Paschen series, hydrogen

C07-0126. The series of emission lines that results from excited hydrogen atoms undergoing transitions to the n — 3 level Is called the Paschen series. Calculate the energies of the first five lines In this series of transitions, and draw an energy level diagram that shows them to scale. 

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. 

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... 

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 ... 

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. 

PROBLEM 5.5 What is the longest-wavelength line (in nanometers) in the Paschen series for hydrogen ... 

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. ... 

Paschen Series This series is formed when electrons in hydrogen atoms fall from a higher energy level to third energy level. This series lies in infrared region. 

Paschen series. One of the hydrogen spectral series in the infrared region. 

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. 

Extend the Bohr model by calculating the wavelength and energy per quantum for the electron orbit transition for which nf= 3 and n, = 5. This transition accounts for a spectral line in hydrogen s Paschen series. 

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. 

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