# hydrogen spectrum

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## hydrogen spectrum

Emission and absorption spectra of hydrogen are relatively simple compared with spectra of heavier elements. Atomic hydrogen (H I) has a line spectrum in which several series of lines can be distinguished. The Swiss physicist Johann Balmer showed, in 1885, that lines in the visible region of the hydrogen spectrum formed a series represented by the equation*R*

_{∞}(1/4 – 1/

*m*

^{2})

λ is the wavelength of the line and *m * an integer greater than two. The constant *R * _{∞} has a value of 1.097 37 × 10^{7} m^{–1}, and is called the *Rydberg constant*.

This series of spectral lines is called the *Balmer series*. Its existence was first explained by Niels Bohr in his theory of the atom (1913). Bohr postulated that only a discrete number of orbits is allowed to an electron in an atom and that when the electron jumps from one orbit to another, a photon of radiation is emitted or absorbed (see energy level). The Balmer series is produced by transitions of the electron between the second permitted orbit, in order of distance from the nucleus, and higher orbits. When *m * = 3, the spectral line is produced by a transition from the second to the third orbit (or from the third to the second orbit). This line is referred to as Hα (the *hydrogen alpha line*) and has a wavelength of 656.4 nm, i.e. it falls in the red region of the visible spectrum. The next line, Hβ (*m * = 4), is at 486.1 nm in the blue. Hγ and Hδ occur at 434.2 nm and 410.2 nm, respectively. The lines in such a series get closer together at shorter wavelengths and the Balmer series converges to a limit at 364.6 nm in the ultraviolet region of the spectrum. Emission lines are produced by transitions from higher levels to the second orbit; absorption lines result from transitions from the second orbit to higher orbits.

In general, lines in the hydrogen spectrum can be represented by the equation 1/λ = *R * _{∞} (1/*n *^{2} – 1/*m *^{2})

where *n * and *m * are integers; *n * is called the *principal quantum number* and can have values from one to infinity. The Balmer series is formed for *n * = 2, i.e. the second orbit of the atom. Transitions from or to the first orbit, i.e. the ground state (*n * = 1), produce the Lyman series of spectral lines. This is in the far ultraviolet and extreme ultraviolet regions. *Lyman alpha*, denoted Ly α (*n * = 1, *m * = 2), occurs at 121.6 nm; the series Ly α, Ly β, Ly γ…, converges to a value of 91.2 nm, the *Lyman limit*. The *Paschen series* is produced by transitions to or from the third permitted orbit (*n * = 3) and occurs in the near infrared region of the spectrum. The *Brackett series* occurs at longer infrared wavelengths involving the fourth orbit (*n * = 4).