What is the Shortest Wavelength in the Balmer Series of Hydrogen Spectral Lines?

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Homework Help Overview

The discussion revolves around calculating the shortest wavelength in the Balmer series of hydrogen spectral lines, as well as in other series like Lyman, Paschen, and Brackett. Participants are exploring the implications of the equations related to these spectral lines and the concept of limits in relation to wavelength and energy.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the application of Rydberg's formula in terms of wavelength and express confusion regarding the behavior of wavelength as it approaches limits. There are reflections on the relationship between wavelength and energy, particularly in the context of the shortest wavelength corresponding to the highest energy photon.

Discussion Status

Some participants have begun to clarify their understanding of the limits involved in the equations, with one noting a realization about the existence of wavelengths despite initial assumptions of them becoming infinitely small. There is an acknowledgment of the need to set certain variables to infinity to find the shortest wavelength.

Contextual Notes

Participants mention challenges related to their understanding of limits, suggesting that prior coursework may have impacted their grasp of the concepts being discussed.

Pengwuino
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I have this problem that asks me to compute the shortest wavelength in each of these hydrogen spectral series: Lyman, Balmer, Paschen, and Brackett and to compute the energy for each. I am looking at the equations associated with each and it seems as if the wavelength can become infinitely small so there would be no answer for this. What am i missing?
 
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A lot.Write Rydberg's formula not in terms of the frequency number,but in terms of wavelength.U'll see what to do then.

Daniel.
 
I do it in terms of wavelength and was still lost but...

I think my 6 months away from the idea of limits screwed me up here. I notice the first few n's and the wavelength is getting smaller and smaller and i assumed wow, its getting smaller and smaller, it must become infinitely small! Then i realized that only one part of the equation goes towards 0 and that the wavelength actually exists and bleh, now my homework won't look as empty as usual :D And yes, i did realize what the answer now is.
 
Well,the shortest wavelength means the highest energy of the emitted photon.I have a hunch,u'll have to set something to go to infinity.And since that something in involved in a denominator,everything will be okay;

Daniel.
 
Yah, whole limits things seemed to have went bye bye after last semester. I got it now though.
 

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