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

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The discussion centers on calculating the Balmer wavelength for a hydrogen-like Fe atom (Z=26) transitioning from n=3 to n=2. The correct wavelength is identified as 0.971 nm. Initial calculations using the standard formula yielded incorrect results of 654 nm and 1200 nm. The correct approach involves using the modified formula for hydrogen-like atoms, incorporating the atomic number Z. The final formula provided leads to the accurate wavelength of 0.97 nm, confirming the initial query.
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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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