Balmer Wavelength for Hydrogen-like Fe Atom (Z=26): 0.971 nm

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SUMMARY

The Balmer wavelength for a hydrogen-like Fe atom (Z=26) transitioning from n=3 to n=2 is calculated to be 0.971 nm. The correct formula for this calculation is 1/lambda = R*Z^2(1/n'^2 - 1/n^2), where R is the Rydberg constant. Initial attempts using the incorrect formula yielded values of 654 nm and 1200 nm, demonstrating the importance of using the appropriate equations for hydrogen-like atoms. This discussion highlights the critical role of accurate formulas in obtaining precise spectral wavelengths.

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  • Understanding of the Rydberg formula for hydrogen-like atoms
  • Familiarity with quantum mechanics concepts, particularly energy levels
  • Knowledge of Bohr's model of the atom
  • Basic proficiency in unit conversions related to wavelength
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  • Study the Rydberg formula in detail for hydrogen-like atoms
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Students of physics, particularly those studying atomic structure, quantum mechanics, and spectroscopy, as well as educators seeking to clarify concepts related to hydrogen-like atoms and their spectral emissions.

Meekay
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I have been having trouble with this Balmer wavelength problem and was hoping I can get a little guidance.

The question: Find the balmer wavelength (n=3 --> n=2) emitted from a hydrogen-like Fe atom (z=26)

The answer is supposed to be 0.971 nm

My attempt:

1/lambda = R(1/n'^2 - 1/n2)
Since this is a hydrogen-like atom, it should be straight forward

I get lambda = 36/5*R which comes out to be 654 nm

And if I use one of Bohrs equations: E = -Z^2(R/n^2) and E3 = E2+ (hc/lambda) I get a value of 1200 nm
 
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I figured it out, my book did not give me this equation for hydrogen-like atoms:

1/lambda = R*Z^2(1/n'^2 - 1/n^2) this gives me 0.97 nm

Thanks wikipedia!
 

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