Predicts spectral line wavelengths of hydrogen from the initial and final principal quantum numbers.
Practise Atomic Structure & Periodicity All Atomic Structure & Periodicity topics
The Rydberg equation gives the wavelength of hydrogen spectral lines as 1/lambda = R_H (1/n1^2 - 1/n2^2), where n1 is the lower level, n2 the higher level, and R_H = 1.097 x 10^7 per metre is the Rydberg constant. It reproduces all the hydrogen series with one formula. Johannes Rydberg developed the general empirical form in 1888, and Niels Bohr later derived the constant from his model. The formula extends to hydrogen-like ions when R_H is multiplied by Z squared. It shows that spectral lines arise from differences between quantized energy levels.
Key ideas: 1 / lambda = R_H (1 / n1^2 - 1 / n2^2), with R_H = 1.097 x 10^7 per m (109677 per cm) and n2 greater than n1. For Balmer H-alpha, n1 = 2, n2 = 3, so 1 / lambda = 1.097e7 x 5/36 giving 656 nm. For hydrogen-like ions multiply by Z^2.
Common mistakes and connections: Students swap n1 and n2 giving a negative wavelength, or forget that result is in inverse meters so must be inverted. The equation works only for one-electron species like H, He+ and Li2+. It was empirical before Bohr derived R_H from constants.
The Rydberg equation predicts the Balmer wavelengths 656, 486, 434, 410 nm and so on, converging toward 365 nm as n2 grows. The interactive lesson shows this as a live animation or chart.
For the transition n = 3 to n = 2, 1/lambda = 1.097 x 10^7 x (1/4 - 1/9), giving a wavelength of about 656 nm.
Predicts spectral line wavelengths of hydrogen from the initial and final principal quantum numbers.
Rydberg Equation is a intermediate topic in Atomic Structure & Periodicity. It builds on the vocabulary of beginner topics in this area.
Study these earlier topics in Atomic Structure & Periodicity first: Atomic Emission Spectra, Atomic Absorption Spectra, Hydrogen Spectrum Series.
The next topics in Atomic Structure & Periodicity are Bohr Model and Bohr Energy Levels.
Yes. The interactive lesson includes a self-check question on Rydberg Equation, and the Atomic Structure & Periodicity quiz draws on every topic in this area.
Rydberg Equation is topic 44 of 115 in Atomic Structure & Periodicity.