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# Hydrogen spectral series

In physics, the spectral lines of hydrogen correspond to particular jumps of the electron between energy levels. The simplest model of the hydrogen atom is given by the Bohr model. When an electron jumps from a higher energy to a lower, a photon of a specific wavelength is emitted according to the Rydberg formula: ${1 \over \lambda} = R \left( {1 \over (n')^2} - {1 \over n^2} \right) \qquad \left( R = 10.972 \times 10^6 \mbox{m}^{-1} \right)$

where n is the initial energy level and n' is the final energy level, and R is the Rydberg constant.

The spectral lines are grouped into series according to n' :

#### Series name

1Lyman series
2Balmer series
3Paschen series
4Brackett series
5Pfund series
6Humphreys series

## Balmer Series

#### λ(nm)

21223656
31034486
497.25434
594.96410
693.77397 $\infty$91.1 $\infty$365

## Brackett Series

#### λ(nm)

4187054050
5128062630
6109072170
7100081940
895491820 $\infty$820 $\infty$1460

## Humphreys Series

#### λ(nm)

67460712372
7465087503
83740105129
93300114673
103040134171 $\infty$2280 $\infty$3282

## Extension

Hydrogen is the element with the simplest-to-analyze emission spectrum. All other atoms possess at least two electrons in their unionized form and the interactions between these electrons makes analysis of the spectrum by such simple methods as described here impractical. The deduction of the Rydberg formula was a major step in physics, but it was long before an extension to the spectra of other elements could be accomplished.