I think I am correct in saying that the Balmer & Rydberg formulas provided the foundation for quantum physics and if not they were significant in contribution. Anyway, I have been examining the original of both formulas and wondered if someone knew and can show me how Rydberg rewrote Balmers equation in such a manner that he was able to determine Balmers equation was a special case of his more generalized equation. I see the end result but don't know how he got there.(adsbygoogle = window.adsbygoogle || []).push({});

Balmer original equation: λ = hm2/(m2 − 4),….OK

Rydberg original equation: n = no − No/(m+m')2,….OK

Rydberg rewrite of Balmer equation: n = no − 4no/m2 ???

The reference link states: “This shows that hydrogen is a special case with m'=0 and No=4no. No is a universal constant common to all elements. Now this constant is known as the Rydberg constant, and m' is known as the quantum defect. Rydberg noted that m' is approximately the same different "diffuse" or different "sharp" series, but that diffuse and sharp series of the same order have essentially the same value of no. “

Note, n = 1/ λ

Also, n0 = n sub 0, and N0 = N sub 0

Likewise, m2 is m squared

Please see link for clarity.

Reference link:

http://w3.msi.vxu.se/~pku/Rydberg/LifeWork.html [Broken]

Thanks a bunch,

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# Balmer & Rydberg equations

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