Paschen series

Term scheme of the hydrogen atom

The sequence of spectral lines in the spectrum of the hydrogen atom , the lower energy level of which lies in the M shell ( main quantum number ) , is called the Paschen series . ${\displaystyle n_{1}=3}$

Other series are the Lyman , Balmer (see also the explanations there), Brackett and Pfund and the Humphreys series .

spectrum

The spectral lines of the Paschen series are all in the infrared range of light. They were discovered in 1908 by the German physicist Friedrich Paschen .

n	4th	5	6th	7th	8th	9	10	11	12	13	${\displaystyle \infty }$
Wavelength (nm)	1874.5	1281.4	1093.5	1004.6	954.3	922.6	901.2	886.0	874.8	866.2	820.1

Mathematical description

The wave numbers of the spectral lines are given by the formula

${\displaystyle {\tilde {\nu }}=R_{\infty }\left({1 \over 3^{2}}-{1 \over n^{2}}\right)}$

given. Are in it

${\displaystyle R_{\infty }=1{,}0973731534\cdot 10^{7}\,{\mathrm {m^{-1}} }}$

the Rydberg constant and n whole numbers greater than 3.

The wavenumber can be determined by the relationship

${\displaystyle \lambda ={\frac {1}{\tilde {\nu }}}}$

in the wavelength, or through

${\displaystyle E={\tilde {\nu }}\cdot c\cdot h}$

convert into the energy of the associated photon . In the latter formula, c is the speed of light in a vacuum and h is Planck's constant .

See also

• Moseley's law

literature

• F. Paschen: To the knowledge of ultra-red line spectra . In Annalen der Physik 27, 1908, pp. 537-570.