen wavelengths in nanometers and is based on algebraic manipulation of Rydberg's formula. The author confirms successful testing of this approach and invites others to verify its accuracy.

PREREQUISITES
  • Understanding of Balmer's constant and its application in spectroscopy
  • Familiarity with Rydberg's formula for hydrogen wavelengths
  • Basic algebraic manipulation skills
  • Knowledge of wavelength measurement in nanometers (nm)
NEXT STEPS
  • Explore the derivation of Rydberg's formula for hydrogen wavelengths
  • Research advanced applications of Balmer's constant in spectroscopy
  • Learn about the implications of wavelength calculations in quantum mechanics
  • Investigate other series in hydrogen spectrum calculations, such as Lyman and Paschen series
USEFUL FOR

Students and professionals in physics, particularly those studying atomic structure and spectroscopy, as well as educators looking for simplified methods to teach hydrogen wavelength calculations.

Gaz
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So the Balmers constant is cool and easy to use compared to the Rydberg constant and I was looking for something simpler and came up with this.

If you change the Balmers constant to B=91.126705 by dividing it by 2² (because 364.50682 is the Balmers series) and use the formula. Wavelength = BN²(n²/(n²-N²)) N being the series N=1 lyman N=2 Balmers etc. Now I can use the Balmers to calculate all the wavelengths of hydrogen with ease and answers in nm.

Any thoughts on this I tested it out and it looks to work great maybe someone else could give it a go and make sure it works thanks.
 
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It follows directly - by some elementary algebraic manipulation - from Rydbergs formula.

So start from Rydbergs formula and try to rewrite it on your desired form.
 
I did from Balmers and it works. I did what Rydberg did but in a different way that I think is a lot simpler
 

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