Physics
Zeeman Effect
The Zeeman Effect refers to the splitting of spectral lines in the presence of a magnetic field. Discovered by Pieter Zeeman in 1896, this phenomenon occurs when the energy levels of atoms or molecules are affected by the magnetic field, causing the spectral lines to split into multiple components. The Zeeman Effect has been instrumental in understanding the behavior of atoms and in the development of spectroscopy.
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11 Key excerpts on "Zeeman Effect"
eBook - ePubAn Introduction to Quantum Physics
A First Course for Physicists, Chemists, Materials Scientists, and Engineers
- Stefanos Trachanas, Manolis Antonoyiannakis, Leonidas Tsetseris, Manolis Antonoyiannakis, Leonidas Tsetseris(Authors)
- 2017(Publication Date)
- Wiley-VCH(Publisher)
Then, an electrical discharge excites the atoms, causing them to emit radiation as they return to their initial state. The observation of this radiation yields the spectrum in the form of bright lines on a dark background. So, the question for the experimentalist is how these spectral lines are modified when we obtain the spectrum in the presence of a magnetic field. The answer is provided in Figure 10.5, where we sketched two allowed transitions (and) before and after we switch on the magnetic field. Figure 10.5 The Zeeman Effect. Owing to the selection rules,, each spectral line becomes a triplet, with the middle line positioned at the original one and the other two lines placed symmetrically on either side. The distance between the “Zeeman components” of each spectral line is proportional to the magnetic field. As is evident from the figure, the splitting of the initial spectral line into a triplet is a consequence of the selection rule. Transitions with correspond to a vanishing frequency shift, that is, to the middle component of the line; transitions with correspond to the left component; and transitions with correspond to the right component. This holds for all allowed transitions for arbitrary. Note also that the quantity known as the Larmor frequency, corresponds to the classical frequency of precession of the angular momentum vector for a charged particle in a magnetic field. (The vector rotates with frequency on a cone of constant angle around the magnetic field direction.) But is the splitting of spectral lines large enough to be experimentally observable? This depends on the magnitude of the Zeeman energy,, relative to the energy difference between the transition levels, which is typically on the order of a few eV
- Robert Kolenkow(Author)
- 2022(Publication Date)
- Cambridge University Press(Publisher)
9.2 Zeeman: An Important Experiment (1897) 227 moving charges, atoms might contain moving charged particles responsible for spec- tral lines. Lorentz theorized that the motion, hence the emitted spectra, could be affected by an applied magnetic field. His former student Pieter Zeeman (1865–1943) took up this research topic after assuming a post at the University of Amsterdam. The light source in Zeeman’s first experiments was asbestos soaked in sodium chloride and heated in a Bunsen burner to generate bright yellow sodium D spectral lines. With the source placed between the poles of a magnet, Zeeman observed in 1897 a broadening of spectral lines when the magnet was turned on and an imme- diate disappearance of the broadening when the magnet was turned off. Although imperfect, this was the first observation of what is now known as the Zeeman Effect. Zeeman then obtained a stronger electromagnet and used an electric arc struck between cadmium electrodes as the light source. Cadmium vapor is toxic, but Zeeman lived to age 78; experiments today use a spectral lamp with cadmium vapor enclosed in a protective glass bulb. Cadmium has a bright blue spectral line at 480 nm, and Zee- man observed the line to be split by the magnetic field into a triplet of three separate spectral lines. The center line had the same wavelength as the original unperturbed line, with the two new lines equally spaced higher and lower in wavelength. Lorentz explained the triplet using classical mechanics and classical electromag- netism, the only tools available before quantum mechanics. His model pictured an atom with a particle of charge q and mass m bound by a spherically symmetric force with force constant k and executing harmonic motion about equilibrium. In a magnetic field B a charge of mass m moving with speed v experiences a magnetic force qv B.
eBook - PDFThe Porphyrins V3
Physical Chemistry, Part A
- David Dolphin(Author)
- 2012(Publication Date)
- Academic Press(Publisher)
In one of his last endeavors he tried to 531 Copyright (c) 1978 by Academic Press, Inc. All rights of reproduction in any form reserved. ISBN 0-12-220103-5. 532 G. W. CANTERS AND J. H. VAN DER WAALS observe an effect of a magnetic field on the color of the light emitted by a sodium flame. 3 Although he reports his experiment to be unsuccessful, it was precisely the account of this work that inspired Zeeman, 30 years later, as he writes in the introduction to his famous paper for the Royal Netherlands Academy of Sciences in 1896, 4 to repeat the experiment with better instru-mentation. This time the attempt was successful. At first only a broadening of the sodium D lines was observed when a sodium flame was brought in between the poles of an electromagnet, but later the splitting of the lines could be resolved. Nowadays the effect that carries the name of Zeeman, and, in particular, the large effect linear in the applied field, is most readily described by relating it to the concept of degeneracy : in the absence of a magnetic field degeneracies exist in the term scheme of an atom, and these are lifted under the perturba-tion of an external magnetic field. Lorentz was aware of the intimate connec-tion between degeneracy and the Zeeman Effect although he used the term equivalent degrees of freedom. 5 In his classical explanation of the Zeeman Effect, for instance, he showed that an electrically charged particle performing a harmonic motion in a central force field has three principal oscillations, the frequencies of which are equal in the absence, but different in the presence of a magnetic field. 6 ' 7 B. The Orbital Zeeman Effect in Atoms and Molecules 1. FREE ATOMS The description of the Zeeman Effect of an atom starts with the observation that in the absence of a field the electrons in the atom move in a potential with spherical symmetry.
eBook - PDFQuips, Quotes and Quanta
An Anecdotal History of Physics
- Anton Z Capri(Author)
- 2011(Publication Date)
- WSPC(Publisher)
This was the beginning of the Zeeman Effect. When Zeeman told Onnes about his wonderful result, this worthy fired him for his efforts. Zeeman was for-tunate to then get a position at the University of Amsterdam. Here he was able to show that a magnetic field actually split the sodium lines into two 203 204 Quips, Quotes, and Quanta: An Anecdotal History of Physics lines of almost the same color. The final sentence in the paper that Zee-man published from Amsterdam to announce this result reads as follows. “I return my best thanks to Prof. Kammerlingh Onnes for the interest he has shown in my work.” Hendrik Antoon Lorentz, interpreted these new lines as being due to a particle whose charge to mass ratio was about 2000 times that of the hydro-gen ion. This was, of course the electron, but the interpretation preceded Wiechert’s and J. J. Thomson’s discovery of the electron by one whole year. This splitting of the spectral lines is now called the Zeeman Effect. Zeeman shared the 1902 Nobel Prize in Physics with Lorentz “in recognition of the extraordinary service they rendered by their researches into the influence of magnetism upon radiation phenomena”. Later in 1913 Onnes also won the Nobel Prize in Physics “for his investigations on the properties of matter at low temperatures which led, inter alia, to the production of liquid helium”. Left to right: Pieter Zeeman, Albert Einstein, Paul Ehrenfest in Zeeman’s laboratory. Faraday, who had inspired Zeeman’s efforts, had also discovered elec-tromagnetic induction. When he demonstrated to a lady visitor the tiny The Electron Spins 205 current that was produced when he plunged a magnet into a coil of wire, she asked, “What is the use of that?” He replied, “Madam, what use is a newborn baby?” His “baby” later grew up to become the basis of almost all electric power generated today.
- C. Minoia, S. Caroli(Authors)
- 2013(Publication Date)
- Pergamon(Publisher)
As was stated at the very beginning of this chapter, this short discussion has been necessary to explain why three components were observed by Zeeman in his early experiments. However, in the following experiments the splitting of the spectral lines into five, seven or even more components, dependening on the transitions considered, was observed. In reality, the cases of splitting leading to more than three components are so numerous that a proper explanation of the problem can be given only by a theory explaining the splitting for all the observed components, thus considering the normal Zeeman Effect as an anomalous case of the true Zeeman Effect. The key concept for a proper understanding of the Zeeman Effect is represented by the electron considered as a non point charge associated 20 Applications of Zeeman GFAAS with an intrinsic angular momentum of spin S, due to the simultaneous rotatory motion of the electron both around its axis and the nucleus. ^ Similarly to L in equations [11] and [12], S is also quantized as far as the modulus and the direction are concerned, i.e. |S I = Hs +1) h /2n [19] where s=l/2, and S z = ms.(h/2ji) [20] where m s =±1/2. In_addition, an intrinsic magnetic momentum, ps, exists, connected with S. The expression which can be obtained is lis = -gse/2mS [21] where g s , the gyromagnetic ratio, is equal to 2. By comparison with the analogous expression [9] one can obtain μβ/S gs= „ [22] μι/L. Thus the ratio between the magnetic momentum and the angular momentum for the spin is twice the corresponding ratio for the orbital motion. This result is obtained from the undulatory relativistic Dirac theory. The introduction of the spin and of its quantum number^has two main consequences. First of all, the vector coupling of L and S leads to the total angular momentum (orbital + spin) J.
eBook - PDFQuips, Quotes and Quanta
An Anecdotal History of Physics
- Anton Z Capri(Author)
- 2007(Publication Date)
- WSPC(Publisher)
The results are negative. They do not shake my strong feelings of the existence of a relation between gravity and electricity, though they give no proof that a relation exists.” The Zeeman Effect remained a mystery for quite a while since the ob-served splitting of only a few lines could be explained. These constituted the “normal” Zeeman Effect. But, according to standard theory, most of the lines observed should not even have occurred and could not be explained. These were dubbed the “anomalous” Zeeman Effect. The explanation for the anomalous Zeeman Effect was published at about the same time as the The Electron Spins 179 development of quantum mechanics. In the period from 1922 to about 1925 there was extreme, but friendly, competition between several physicists — most prominently Alfred Land´ e (1888 – 1976), Wolfgang Pauli, and Arnold Sommerfeld — to explain the Zeeman Effect. A. Land´ e gathered as much of the experimental data as were available. After much analysis of these data he constructed a model and was able to obtain a formula that accounted for the number of lines into which a given line would split. However, after more study, he realized that his model did not account for the size of the splitting. In 1924 Pauli had already rejected the Sommerfeld-Land´ e model for the multiplicity of spectral lines since it forced Land´ e to assume that the two electrons in Helium played different roles. In fact he warned Land´ e, “The very fact that the two electrons in Helium have to play entirely different roles — one the core electron and the other the radiant electron — is the failure of the model.” Pauli warned repeatedly against the use of models. He called this a “classic” fault of excessive confidence in a model. He further stated, “I can hardly believe in the models that are currently being considered. Why don’t we study the role of multiplet terms just from the experimental results?” Perhaps there was a spiritual link with his godfather, Ernst Mach.
eBook - PDFAstrophysics
Decoding the Cosmos
- Judith Ann Irwin(Author)
- 2007(Publication Date)
- Wiley(Publisher)
The result is a lowering (more negative) of the energy of the n ¼ 1 level ( j ¼ 1 = 2) by, D E ¼ m e c 2 a 4 8 ¼ 2 10 4 eV ð C : 12 Þ and a lowering of the j ¼ 1 = 2 and j ¼ 3 = 2 states in the n ¼ 2 level by different amounts resulting in a splitting of this level into two sublevels separated by, D E ¼ m e c 2 a 4 32 ¼ 4 : 5 10 5 eV ð C : 13 Þ (Ref. [100]). If the atom is placed in a magnetic field, B , with direction, z , the total angular momentum vector precesses about the field direction, called classically Larmor pre-cession , and there is a magnetic moment in the atom whose quantization is given by, m ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi j ð j þ 1 Þ p m B , where m B ¼ e 2 m e c h 2 p ¼ 9 : 24 10 21 erg G 1 is called the Bohr magneton . It is the magnetic quantum number, m j , that describes the projection of the total angular momentum along the z axis. The energy state will split into sub-levels whose separation depends on the strength of the field. If a transition between energy states occurs such that D m j ¼ 0 or D m j ¼ 1, then, respectively, the resulting line will be unshifted, or there will be a shift in the frequency of the spectral line according to, n ¼ n 0 m B h B ¼ n 0 1 : 4 10 6 B Hz ð C : 14 Þ C.3 FINE STRUCTURE AND THE Zeeman Effect 353 where n 0 is the frequency of the line in the absence of the field. In a gas in which many such transitions are occurring, then three lines can be observed instead of one 3 . This is called the Zeeman Effect 4 and, if measurable, is a very important way to obtain the strength of the magnetic field in an object. Since interstellar magnetic fields have strengths of order a few 10 6 G, a typical shift for interstellar lines is of order a few Hz. Most of the lines given in Table C.1, have frequencies of 10 14 to 10 15 Hz, so this is a negligible shift. However, if the magnetic field is stronger or a lower frequency line is chosen, then the Zeeman Effect becomes measurable.
eBook - PDFPhoton's Magnetic Field, The: Optical Nmr Spectroscopy
Optical NMR Spectroscopy
- Myron W Evans(Author)
- 1993(Publication Date)
- World Scientific(Publisher)
Discussion of the physical meaning of this result is given later. The quantum field theory of the anomalous optical Zeeman Effect in the coupled representation splits the original visible frequency spectral line into five, each displaced from the original frequency. 130 The Photon's Magnetic Field Quantum Field Theory, Semi-Coupled Representation, Eqn. (17). In this case the selection rules on the electric dipole transitions are obtained by the development (for the Z component): J 1 J 1 = (-i) J Mj ( ,) 'L>'Jh -Mj 0 Mb (36) so that the 3-j symbol is non zero if and only if J = 0, ±1; Mj 0 (37) Similarly, for X and Y components of ^ '■ AJ- = 0 , ±1; Mj = ±1 (38) The Lande gL factor of eqn. (17) is the same for each level of the 2 Pi/2 term. For each level of the split 2 D 3/2 term the Lande factor is again the same, g L1 . Transitions between the levels are controlled by the selection rule AMj = 0, +1. The resulting spectral pattern is three groups of doublets, i.e. six lines. This is recognisable as being the same pattern as observed in the conventional semi-classical theory of the anomalous Zeeman Effect, as illustrated, for example, in Fig. (9.27) of ref. {22}. J'M<; < JRM^> ■■ -- . . . The Anomalous Optical Zeeman and Optical Paschen Back Effects 131 Quantum Field Theory, Uncoupled Representation, Eqn.
eBook - PDF- J.R. Nielsen(Author)
- 2013(Publication Date)
- North Holland(Publisher)
This effect may be discussed by considering the resultmt motion as a small perturbation of the motion holding in the presence of the magnetic field alone, and the problem may be treated by a method closely analogous to that applied above to the perturbations of a periodic motion. In the present case it may be shown that the electric forces will, in a first approximation, not give rise to the appearance of new fundamental frequencies in the secular changes of the periodic orbit ; nor-so far as quantities proportional to the intensity of the electric field are concerned-will this field have any effect on the energy in the stationary states of the aton;. The presence of this field, nevertheless, will give rise to the appearance of new harmonic oscillations with amplitudes proportional to the intensity of the field, and with'frequencies equal to the sum or difference of two frequencies appearing in the atom when the magnetic field alone is present. On the correspondence principle this will, in addition to probabilities of transitions responsible for the components of the usual Zeeman Effect, give rise to small pro- babilities of the occurrence of new types of transitions. Besides irregularities in the polarisation of the usual components, the electric field may therefore be expected to cause the appearance of new weak components, at distances from the * Q.L.S., p. 92. t Garhasso, Phys. Zs., 1.5, p. 729 (1914). 296 €+of, Niels B o h on original lines twice that of the outer components in the normal effect. Such effects have actually been observed.* Before concluding our consideration of the effect of external fields on the hydrogen spectrum, it may be of interest to characterise, in a few words, the difference between the treatment given here and the method applied in their original investigations on the Stark and Zeeman Effects for the hydrogen lines by the authors mentioned in Section IV.
- Brain Judd(Author)
- 2012(Publication Date)
- Academic Press(Publisher)
Including the interaction between Η and the magnetic moments of the particles, we have Hz = -f e f o H -R + 0 H . ( L + 2S) -e u f r H -L i -M f o H -I * , (8.15) where g r = M P (Z A M B 2 + Z B M A 2 )/M A M B (M A + M B ). (8.16) 8.3 The Zeeman Effect 171 For Hund's cases (a) and (b), we replace R by J — Ρ and Ν — L respec-tively. The principal term on the right-hand side of Eq. (8.15) is the second one, representing the interaction between the electrons and the magnetic field. Since L + 2S is a vector, the analysis for Hund's case (a) proceeds in a similar manner to that for the Stark effect: the main difference is that Hz conserves parity. Thus Eq. (8.9) is replaced by (a+H z a+) = < a -Hza-) = /8<[μΑ5Σ][»][/Μ/ -f l ] I H -( L + 2S) | [ * A S 2 ] [ » ] [ / M / -fl]>, and from this point the analysis proceeds as before. We have merely to make the replacement -Εμ, -+ Ηβ(ΙνΑ8ΣΧυ2 U + 2 5 , | [*ASS][i>]> = Ηβ(Α + 2Σ). Since the secular determinant for Hz is diagonal, the effect of a splitting 28 between companion levels of opposite parity is to add and subtract δ to and from the common value of ( α ± | Hz | a=fc). The energies of the com-ponents of a level relative to the average energy of the pair of levels in zero field are Ηβ(Α + 2Z)MjQ 7(7+1) ( 8 , 1 7 ) The zero-field splitting is thus superposed on every component of the Zeeman multiplet and all the degeneracy is thereby removed. The possi-bility of lifting the degeneracy stems from the fact that Η ζ is of the form Η · Ζ , where the vector Z, unlike its electric analog d, changes sign under time reversal. The invariance of the Hamiltonian with respect to time re-versal is lost, and we can no longer draw any conclusions as to the degen-eracy of the levels. A consequence of the expression (8.17) is that 2 Πι/ 2 states (for which the subscript % denotes the value of | Ω |) are nonmagnetic, since A = ± 1 , Σ = =T=i. However, deviations from pure case (a) coupling are common.
eBook - PDF- U. Hoyer(Author)
- 2013(Publication Date)
- North Holland(Publisher)
PART I11 CONSOLIDATION OF THE QUANTUM THEORY OF THE ATOM This Page Intentionally Left Blank INTRODUCTION ULRICH HOYER 1. BEGINNINGSOF THE QUANTUM THEORY OF STARK AND Zeeman EffectS (1 9 13-1 9 14) On December 11, 1913, Rutherford wrote to Bohr*: “Just a note to draw your attention to the recent discovery of Stark, that an electric field produces separation of lines of hydrogen and helium very similar to the Zeeman Effect. I have just received a copy of his paper from the Prussian Academy**. I expect Knudsen will have received a copy, if you have not got one yourself. I made some rough calculations, and it appears to me that you ought to be able to explain the effect of your theory and deduce its magnitude. I think it is rather up to you at the present time to write something on the Zeeman and electric effects, if it is possible to reconcile them with your theory.” ; oc ; ; ; l r ; ~h ; Ruthrrford I I ~ r r 13 Bohr wrote to Stark three days later, apparently independently of Rutherford‘s letter*** : “I have with the greatest interest read your short account in Nature? of ~ ; e ; t ~ ; ; v l e l s B o h r your very important discovery of the effect of an electric field on spectral lines. I am very anxious to see whether my attempt of an explanation of the laws of line-spectra, published a few months ago in the Phil Mag, will fit in with your result. I shall therefore be very much obliged to you, if you kindly would let me have a copy of your detailed account to the Prussian Academy.” Bohr promptly received the desired copy. Yet, since he was working on a paper on the theory of the hydrogen spectrum to be read in December 1913 before the * For the text of this letter, see p. [589]. ** [See Johannes Stark, Beobachtungen iiber den Effekt des elektrischen Feldes auf Spektrallmien. I. Querfeld, Ann. d. Phys. 43 (1914) 965-982.1 *** For the text of this letter, see p. [606].
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