Lyman spectral series

This has a non-vanishing value for all values of n greater than 1. Hence there is no selection rule for n for the Lyman series, all transitions being allowed. It is similarly found that there is no selection rule for n for spectral series in general. 

Figure 1. Diagram showing the electron jumps producing the spectral lines in the Balmer (visible) series, the Paschen (infrared) series, and the Lyman (ultraviolet) series.

The equations of Bohr s theory are in agreement with the observed frequencies in the hydrogen spectrum, as are the observed spectral series— Lyman series (when electrons excited to higher levels relax to the n 1 state) and Balmer series (when electrons excited to higher levels relax to the n 2 state, and so on). Working backward, the observations can also be used to determine the value of Planck s constant. The value obtained in this way was found to be in agreement with the result deduced from the blackbody radiation and photoelectric effect. ... 

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 ... 

Electron Energy Transitions This energy-state diagram for a hydrogen atom shows some of the energy transitions for the Lyman, Balmer, and Paschen spectral series. Bohr s model of the atom accounted mathematically for the energy of each of the transitions shown. 

The values of the constant of proportionality, R, found from atomic spectral series must be compared with this theoretically calculated value of R. It is shown below that this value is about 1.25cm smaller than that found from the Lyman UV series of atomic spectral lines, namely, 109,678.7717cm . Attention is also drawn to the fact that the theoretically calculated value of R does not agree with the experimental ionization energy 109,678.7717cm . However, the experimental ionization energy agrees within experimental error with the experimental values found for / intercept, as discussed below. This is further taken up in Sect. 2.3. 

Table 3-4 Spectral Wavenumbers v for the Lyman Series of Hydrogen...

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... 

Lyman-alpha radiation spect Radiation emitted by hydrogen associated with the spectral line in the Lyman series whose wavelength is 121.5 nanometers. iT-man al-fo, rad-e a-sh3n ... 

Lyman limit spect The lower limit of wavelengths of spectral lines in the Lyman series (912 angstrom units), or the corresponding upper limit in frequency, energy of quanta, or wave number (equal to the Rydberg constant for hydrogen). iT-mon, lim-3t ... 

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. 

Bob looks at Miss Muxdroozol. Jumps that land on or come from the second orbit produce what is called the Balmer series, which correspond to spectral lines observable in optical spectra. The Lyman series correspond to more energetic changes and produces spectral lines in the ultraviolet. Paschen and higher order series produce low-energy infrared and even radio signals. He pronounces the last series PA-SHUN. 

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. ... 

The wave-mechanical calculation of the 2nd order perturbation energy (the ist order perturbation energy is zero) gives the same result, but it then appears at the same time that b)Q for these fictitious oscillators is the ionization energy, that is, the energy of the electron in the lowest energy state, so that v0 is also equal to 4/s of the frequency of the spectral transition of the electron from this state to the first higher state (ist line of the Lyman series). 

Each set of arrows in step 2 represents a spectral emission series. Label five of the series, from greatest energy change to least energy change, as the Lyman, Balmer, Paschen, Brackett, and Pfund series. 

FIGURE 19. (Courtesy of Kurt Adelberger). An illustration of the principles behind the Lyman break technique. Hot stars have flat far-UV continua, but emit fewer photons below 912 A, the limit of the Lyman series of hydrogen (top panel). These photons are also efficiently absorbed by any H I associated with the sites of star formation (middle panel) and have a short mean free path—typically only 40 A—in the IGM at z = 3. Consequently, when observed from Earth (bottom panel), the spectrum of a star forming galaxy at z cs 3 exhibits a marked break near 4000 A. With appropriately chosen broad-band filters, this spectral discontinuity gives rise to characteristic colours objects at these redshifts appear blue in (G — 72.) and red in ([/ — G). For this reason, such galaxies are sometimes referred to as [/-dropouts. A more quantitative description of the Lyman break technique can be found in Steidel, Pettini, Hamilton (1995). 

Spectral lines of the Lyman and Balmer series do not overlap. Verify this statement by calculating the longest wavelength associated with the Lyman series and the shortest wavelength associated with the Balmer series (in nm). 

Other series of spectral lines occur in the ultraviolet (Lyman series) and infrared (Paschen, Brackett and Pfund series). All... 

Aware of only these four hues, Balmer calculated 1 for a fifth hue lyn = 7). A hue with a wavelength very close to the predicted value was observed experimentally. Balmer suggested that his formula might also predict wavelengths of other series of spectral fines by using integer values for n other than 2 and rw n L 1. Other series of hydrogen lines were not known then, but were subsequently discovered (the Lyman, Paschen, Brackett, and Pfund series of fines). 

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. 

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... 

Soon after the development of the Balmer equation another series of spectral lines of hydrogen in the ultraviolet region were reported by Lyman. These lines were found to fit the Balmer equation (2-2) if the first term in the parentheses is 1/1 rather than 1/4. It appeared therefore that a more general form of the Balmer equation would be... 

Analysis of equation (2-2) for the Balmer series of hydrogen lines indicates that the spectral emission lines are given by the difference between R /4 and R /n. The ratio Ryi/4 is called a fixed term, while Ru/n is called a running term. Similar treatment of the Lyman series produces similar results if the fixed term is Rh/, a fact suggested by Ritz. Thus, the wave-numbers of lines of any series are the results of differences between two terms, one of them being of fixed value. 

Q A line in the hydrogen atomic spectrum at a wavelength of 94.93 nm is a member of the Lyman series. Calculate the value of the principal quantum number of the energy level from which the spectral line is emitted. 

The Lyman series of emission spectral lines arises from transitions in which the excited electron falls back into the n = 1 level. Calculate the quantum number of the initial state for the Lyman line that has v = 97,492.208 cm". ... 

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