Brackett series nearest to Paschen series

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The discussion centers on identifying which spectral line of the Brackett series is nearest to the first spectral line of the Paschen series, specifically the line at 18,751.1 Å. The closest Brackett line corresponds to n=9, with a wavelength difference of 577 Å from the Paschen line. Participants express confusion about the calculations leading to this conclusion and seek clarification on the underlying principles. The conversation suggests that understanding the formula for calculating series wavenumbers could provide valuable insights. Overall, the thread emphasizes the need for a clearer explanation of the spectral series and their relationships.
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Which of the spectral lines of the Brackett series is closest in wavelength to the first spectral ine of the Paschen series? By how much do the wavelengths differ?

Know:
The first line of the Paschen series occurs at 18,751.1A with an energy of En=-13.6/(3)2.
I know the answer is n=9 with a sepperation of 577A but I'm super confused how they arrived at this answer.

If anyone could help at least to explain what is esentially going on here, or point me in the right direction it would be much appreciated!

Thanks!
 
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I suppose formula that is used to calculate series wavenumbers could be a good starting point.
 

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