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Rydberg Formula Calculator

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Use our rydberg formula calculator for quick and accurate calculations. Free online tool.

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Rydberg Formula Calculator

1/λ = R(1/n₁² - 1/n₂²)

About the Rydberg Formula Calculator

The Rydberg Formula Calculator predicts the wavelengths of spectral lines emitted or absorbed by hydrogen and hydrogen-like atoms during electron transitions between energy levels. It is an essential tool in atomic spectroscopy, helping students and scientists identify spectral series and calculate precise photon wavelengths without complex manual computation.

The Rydberg formula is: 1/lambda = R_H * (1/n1^2 - 1/n2^2), where R_H = 1.097 x 10^7 m^-1 (Rydberg constant for hydrogen), n1 is the lower energy level and n2 is the upper level (n2 > n1). Example: for the first Balmer line (n1 = 2, n2 = 3): 1/lambda = 1.097 x 10^7 * (1/4 - 1/9) = 1.524 x 10^6 m^-1, giving lambda = 656.3 nm (red H-alpha line).

Enter the initial and final quantum numbers (n1 and n2) to obtain the photon wavelength in nm, the series name (Lyman, Balmer, Paschen, Brackett, or Pfund), and the spectral region (UV, visible, or IR). Applications: spectroscopy labs, stellar classification, astrophysics, and teaching atomic physics.

Frequently Asked Questions

What is the Rydberg formula?

The Rydberg formula mathematically describes the wavelengths of spectral lines in hydrogen by relating them to the initial and final principal quantum numbers of the electron transition.

What is the Rydberg constant?

The Rydberg constant R_H = 1.097 x 10^7 m^-1 (or 1.097 x 10^-2 nm^-1) is derived from fundamental constants and predicts hydrogen spectral line wavelengths with high accuracy.

Which series are visible to the human eye?

The Balmer series (n1 = 2, n2 = 3, 4, 5, 6...) falls in the visible range: H-alpha at 656.3 nm (red), H-beta at 486.1 nm (blue-green), H-gamma at 434 nm (violet), and H-delta at 410 nm (violet).

Does the Rydberg formula apply to other atoms?

Yes, for hydrogen-like ions the formula becomes 1/lambda = R_inf * Z^2 * (1/n1^2 - 1/n2^2), where Z is the atomic number and R_inf is the infinite-mass Rydberg constant.

What is the ionization limit in the Rydberg formula?

When n2 approaches infinity, the wavelength reaches its minimum (series limit), corresponding to the energy needed to ionize the atom from level n1 — for n1 = 1, this equals 91.18 nm (13.6 eV).