Visible Light Transitions in Li++ (Z=3)

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SUMMARY

The discussion focuses on identifying visible light transitions in Li++ (hydrogenic lithium ions, Z=3) within the wavelength range of 300nm to 700nm. The relevant formula for energy transitions is E=13.6eV*(Z^2)*((1/n)^2-(1/m)^2), with λ=1240/E for calculating wavelengths. Participants noted that they were obtaining wavelengths identical to those of hydrogen, indicating a misunderstanding in applying the formula, particularly regarding the principal quantum numbers. The HyperPhysics calculator is recommended for accurate calculations of wavelengths and energies based on initial and final quantum numbers.

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  • Understanding of quantum mechanics and principal quantum numbers
  • Familiarity with the Rydberg formula for hydrogen-like atoms
  • Knowledge of energy levels in hydrogenic ions
  • Basic proficiency in using online calculators for physics
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  • Study the Rydberg formula for hydrogen-like atoms in detail
  • Learn how to apply the formula E=13.6eV*(Z^2)*((1/n)^2-(1/m)^2) specifically for Li++
  • Explore the use of the HyperPhysics calculator for various transitions
  • Research the differences in spectral lines between hydrogen and hydrogenic ions
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Students of quantum mechanics, physicists studying atomic transitions, and anyone interested in the spectral analysis of hydrogenic ions.

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1. Assuming that the wavelengths of visible light lie between about 300nm and 700nm, what transitions in Li++ (hydrogenic lithium ions, Z=3) would be visible. Identify each transition by initial and final principal quantum number n. Also identify those transitions that are also seen in hydrogen (3->2, 4->2, 5->2 in hydrogen)

2. E=13.6eV*(Z^2)*((1/n)^2-(1/m)^2)
λ=1240/E


3. I ran through it but I keep getting the same wavelengths as hydrogen. I don't know what I'm doing wrong. Do I multiply n*Z on the bottom before I square it?
 
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