C 11u r

»1 "2/ \"1 "2-where R is the Rydberg constant, R = 1.097 x 107 m-1.

Equation (5.8) was derived experimentally for n 1 = 2 by Johann Jakob Balmer as early as 1885. That is why we call the set of lines produced by transitions En ^ E2 the Balmer series. These lines are in the visible part of the spectrum. For historical reasons the Balmer lines are often denoted by symbols Ha, Hp, HY etc. If the electron returns to its ground state (En ^ Ei), we get the Lyman

Fig. 5.4. Transitions of a hydrogen atom. The lower picture shows a part of the spectrum of the star HD193182. On both sides of the stellar spectrum we see an emission spectrum of iron. The wavelengths of the reference lines are known, and they can be used to calibrate the wavelengths of the observed stellar spectrum. The hydrogen Balmer lines are seen as dark absorption lines converging towards the Balmer ionization limit (also called the Balmer discontinuity) at X = 364.7 nm to the left. The numbers

(15 40) refer to the quantum number n of the higher energy level. (Photo by Mt. Wilson Observatory)

en

H

CN

vn

vn

Tt

O

10

00

vn

vn

m

SC

£

si

00 m

Balmer series

Paschen series Brackett series Pfund series

Lyman series 364.7 nm

373.5 nm

Lyman series 364.7 nm

373.5 nm

Balmer ¿40 ¿0 discontinuity

series, which is in the ultraviolet. The other series with specific names are the Paschen series (ni = 3), Bracket series (ni = 4) and Pfund series (ni = 5) (see Fig. 5.4).

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