Rydberg formula

The Rydberg formula (Rydberg-Ritz formula) is used in atomic physics for determining the full spectrum of light emission from hydrogen, later extended to be useful with any element.

Rydberg formula for hydrogen

:rac{1}{lambda_{mathrm{vac}}} = R_{mathrm{H}} left(rac{1}{n_1^2}-rac{1}{n_2^2} ight)

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Where

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• $lambda\_\{mathrm\{vac\}\}$ is the wavelength of the light emitted in vacuum.
• $R\_\{mathrm\{H\}\}$ is the Rydberg constant for hydrogen.
• $n\_1$ and $n\_2$ are integers such that .

By setting n_1 to 1 and letting n_2 run from 2 to infinity, the spectral lines known as the Lyman series converging to 91nm are obtained, in the same manner:

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n_1

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n_2

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Name

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Converge toward

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1

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2 ightarrow infty

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Lyman series

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91nm

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2

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3 ightarrow infty

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Balmer series

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365nm

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3

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4 ightarrow infty

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Paschen series

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821nm

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4

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5 ightarrow infty

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Brackett series

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1459nm

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5

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6 ightarrow infty

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Pfund series

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2280nm

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6

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7 ightarrow infty

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Humphreys series

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3283nm

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The Lyman series is in the ultraviolet while the Balmer series in is the visible and the Paschen, Brackett, Pfund, and Humphreys series are in the infrared.

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