Balmer series of spectral lines

Fig. 2-1.—The Balmer series of spectral lines of atomic hydrogen. The line at the right, with the longest wavelength, is Ha. It corresponds to the transition from the state with n = 3 to the state n 2. The other lines correspond to the transitions from the states with n — 4, 5, 6, to the state with n = 2.

The name of Johann Jakob Balmer is immortalized in the Balmer series of spectral lines emitted from the hydrogen atom. Atoms that are excited to higher energies return to lower energies by emitting electromagnetic radiation at specific frequencies. Gustav Kirchhoff had shown in 1859 that each element has its own unique spectrum, but attempts to predict the frequencies of these spectral lines were tmsuccessful until Balmer. 

Balmer series (of spectral lines) n. The wavelengths of a series of lines in the spectrum of hydrogen are given in angstroms by the equation... 

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 series of spectral lines for hydrogen became known as Balmer s series, and the wavelengths of these four spectral lines were found to obey the relationship... 

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. 

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. 

Different series of spectral lines are associated with the quantum number According to the quantum number n , the so-called series is distinguished Lyman series ( = 1), Balmer series ( = 2), Pashen series ( = 3), etc. The Balmer series lies in the visible region of the spectrum. The eigenfunctions R(r) are presented in Section 7.5.7 and in Figure 7.22. 

Balmer series A family of spectral lines (some of which lie in the visible region) in the spectrum of atomic hydrogen. 

Calculate the frequency, wavelength, and wave number for the series limit of the Balmer series of the hydrogen-atom spectral lines. 

B) In the Balmer series of hydrogen, one spectral line is associated with the transition of an electron from the fourth energy level (n = 4) to the second energy level (n = 2). 

The reaction to Bohr s model is understandable. Bohr s atomic model was based on older laws of physics with quantum assertions added. As such, it was clearly a jumbled affair. But the model provided a pictorial explanation of the origin of spectral lines and from the model the wavelengths of the Balmer series could be calculated. The model failed for the next simplest atom, helium. Had... 

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). 

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 ... 

The first set of transitions shown in Figure 14.15, in which the lower-energy state ( 2 state) is the n = 1 state, corresponds to the series of spectral hnes in the ultraviolet that is known as the Lyman series. The second set of transitions, in which ri2 = 2, is the Balmer series. The first four lines of the Balmer series are in the visible region and the others are in the ultraviolet. The next series, in which 2 = 3, is the Paschen series. It lies in the infrared. It is not shown in the figure. 

The Balmer series of hydrogen atom spectral lines corresponds to transitions from higher values of n to = 2 in the Bohr energy expression. Find the wavelengths in vacuum of all lines in the Balmer series that lie in the visible region. 

Historically, the visible emission lines shown in Figure 15-3 were the first atomic hydrogen lines discovered. They were found in the spectrum of the sun by W. H. Wollaston in 1802. In 1862, A. J. Angstrom announced that there must be hydrogen in the solar atmosphere. These lines were detected first because of the lesser experimental difficulties in the visible spectral region. They are called the "Balmer series because J. J. Balmer was able to formulate a simple mathematical relation among the frequencies (in It S). The ultraviolet series shown in Figure 15-3 was... 

Figure 2.1 Electronic orbitals and the resulting emission spectrum in the hydrogen atom, (a) Bohr orbitals of the hydrogen atom and the resulting spectral series, (b) emission spectrum of atomic hydrogen. The spectrum in (b) is calibrated in terms of wavenumber (P), which is reciprocal wavelength. The Balmer series, which consists of those transitions terminating on the second orbital, give rise to emission lines in the visible region of the spectrum. ( 1990 John Wiley Sons, Inc. Reprinted from Brady, 1990, by permission of the publisher.)...

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