Series Balmer

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. 

Lyman series See Balmer series, lyogels See xerogels. 

In 1885 Balmer was able fo fif fhe discrete wavelengfhs X of part of fhe emission specfrum of fhe hydrogen atom, now called fhe Balmer series and illusfrafed in Figure 1.1, fo fhe empirical formula... 

Comparison with the empirical Equation (1.4) shows that = /re /S/z eg and that n" = 2 for the Balmer series. Similarly n" = 1, 3, 4, and 5 for the Lyman, Paschen, Brackett and Pfimd series, although it is important to realize that there is an infinite number of series. Many series with high n" have been observed, by techniques of radioastronomy, in the interstellar medium, where there is a large amount of atomic hydrogen. For example, the (n = 167) — ( " = 166) transition has been observed with V = 1.425 GFIz (1 = 21.04 cm). 

Question. Using Equations (1.11) and (1.12) calculate, to six significant figures, the wavenumbers, in cm of the first two (lowest n") members of the Balmer series of the hydrogen atom. Then convert these to wavelengths, in nm. 

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. 

Lyman Series) (Balmer Series) (Paschen Series)... 

Calculate the wavelength in nanometers of the line in the Balmer series that results from the transition n = 4 to n = 2. 

Reality Check Compare this value with that listed in Table 6.1 for the second line in the Balmer series. 

All of the lines in the Balmer series (Table 6.1) come from transitions to the level n = 2 from higher levels (n = 3, 4, 5,. . . ). Similarly, lines in the Lyman series arise when electrons fall to the n = 1 level from higher levels (n = 2, 3, 4,. . . ). For the Paschen series, which lies in the infrared, the lower level is always n = 3. 

Some Balmer series lines for hydrogen. The lhe kinelic energy of an electron is inversely related to the volume of the region to which... 

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... 

STRATEGY The frequency is given hy Eq. 2. Convert frequency into wavelength by using Eq. 1. The wavelength should match one of the lines in the Balmer series in Fig. 1.10b. 

This wavelength, 657 nm, corresponds to the red line in the Balmer series of lines in the spectrum. 

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. 

Derive an expression in terms of Rqo for the difference in wavelength, AA = Ah — Ad, between the first line of the Balmer series n = 2) for a hydrogen atom and the corresponding line for a deuterium atom Assume that the masses of the proton and the neutron are the same. 

Local thermal equilibrium (LTE) is an assumption that allows for the molecules to be in equilibrium with at least a limited region of space and remains an assumption when using the Boltzmann law for the relative populations of energy levels. The LTE assumption notwithstanding, observation of a series of transitions in the spectrum and measurement of their relative intensities allows the local temperature to be determined. We shall see an example of this in Section 4.4 where the Balmer temperature of a star is derived from the populations of different levels in the Balmer series. 

Calculate the wavelengths of the first three transitions in the Balmer series. Using the value for RH above with n = 2 and n2 = 3,4 and 5 gives the following ... 

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. 

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