Paschen series, hydrogen spectrum

The discovery of two other series of emission lines of hydrogen came later. They are named for their discoverers the Lyman series in the ultraviolet range and Paschen series in the infrared region. Although formulas were devised to calculate the spectral lines, the physics behind the math was not understood until Niels Bohr proposed his quantized atom. Suddenly, the emission spectrum of hydrogen made sense. Each line represented the energy released when an excited electron went from a higher quantum state to a lower one. 

Paschen series The series of the hydrogen atom spectrum with n = 3 as the starting level. 

Paschen series spect A series of lines in the infrared spectrum of atomic hydrogen whose wave numbers are given by Rh 1(1/9) - (l/n ), where Rh is the Rydberg constant for hydrogen, and n is any integer greater than 3. pash-on, sir-ez ... 

Eventually, this series of lines became known as the Balmer series. Balmer wondered whether his little formula might be extended to study the spectra of other elements. He knew similar patterns exist in the line spectra of many elements. He also wondered about spectral lines that the human eye can t see. A few years later, in 1906, additional series of lines were in fact discovered for hydrogen in the ultraviolet region of the spectrum. These were called the Lyman series after their discoverer, Theodore Lyman. Other famous series are the Paschen series, named after German scientist Friedrich Paschen, the Brackett series, named after U.S. scientist F. S. Brackett, and the wonderful Pfund series, named after U.S. scientist August Herman Pfund. The Paschen, Brackett, and Pfund series lie in the infrared region. ... 

Further support for Bohr s theory came from the discovery of line series in the hydrogen spectrum for which the other integer m took values other than 2. The far ultra-violet series for which m — l has already been mentioned. Lyman announced the discovery of the first two members a year after Bohr s paper, recognizing the close connection between the wavelengths of these lines and Balmer s formula. Balmer himself had asked whether ther- might not exist a series for which m — 3, and Paschen had observed its first two members in the infra-red in 1908 [101], The series with m = 4 was found by Brackett in 1922 [18], with ra — 5 by Pfund in 1924 [108], and with m = 6 by Humphreys in 1953 [66]. It is to be understood that in all these series, the running integer n takes (m +1) as its first value. 

State which of the following n — n transitions in the emission spectrum of atomic hydrogen belong to the Balmer, Lyman or Paschen series (a) 3 — 1 (b) 3 — 2 ... 

Paschen series - The series of lines in the spectrum of the hydrogen atom which corresponds to transitions between the state with principal quantum number n = 3 and successive higher states. The wavelengths are given by 1/X = R ( l9- hf), where n = 4,5,6,... and R is the Rydberg constant. The first member of the series ( = 3<- ), which is often called the P line, falls in the infrared at a wavelength of 1.875 pm. 

Figure 5.12 shows that, unlike rungs on a ladder, however, the hydrogen atom s energy levels are not evenly spaced. Figure 5.12 also illustrates the four electron transitions that account for visible lines in hydrogen s atomic emission spectrum, shown in Figure 5.8. Electron transitions from higher-energy orbits to the second orbit account for all of hydrogen s visible lines, which form the Balmer series. Other electron transitions have been measured that are not visible, such as the Lyman series (ultraviolet), in which electrons drop into the n = I orbit, and the Paschen series (infrared), in which electrons drop into the n = 3 orbit.

What electron transitions account for the Balmer series Hydrogen s emission spectrum comprises three series of lines. Some wavelengths are ultraviolet (Lyman series) and infrared (Paschen series). Visible wavelengths comprise the Balmer series. The Bohr atomic model attributes these spectral lines to transitions from higher-energy states with electron orbits in which n = n, to lower-energy states with smaller electron orbits in which n = nf. 

Paschen series the lines from the infrared spectrum of the hydrogen atom... 

Fig. 1.2 A schematic representation of part of the emission spectrum of hydrogen showing the L5unan, Balmer and Paschen series of emission lines. The photograph shows the predominant lines in the observed, visible part of the spectrum of hydrogen which appear at 656.3 (red), 486.1 (cyan) and 434.0 nm (blue). Other fainter lines are not visible in this photograph.

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. 

The Paschen series of lines in the line spectrum of hydrogen occur in the near-IR. (a) Calculate the wavelength (in nm) of the series limit for the Paschen series of lines in the line spectrum of hydrogen, (b) The frequency of one line in the Paschen series of hydrogen is 2.34 x 10 Hz. Using the Bohr model of the atom with its circular orbits, sketch this specific electronic transition. 

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. 

The emission spectrum of hydrogen includes a wide range of wavelengths from the infrared to the ultraviolet. Table 6.1 lists the series of transitions in the hydrogen spectrum, each with a different value of f. The series are named after their discoverers (Lyman, Balmer, Paschen, and Brackett). The Balmer series was the first to be studied because some of its lines occur in the visible region. 

Bafmer series Frequencies of certain lines in the spectrum of hydrogen are simply related to each other, and can be expressed by a general formula. One group of lines is termed the Balmer series. Other series were later discovered in the spectrum of hydrogen by Lyman, Paschen, Brackett and Pfund. 

Eventually, other series of lines were found in other regions of the electromagnetic spectrum. The Lyman series was observed in the ultraviolet region, whereas the Paschen, Brackett, and Pfund series were observed in the infrared region of the spectrum. All of these lines were observed as they were emitted from excited atoms, so together they constitute the emission spectrum or line spectrum of hydrogen atoms. 

Subsequent to the discovery of the Balmer series of lines in the visible region of the electromagnetic spectrum, it was found that many other spectral lines are also present in nonvisible regions of the electromagnetic spectrum. Hydrogen, for example, shows a series of spectral lines called the Lyman series in the ultraviolet region and still other series (the Paschen, Brackett, and Pfund series) in the infrared region. 

In 1913 Bohr amalgamated classical and quantum mechanics in explaining the observation of not only the Balmer series but also the Lyman, Paschen, Brackett, Pfund, etc., series in the hydrogen atom emission spectrum, illustrated in Figure 1.1. Bohr assumed empirically that the electron can move only in specific circular orbits around the nucleus and that the angular momentum pe for an angle of rotation 9 is given by... 

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