Physics
Hydrogen Spectrum
The hydrogen spectrum refers to the unique set of wavelengths of light emitted or absorbed by hydrogen atoms. When an electron in a hydrogen atom transitions between energy levels, it emits or absorbs photons of specific energies, resulting in distinct spectral lines. These lines are characteristic of hydrogen and are used to study atomic structure and energy levels.
Written by Perlego with AI-assistance
Related key terms
1 of 5
11 Key excerpts on "Hydrogen Spectrum"
eBook - PDF- Michael Seeds, Dana Backman(Authors)
- 2016(Publication Date)
- Cengage Learning EMEA(Publisher)
Emission spectrum Gas atoms Absorption spectrum Absorption spectrum Telescope Spectrograph Continuous spectrum Copyright 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. The shorter-wavelength lines in each series blend together. Electron orbits in the hydrogen atom are shown here as energy levels. When an electron makes a transition from one orbit to another, this means that the energy stored in the atom has changed. In this diagram, arrows pointed inward toward the nucleus represent transitions that result in the emission of a photon. If the arrows pointed outward, they would represent transitions that result from the absorption of a photon. Long arrows represent large amounts of energy and correspondingly short-wavelength photons. Modern astronomers rarely work with spectra in the form of images of bands of light. Spectra are usually recorded digitally, so it is easy to represent them as graphs of intensity versus wavelength. Here, the artwork above the graph suggests the appearance of a stellar spectrum. The graph at right reveals details not otherwise visible and allows comparison of relative intensities. Notice that dark absorption lines in the spectrum appear as dips in the intensity graph. Transitions in the hydrogen atom can be grouped into series—the Lyman series, Balmer series, Paschen series , and so on, named after scientists who carefully investigated the spectra of hydrogen atoms. Transitions and the resulting spectral lines are identified by Greek letters. Only the first few transitions in the first three series are shown at left.
eBook - ePubTheoretical Spectroscopy of Transition Metal and Rare Earth Ions
From Free State to Crystal Field
- Mikhail G. Brik, Ma Chong-Geng, Mikhail G. Brik, Ma Chong-Geng(Authors)
- 2019(Publication Date)
- Jenny Stanford Publishing(Publisher)
Chapter 3The Theory of Atom of Hydrogen
3.1 Introduction
In the previous chapter, the basic processes of light absorption and emission in simple quantum mechanical systems were considered. Very important concepts of the induced and spontaneous transitions were introduced; general results were obtained for the probabilities of those transitions. At the same time, we did not specify yet what the nature of the energy levels involved in these transitions was. It was not mentioned at all what the main characteristics of those levels are, how their energetic positions can be obtained or how the energy levels can be described in a unified way. Moreover, a mixed approach, in which the atom was considered quantum-mechanically, and the incident radiation was treated as a monochromatic wave, was employed. A deeper quantum mechanical analysis of the energetic spectra of free atoms/ions will constitute the main content of this and next chapters. Certain quantum mechanical ideas and mathematical tools will be used for a quantitative description of the atomic states.3.2 Experimental Spectroscopic Results Known by the End of the 19th Century-Beginning of the 20th Century
The second half of the 19th century was marked by fast development of the experimental spectroscopy as a separate part of physics. It was preceded by pioneering works by J. von Fraunhofer (discovery of the dark lines in the solar spectrum, which later were explained as the absorption lines of various atoms), G. Kirchhoff and R. Bunsen (the laws of thermal radiation, discovery of several chemical elements, etc.). By that time, considerable amount of information about absorption and emission spectra of various elements and compounds had been collected. In particular, it was well established that the spectrum of atomic hydrogen in the visible region consists of four very sharp lines with the wavelengths of 410, 434, 486, 656 nm. However, no clear understanding of physical reasons for those experimental results was developed. In an attempt of finding any explanation (or, at least, description of this spectrum), a Swiss mathematician and physicist J. J. Balmer noticed in 1885 that these wavelengths fit the following expression:
eBook - PDF- James Shipman, Jerry Wilson, Charles Higgins, Bo Lou, James Shipman(Authors)
- 2020(Publication Date)
- Cengage Learning EMEA(Publisher)
Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 9.3 Bohr Theory of the Hydrogen Atom 249 A schematic diagram of the process of photon emission is shown in ●● Fig. 9.12a. Hydrogen’s line emission spectrum results from the relatively few allowed energy transitions as the electron de-excites. Figure 9.12b illustrates the reverse process of photon absorption to excite the electron. Hydrogen’s line absorption spectrum results from exposing hydrogen atoms in the ground state to visible light of all wavelengths (or frequencies). The hydrogen electrons absorb only those wavelengths that can cause electron transitions “up.” These wavelengths are taken out of the incoming light, whereas the other, inappropriate wavelengths pass through to produce a spectrum of color containing dark lines. Of course, in a hydrogen atom, a photon of the same energy emitted in a “down” transition will have been absorbed in an “up” transition between the same two levels. Therefore, the dark lines in the hydrogen absorption spectrum exactly match up with the bright lines in the hydrogen emission spectrum (see Fig. 9.9b and c). The transitions for photon emissions in the hydrogen atom are shown on an energy level diagram in ●●Fig. 9.13. The electron may “jump down” one or more energy levels n 5 n 5 4 n 5 5 20.85 0 21.51 23.40 213.60 n 5 3 n 5 2 n 5 1 Lyman series (ultraviolet, n f 5 1) Energy in eV Visible spectrum Balmer series (n f 5 2) Paschen series (infrared, n f 5 3) E ` Figure 9.13 Spectral Lines for Hydrogen The transitions among discrete energy levels by the electron in the hydrogen atom give rise to discrete spectral lines. For example, transitions down to n 5 2 from n 5 3, 4, 5, and 6 give the four spectral lines in the visible region that form the Balmer series. Bohr correctly predicted the existence of both the nonvisible Lyman series and Paschen series.
eBook - ePub- Grant R. Fowles(Author)
- 2012(Publication Date)
- Dover Publications(Publisher)
n = 1. Its value in electron volts is approximately 13.5 eV.The formula for the Hydrogen Spectrum is obtained by combining the energy equation with the Bohr frequency condition. Calling E 1 and E 2 the energies of the orbits n 1 and n 2 , respectively, we find(8.10)The numerical value of R/h is 3.29 x 1015 Hz.1A transition diagram of the hydrogen atom is shown in Figure 8.3 . The energies of the various allowed orbits are plotted as horizontal lines, and the transitions, corresponding to the various spectral lines, are shown as vertical arrows. Various combinations of the integers n 1 and n 2 give the observed spectral series. These are as follows:n1 =1 n2 =2, 3, 4, . . . Lyman series (far ultraviolet) n1 =2 n2 =3, 4, 5, . . . Balmer series (visible and near ultraviolet) n1 =3 n2 =4, 5, 6, . . . paschen series (infrared) n1 =4 n2 =5, 6, 7, . . . Brackett series (infrared) n1 =5 n2 =6, 7, 8, . . . pfund series (infrared) . Some of the series are shown in Figure 8.4 on a logarithmic wavelength scale.The first three lines of the Balmer series, namely, H α at a wavelength of 6563 Å, H β at 4861 Å, and H γ at 4340 A, are easily seen by viewing a simple hydrogen discharge tube through a small spectroscope. The members of the series up to n 2 = 22 have been recorded by photography. The intensities of the lines of a given series diminish with increasing values of n 2 . Furthermore, the intensities of the various series decrease markedly as n 1 increases. Observations using ordinary laboratory sources have extended as far as the line at 12.3 μ in the infrared, corresponding to n 1 = 6, n 2 = 7.1 Spectroscopists usually write Equation (8.10) in terms of spectroscopic wavenumberwhere ℛ is the Rydberg constant in wavenumber units, namely,Figure 8.3 . Energy levels of atomic hydrogen. Transitions for the first three series are indicated.The Hydrogen Spectrum is of particular astronomical importance. Since hydrogen is the most abundant element in the universe, the spectra of most stars show the Balmer series as prominent absorption lines. The series also appears as bright emission lines in the spectra of many luminous nebulas. Recent radiotelescope observations [26] have revealed interstellar hydrogen emission lines corresponding to very large quantum numbers. For instance, the line n 1 = 158, n 2
eBook - PDF- Andrew Fraknoi, David Morrison, Sidney C. Wolff(Authors)
- 2016(Publication Date)
- Openstax(Publisher)
A photon of wavelength 656 nanometers has just the right energy to raise an electron in a hydrogen atom from the second to the third orbit. Thus, as all the photons of different energies (or wavelengths or colors) stream by the hydrogen atoms, photons with this particular wavelength can be absorbed by those atoms whose electrons are orbiting on the second level. When they are absorbed, the electrons on the second level will move to the third level, and a number of the photons of this wavelength and energy will be missing from the general stream of white light. Other photons will have the right energies to raise electrons from the second to the fourth orbit, or from the first to the fifth orbit, and so on. Only photons with these exact energies can be absorbed. All of the other photons will stream past the atoms untouched. Thus, hydrogen atoms absorb light at only certain wavelengths and produce dark lines at those wavelengths in the spectrum we see. Suppose we have a container of hydrogen gas through which a whole series of photons is passing, allowing many electrons to move up to higher levels. When we turn off the light source, these electrons “fall” back down from larger to smaller orbits and emit photons of light—but, again, only light of those energies or wavelengths that correspond to the energy difference between permissible orbits. The orbital changes of hydrogen electrons that give rise to some spectral lines are shown in Figure 5.19. Answer: E = hf = ⎛ ⎝ 6.626 × 10 –34 J-s ⎞ ⎠ ⎛ ⎝ 5.5 × 10 14 Hz ⎞ ⎠ = 3.6 × 10 –19 J 172 Chapter 5 Radiation and Spectra This OpenStax book is available for free at http://cnx.org/content/col11992/1.13 Figure 5.19 Bohr Model for Hydrogen. In this simplified model of a hydrogen atom, the concentric circles shown represent permitted orbits or energy levels. An electron in a hydrogen atom can only exist in one of these energy levels (or states).
eBook - PDF- Brian W. Pfennig(Author)
- 2021(Publication Date)
- Wiley(Publisher)
For example, the bright yellow color of sodium salts in fireworks is readily apparent from the spectrum shown in Figure 2.6. In the case of calcium salts, the yellow and red lines are almost equally intense, leading to the observed orange color of this kind of fireworks. Let us now turn our attention to the line spectrum of hydrogen. Since hydro- gen is a gas, it is not used in fireworks. However, we can view the characteristic emission spectrum of hydrogen using a gas discharge tube, such as the one FIGURE 2.5 Illustration of the electron accelerating toward the nucleus in the planetary model of the atom. [Reproduced from http:// www.sr.bham.ac.uk/xmm/fmc2. html (accessed July 7, 2015).] 48 2 THE STRUCTURE OF THE ATOM shown at the top of Figure 2.7. Inside the hollow glass tube, a strong electrical field is used to ionize the gas and a line spectrum is observed as a result of the excited electron-emitting electromagnetic radiation in the form of light as it drops back down to the initial ground state. The line spectrum of hydrogen, shown in the bottom panel of Figure 2.7, was well established even before the discovery of the electron itself. As early as 1885, a Swiss math teacher by the name of Johann Balmer noticed a mathematical pattern in the frequencies of the spectral lines of hydrogen in the visible region and derived an empirical relationship to explain them. When other, similar patterns of emission lines were discovered in the UV and near-IR regions of the electromagnetic spec- trum, the Swedish physicist Johannes Rydberg simply expanded upon Balmer’s ini- tial equation to include these additional lines in his calculations. The resulting Rydberg formula, shown in Equation (2.3), can be used to calculate the wavenum- ber (1/λ) of any given line in the emission spectrum of hydrogen. Here, R H is the empirical Rydberg constant (109,737 cm -1 ) and n f and n i are both positive integers where n i > n f .
eBook - PDFIntroduction to the Theory of Atomic Spectra
International Series of Monographs in Natural Philosophy
- I. I. Sobel'Man, G. K. Woodgate, D. Ter Haar(Authors)
- 2016(Publication Date)
- Pergamon(Publisher)
The Hydrogen Spectrum consists of clearly defined series of lines, whose wavelengths satisfy the following formulae: = R1 1 ), n = 2, 3, 4, ... Lyman series, — = RI — ), n = 3, 4, 5, ... Balmer series, A 2 2 n 2 ) * Depending on convenience of writing, we shall use below two notations for the matrix elements, V ab and>. THE Hydrogen Spectrum 11 Hi Hi i-*f ( 1 1 ^3 2 ~~^ f 1 1 ' 1 1 X n = 4, 5, 6, ... Paschen series, n = 5,6,7, ... Brackett series, n = 6, 7, 8, ... Pfund series. Here, i? is a constant, which has received the name Rydberg constant, equal to 109,677.581 cm 1 . The wavelengths X of the leading (longest-wavelength) lines of these series equal respec-tively 1215.68 A (vac), 6562.79 A, 1.8751 microns, 4.051 microns and 7.456 microns (1 micron = 10~ 4 cm = 10 4 A).
- Arthur Haas, T. Verschoyle(Authors)
- 2020(Publication Date)
- De Gruyter(Publisher)
152 THEORETICAL PHYSICS readily excited belong to the ultra-violet. 4 In the higher regions of the sun's atmosphere, where the temperature is less than in the lower regions, the energy transferred by molecular collisions therefore suffices to excite the visible calcium lines, but not the visible hydrogen lines. § 120. Optical Spectra. The optical spectra of the elements can be produced both by the emission and by the absorption of light-quanta. As was pointed out in the previous section, absorption spectra arise from the transition of an electron into a higher-quantum level, either from the normal orbit or from an orbit due to previous excitation. Emission spectra are produced by the return of the atom from an unstable to the normal state, whether this return takes place in one or in several stages. Researches on optical spectra commenced with the observation by Fraunhofer, in 1814, of the absorption lines in the solar spectrum. In 1860 Kirchkoff and Bunsen founded spectrum analysis with their discovery of emission spectra. They proved that the bright lines in these spectra are characteristic of the elements, and the constant wave-lengths entirely independent of the temperature and chemical combination. Furthermore, they were able to demonstrate the coincidence of the Fraunhofer lines with the emission lines of certain elements, and to give a theoretical explanation of the former. The possibility of the existence of simple numerical relations between the wave-lengths of the lines in a spectrum was first pointed out by Balmer in 1885, in the particularly simple instance of the Hydrogen Spectrum (as has been discussed at length in an earlier section).
eBook - PDFAtomic Theory
An Elementary Exposition
- Arthur Haas, T. Verschoyle(Authors)
- 2020(Publication Date)
- De Gruyter(Publisher)
4.—Scheme of the Hydrogen Spectrum. THEORY OF THE HYDROGEN ATOM 31 the third, fourth, and fifth lines of the Paschen series, of which only the first two lines had up till then been known.) The origin of the Lyman, S aimer, and Paschen series is diagrammatically represented in Fig. 4, in which the various circular quantum orbits and the transitions from one to another orbit are shown. Another very clear illustra-tion of the origin of the spectral lines is given by the graphical representation of the energy-levels in the atom (Fig. 5). By Zero Line „ 4 t BRACKETT Series PASCHEN Series 1 BALMER Series * V 1 LYMAN Series Fid. 5.—Energy-Jevela in the hydrogen atom. means of a so-called zero-line, we represent the zero energy possessed by an electron revolving at an infinite distance from the nucleus. The energy in the one-quantum (normal) state is represented by a second line drawn parallel to the zero-line and below it (it is drawn below because the sign of the energy is negative). Since the energy in the n-quantum state is equal to the normal energy divided by the square of the quantum number, the line representing the two-quantum state lies between the one-quantum line and due to a transition to a five-quantum end state has been found at a wave-length of 74,000 A. by Pfund [J. Opt. Soc. Am. 9 (1924), p. 196]. 32 ATOMIC THEORY the zero-line. The line for the three-quantum state lies between that for the two-quantum state and the zero-line, and so on. If we wished our drawing to be to scale, the dis-tances between the individual lines and the zero-line would have to be equal to l/4th, l/9th, l/16th, l/25th, l/36th, etc., of the distance between the one-quantum or normal line and the zero-line. In Fig. 5, however, the scale has been inten-tionally distorted, in order to obtain a clearer diagram.
eBook - PDF- John Mcgervey(Author)
- 2012(Publication Date)
- Academic Press(Publisher)
The l s 1 /2 level of hydrogen is split into two levels by the hyperfine splitting, and a transition between one of these levels and the other leads to emission of a photon of wavelength 21 cm. This 21-cm radiation is quite prominent in radiation from atomic 266 THE HYDROGEN ATOM hydrogen throughout the galaxy, 21 and it has provided a means for determining the structure of the galaxy. Notice that the energy of such a photon is less than 10~ 5 eV, while the fine structure splitting is of order 1 0 -4 eV; the energy is in perfect agreement with the theory. You may notice that the transition between the two substates of the l s 1 /2 level is in violation of the selection rule Δ/ = ± 1. However, the total angular momentum of the atom does change by h; the transition is forbidden by the selection rule only because it is a magnetic dipole transition, which involves a change in magnetic dipole moment of the atom, rather than a change in its electric dipole moment, as in the allowed transitions. But a change in magnetic dipole moment is possible; it is simply far less probable than a change in electric dipole moment. In other words, it is much easier for an electron to change orbits than it is for it to flip its spin. Thus the selection rule does not say that such a transition never occurs, but it indicates that you are not likely to observe one. It is only the enormous number of isolated hydrogen atoms in the galaxy (of the order of one per cubic centi-meter) which makes the observation possible. Again, you are referred to Chapter 10 for further discussion of selection rules. We have now carried our analysis of the hydrogen energy levels as far as is practical here, from the 10-eV energy range down to the 10~ 5 -eV range. The agreement between theory and experiment over this enormous range indicates that our basic quantum theory is valid and that we understand the electromagnetic interaction very well on the atomic level.
eBook - ePubAtomic Emission Spectrometry
AES - Spark, Arc, Laser Excitation
- Heinz-Gerd Joosten, Alfred Golloch, Jörg Flock, Susan Killewald(Authors)
- 2020(Publication Date)
- De Gruyter(Publisher)
2 Atomic emission spectrometry: fundamentalsThe following facts are fundamental to atomic emission spectrometry (AES):- Material can be vaporized, atomized and ionized when sufficient energy is applied using, for example, an electrical arc or spark.
- The energy input causes the atoms and ions to emit radiation.
-
The radiation is not regularly distributed over the entire spectral range but occurs only in a finite number of narrow wavelength ranges. If a spectral apparatus breaks the spectrum down into a band of radiation in a way that the shortest wavelengths appear on the left edge and the longest wavelengths on the right edge, then the previously mentioned wavelength intervals appear within this spectrum as vertical lines with different positions and intensities.
- Atoms and ions from every element generate spectra that are characteristic in respect to position for the given element.
- The elemental content can be determined from the radiation intensity.
This chapter roughly outlines how these line spectra, which are so fundamental for the method of AES, occur. The theoretical foundations outlined in Chapter 2 serve the general understanding of the key relationships. Spectral lines for arc/spark spectrometry are empirically examined for their suitability. The purely practice-oriented reader can omit this chapter.2.1 Researching the Hydrogen Spectrumin the nineteenth century
The emission spectra for hydrogen were measured in the nineteenth century in the course of the development of AES. The discovery of series of lines in the spectrum led to equation-like relationships between the wavelengths of these signals.In 1885, Balmer described a series that followed the equation:(2.1)λ = An 2n 2− 4Here, A is at first an empirically determined constant length of 364.56 nm, n is an integer ≥ 3 and λ is the wavelength in nanometers.In molecular spectroscopy, the notation of wave numbers as oscillations per centimeter is more common. However, wave numbersν ˉare expressed exclusively in m−1 in this chapter to avoid confusion. The wave numberν ˉis then the reciprocal value of the wavelength λ
Index pages curate the most relevant extracts from our library of academic textbooks. They’ve been created using an in-house natural language model (NLM), each adding context and meaning to key research topics.
