Paschen equation

Comparison with the empirical Equation (1.4) shows that = /re /S/z eg and that n" = 2 for the Balmer series. Similarly n" = 1, 3, 4, and 5 for the Lyman, Paschen, Brackett and Pfimd series, although it is important to realize that there is an infinite number of series. Many series with high n" have been observed, by techniques of radioastronomy, in the interstellar medium, where there is a large amount of atomic hydrogen. For example, the (n = 167) — ( " = 166) transition has been observed with V = 1.425 GFIz (1 = 21.04 cm). 

The study of the hydrogen atom also played an important role in the development of quantum theory. The Lyman, Balmer, and Paschen series of spectral lines observed in incandescent atomic hydrogen were found to obey the empirical equation... 

This equation was discovered by Balmer in 1885.7 These speotral lines constitute the Balmer series. Other series of lines for hydrogen correspond to transitions from upper states to the state with n = 1 (the Lyman series), to the state with n = 3 (the Paschen series), and sp on. 

For the Paschen series /i = 3 and ni = 4, 5, 6,... The second line in the Paschen series is observed when 2 5. Hence, starting from equation I.l, we have... 

For the Balmer series, nf is simply 2 and n, takes the values 3, 4, 5, or 6. In 1908 the German physicist Friedrich Paschen (1865-1947) discovered new spectral lines fitting the above equation if nf = 3 and n = 4 and n, = 5. In 1906, Harvard physicist Theodore Lyman (1874-1954) discovered an ultraviolet series of spectral lines from hydrogen corresponding to nf = 1 and some 16 years later infrared spectral lines were discovered corresponding to nf = 4 and nf = 5. 

Other series of spectral lines occur in the ultraviolet (Lyman series) and infrared (Paschen, Brackett and Pfund series). All lines in all the series obey the general expression given in equation 1.5 where n > n. For the Lyman series, n=, for the Balmer series, n = 2, and for the Paschen, Brackett and Pfund series, k = 3, 4 and 5 respectively. Figure 1.3 shows some of the allowed transitions of the Lyman and Balmer series in the emission spectrum of atomic H. Note the use of the word allowed, the transitions must obey selection... 

Theoretical considerations of emission spectra were slow to develop, although they started in the later 1800 s and extended into the twentieth century. Balmer s equation for the Balmer series of lines of hydrogen started the search for an explanation for the origin of atomic spectra. Later Ritz (1908) noted that lines of hydrogen observed in the ultraviolet by Lyman (1904) fit the Balmer equation if the constant was changed. This work was extended by Rydberg, Kayser, Runge, and Paschen. It was the work of Bohr, with his concept of the astronomical atom and certain postulates... 

Equation (2-6) led to the identification of other series of the lines for hydrogen, including the Paschen series (n = 3), the Brackett series (nj = 4), and the Pfund series (n = 5). The Balmer series is in the visible region of the spectrum, the Lyman series is in the ultraviolet, and the Paschen, Brackett, and Pfund series appear in the infrared. Their distribution is shown in Figure 2-2. Equation (2-6), which accounts for all presently known lines of hydrogen, led Ritz (1908) to propose his combination principle, that the wavenumbers of all lines in a series are the result of the difference in energy between a fixed and a running term. 

Figure 19.4. Paschen curves for air, nitrogen and sulfur hexafluoride from Husain, E. and Nema, R.S. - Analysis of the Paschen curves for air, N2, SF using the Townsend breakdown equation IEEE Transactions El-17 (4) 350-353. Copyright 1982 IEEE and used with permission.

The longest wavelength line of the Balmer series in the emission spectrum of the hydrogen atom is 656.3 nm. Use the Rydberg equation to calculate the wavelengths of (i) the second line of the Balmer series, (ii) the first line of the Paschen series and (iii) the first line of the Lyman series. 

In this relationship, m is an integer greater than 2, with each value of m representing a different spectral line. Balmer was able to predict the wavelength of some spectral lines that were in the near ultraviolet range. The success of Balmer s equation was strengthened when other spectral series of emission lines were discovered in the ultraviolet (Lyman series) and in the infrared (Paschen series). The lines in their series could be determined by modified Balmer equations ... 

AMj=0, AMj= 1 transitions at fields which were not quite large enough for the complete Paschen-Back formula, equation (18.37), to be applicable. By expanding the Breit-Rabi formula up to terras of order... 

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