Lyman series

Energy levels of the hydrogen atom with transitions arranged in series

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

Further series are the Balmer series (see also the versions there), the Paschen series , the Brackett , Pfund and Humphreys series .

spectrum

The spectral lines of the Lyman series are all in the ultraviolet range of light between approx. 91 and approx. 121 nm. They were discovered in 1906 by the American physicist Theodore Lyman .

Mathematical description

For the corresponding n there is a wavelength of the lines of

n	designation	Wavelength in nm
2	Lyman-α-Line (Ly-α)	121.5
3	Lyman β line	102.5
4th	...	97.20
5	...	94.92
6th	...	93.73
7th	...	93.03
8th	...	92.57
9	...	92.27
10	...	92.05
11	...	91.89
${\displaystyle n\rightarrow \infty }$		91.13

Lyman series plotted against wavelength

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

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

in which

• ${\displaystyle R_{\infty }=1{,}0973731569\cdot 10^{7}\,{\mathrm {m^{-1}} }}$is the Rydberg constant and
• ${\displaystyle n}$are whole numbers greater than 1 (main quantum numbers of the starting shells). ${\displaystyle n_{2}}$

The wavenumber can be determined by the relationship

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

in the wavelength or through ${\displaystyle \lambda }$

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

convert into the energy of the corresponding photon , where is

• ${\displaystyle c}$the speed of light in a vacuum,
• ${\displaystyle h}$the Planck constant .

Areas of application

The lines of the Lyman series are of particular interest to astronomers studying stars and galaxies . The redshift of distant galaxies and quasars (partly into the visible or infrared spectral range) as well as the large-scale distribution of hydrogen in the universe can be derived from the Lyman α line (see Lyman break technique ). Because of the UV absorption of the earth's atmosphere , the Lyman lines can only be observed from the earth if the objects are redshifted sufficiently.

Another area of ​​application is meteorology . There Lyman-α- hygrometers are used to measure air humidity , especially on research aircraft.

literature

• Theodore Lyman: The Spectrum of Hydrogen in the Region of Extremely Short Wave-Lengths . In: Astrophysical Journal . tape 23 , 1906, pp. 181-210 , doi : 10.1086 / 141330 .