Calculating 5 Longest Lyman Series Wavelengths

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SUMMARY

The discussion focuses on calculating the five longest wavelengths of the Lyman series in hydrogen. The key formula used is ΔE = hc/λ, where ΔE represents the energy difference between initial and final states, and λ is the wavelength. To determine the longest wavelengths, one must minimize ΔE, which occurs when the initial state is n=2 and the final state approaches infinity. The five longest wavelengths correspond to transitions from n=2 to n=3, n=4, n=5, n=6, and n=7.

PREREQUISITES
  • Understanding of quantum mechanics and energy levels in hydrogen
  • Familiarity with the Lyman series of hydrogen
  • Knowledge of the Planck constant (h) and speed of light (c)
  • Ability to manipulate equations involving energy and wavelength
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  • Study the Lyman series transitions in detail
  • Learn how to apply the Rydberg formula for hydrogen
  • Explore the concept of energy levels and quantum numbers
  • Investigate the relationship between energy and wavelength in electromagnetic radiation
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Students of physics, educators teaching quantum mechanics, and anyone interested in atomic spectroscopy and the properties of hydrogen.

Tony11235
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How am supposed to calculate the five longest wavelengths of the Lyman series? What values of n are used? I see how you arrive at a definite limit as n goes to infinity, but the five longest? Sort of a dumb question.
 
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Remember that

\Delta E=\frac{hc}{\lambda}

\Longrightarrow \lambda=\frac{hc}{\Delta E}

\Delta E=E_{initial}-E_{final}

To get the longest wavelength, \Delta E must be at minimum value[/color]
 

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