Solved: Value of Infinity for Hydrogen Atom Wavelength

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The discussion focuses on calculating the shortest wavelength of light emitted by an electron in the Brackett series of the hydrogen atom. The relevant equation involves the Rydberg constant and the principal quantum numbers. The user struggles with substituting the value of infinity in the equation, seeking clarification on how to approach it. The consensus is that for practical calculations, the term representing infinity can be approximated as zero, simplifying the equation. Ultimately, this leads to the correct wavelength value of 1.45 x 10^-6 meters.
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[SOLVED] Value of inifinity?

Edit: typo in title (infinity); sorry

Homework Statement



What is the shortest wavelength of light emitted by an electron in the Brackett series of spectra lines of the hydrogen atom?

Homework Equations



1 / (wavelength) = RH ( (1/nu^2) - (1/nl^2) )

The Attempt at a Solution



1 / (wavelength) = 1.1 x 10^7 ( (1/4^2) - (1/(infinity?)^2) )

I am told the correct answer is 1.45 x 10^-6, but I cannot find it on my calculator because I am not sure what to put in the place of infinity.

Thanks!
 
Last edited:
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One over a number infinitely close to infinity is infinitely close to zero. Just put in zero for the second term.
 
The value of 1/x tends to zero as x tends to infinity.So, just put zero in place of 1/n1^2.
 
(Sorry Dick, it seems we were typing at almost the same time.)
 
Thanks guys! :)
 

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