Balmer series, hydrogen spectrum

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. 

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. 

Whereas the emission spectrum of the hydrogen atom shows only one series, the Balmer series (see Figure 1.1), in the visible region the alkali metals show at least three. The spectra can be excited in a discharge lamp containing a sample of the appropriate metal. One series was called the principal series because it could also be observed in absorption through a column of the vapour. The other two were called sharp and diffuse because of their general appearance. A part of a fourth series, called the fundamental series, can sometimes be observed. 

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... 

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

There are in principle an infinite number of series beginning at higher quantum numbers with i = 6, 7, 8, 9... but they become increasingly difficult to observe. For the higher n series to be seen in the spectrum the levels have to be populated, so some hydrogen atoms must be in the n = 5 level to see the Pfund series. We shall see that the presence of the Balmer series in the spectrum of a star is indicative of the stellar temperature, which is a direct consequence of the population of the energy levels. More of this in Chapter 4. 

Balmer series The series in the spectrum of atomic hydrogen with lower level n = 2 and all other possible levels n = 3,4,5,... 

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.)...

The lines are not spaced at random. In the spectrum of hydrogen, for example, there is a prominent red line wavelength interval a blue-violet line (Hyf and after a still shorter interval another violet line (Hi), etc. One has only to plot the frequencies of these lines as a function of their ordinal number in the sequence to get a smooth curve, which shows that they are spaced in accordance with some law. In 1885, Balmer studied these lines, now called the Balmer series, and arrived at an empirical formula which in modem notation reads... 

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. 

Lines in the Brackett series of the hydrogen spectrum are caused by emission of energy accompanying the fall of an electron from outer shells to the fourth shell. The lines can be calculated using the Balmer-Rydberg equation ... 

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. ... 

In 1885 Balmer was able to fit the discrete wavelengths X of part of the emission spectrum of the hydrogen atom, now called the Balmer series and illustrated in Figure 1.1, to the empirical formula... 

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... 

As a result of his work, the lines in the visible spectrum are known as the Balmer series. The other series of lines in the atomic emission spectrum of hydrogen were discovered later (the next wasn t discovered until 1908). These series are named after the scientists who discovered them for example, the series in the ultraviolet region is known as the Lyman series after Theodore Lyman. 

Balmer s equation was subsequently refined to give an equation that predicts the frequency, v, of any of the lines in any part of the hydrogen spectrum rather than just for his series. It turns out that his was not the most fundamental series, just the first to be discovered. 

Fig. 5.9. Spectrum of hydrogen Balmer series lines observed in a detached divertor plasma [20]. The spectrum was observed with the viewing chord shown in Fig. 5.8. The fitted spectrum is also shown as a broken curve...

At pressures less than 1 Pa, hydrogen atoms are formed by heated wires of W, Pd, or Pt. Under such conditions, concentration hydrogen atoms up to 95% may be obtained using a discharge tube. The half-life of the H atom is about 1.0 s at 30 Pa, which allows it to be transported out of the discharge and its reactions examined. The presence of hydrogen atoms in such experiments is established by observation of the Balmer series of the H atom spectrum and the diminution in intensity of the H2 molecules band spectrum. The very long half-life shows that only about 1 in 10 collisions between atoms leads to recombination. 

Be has a single electron. Calculate the frequencies and wavelengths of light in the emission spectrum of the ion for the first three lines of each of the series that are analogous to the Lyman and the Balmer series of neutral hydrogen. In what region of the spectrum does this radiation lie ... 

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