chemiRry on /tamp/ edited by:
JAMES 0.SCHRECK Unlvers~ty01 Nolthern Colorado Greeley, CO 80639
C. MARVINLANG Unrvers~tyof W8sconsm Stevens Pomt. WI 54481
The Quantum Story on Postage Stamps Walter J. Batfour University of Victoria, Victoria, BC, Canada V8W 2Y2 Far too frequently the pressures of an expanding curriculumand limited time in the chemistry classroom have resulted in the historical and philosophical side of the discipline heine short-chaneed. I t is. however. refreshine in this reeard to observe the increasing inclusion, in chemistry texttax~ks, of hiographicalsketchesand anecdoteson historically significant personalities. Introductory texts have for the past several years contained fracrnentary information ( I ) . Too, a recent physical chemistry text (2) contains a significant amount of anecdotal material regarding the careers and contributions of 18 chemists, physicists, and other related scientists. Such considerations can greatly enhance the reader's oersnective and amreciation of the subiect. There is no . . .. more illustrative case in point than the historical account of the interolav . " between exneriment and theorv that led. in the early part of the present century, to the development of quantum mechanics and its application to chemical and physical problems. Within the last few years, a number of the leading participants in the quantum story have received philatelic recognition (Fig. 1and the table) thus providing a colorful and informative classroom aid. On 14 December 1900, Max Planck (185Z-1947; see stamp no. 1) read to a meeting of the German Physical Society in Berlin, the historic paper "On the Theory of the Energy Distribution Law of the Normal Spectrum" that was to usher in the quantum era. While subsequent developments owe much to 19th century contributions of Friedrich Gauss, William Hamilton, Heinrich Hertz, Joseph Lagrange, Pierre Laplace, James Maxwell, Lord Rayleigh (J. W. Strutt), and Wilhelm Wien-all of whom are to be found on postage stamps, the present account will restrict its contents to material of the current century. Planck was able toexpla& one of theunsolved problems of classical physics, namely, the ultraviolet catastrophe. As such, the catastrophe referred to the curious energy distribution in the continuous spectrum of a black body's emitted radiation. Rayleigh and Wien each had tried to work out mathematical models describing the observed spectral distribution, but each failed to account for the distribution over all wavelengths. Planck combined both mathematical formulations and, in so doing, was forced into postulating energy quanta. His postulate was based on a critical assumption; energy is not continuous, but, like matter, i t exists somewhat like particles. These energy particles Planck called quanta (Lat., "how much?") with values proportional to their frequency through a universal runstant, h, k n o w today as I'lanck's constant. This constant is wed rxtensively in quantum mechanical calculations, often in conjunction with the
quantity "2a" and as such is written h ( h I 2 ~ called ; "hbar"). Stamp no. 2, issued to mark the centenary of his birth, bears his signature surmounted by a large symbolic h. Initially, Planck's quantum idea was considered an ad hoc hypothesis-Planck himself was dissatisfied with its inception-and i t took several vears for the sienificance of it to become apparent. In 1905, Albert Einstein (1879-1955; no. 3), recognizing the implication of Planck's discovery, used the concept (proportionality of light quanta to frequency) to explain the photoelectric effect (no. 4). The photoelectric effect had then recently been studied experimentally hy Philipp Lenard (1862-1947; no. 5). In his paper, Einstein developed the notion that electrons ejected from a photosensitive metallic surface possessed a kinetic energy dependent on the frequency ( u ) of the light falling on the surface through the equation
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mu2/2 = Voe = hu
-P
where Vo is the total retarding potential, P is the "work function" characteristic of each metal, and the remaining symbols have their usual meanings. However, Einstein's deduction did not have its full impact until the next decade when. followine careful measurements hv Robert Millikan (1868-195:1; noY6, of the charge of an eleriron, it was pro\.ed conrlusivelv that theslone in Einstein'seauation is the same as ~lanck'sconstant(h)khen Voe is plotted against v. At the time, perhaps of more direct relevance to Planck's blackbody 6uant"m theory was Einstein's treatment of another contradiction in classical physics, namely, the heat capacities of solids a t very low temperatures. Here again, the postulation of an oscillator with quantized energy of hv gave excellent agreement with experiment. A great deal of current understanding concerning atomic structure and electronic arrangement in atoms is due to the interpretation of atomic spectra. The visible portion of the electromagnetic spectrum consists of a continuous array of wavelengths ranging from approximately 380 nm to nearly 800 nm a ~ p e a r i n eas a rainbow of colors to the normal eve (stamp nos- 7,s) and is observable by allowing "white light" to pass through prism. The spectrum observed from the . a . excitation of gaseous atoms consists of discrete lines (actually, images of the slit used in the experimental design) in contrast to the complete rainbow of white light. Such atomic line spectra had been known for many years prior to the dawn of the quantum era, yet had remained uninterpreted. Johann Balmer (1825-1898) had presented a mathematical formula that accounted for the lines in the simple spectrum Volume 85 Number 3 March 1988
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Figure 1. Stamps, numbered in accordance with the table
observed for atomic hydrogen. This four-line spectrum is presented along the top edge of stamp no. 9, intended to represent a solar spectrum, and the stamp also portrays a spectroscope used in accurately determining wavelengths1 frequencies of the lines. The frequencies of these visible1 near-ultraviolet lines follow a regular converging series whose empirical formula is expressed in terms of integral numbers and a constant, RH,the Rydberg constant named for Johannes Rydberg (1854-1919). The Canadian stamp 256
Journal of Chemical Education
(no. 10) pictures in greater detail the line nature of atomic spectra, which, in the case portrayed, is used in the identification of elements by virtue of their characteristic line spectrum. Beginning in 1906 Ernest Rutherford (1871-1937) experimented with alpha particle scattering from various thin metal foils including gold. These foils were generally 1150,000th inch thick. Most of the alpha particles passed through the foil, unaffected and undiverted. However, some were scat-
ldentlfkatlon of the Stamps NO.
Counby
Yew
ScoU No. (6)
1
Germany (Berlin) East Germany USA West Germany Sweden USA Spain Uruguay Vatican Canada New Zealand USSR Sweden DBnmark Greenland East Germany West Germany France Nicaragua Sweden Sweden Sweden Sweden Sweden Austria Sweden Upper Volta
1952 1958 1979
9N92 363 1774 1299
2
3 4 5
6 7
8 9 10
11 12
13 14 15
16 17
18 19 20 21 22 23 24 25 26 27
1979 1965 1982 1969 1976 1979
1973 1971 1971 1982 1963 1963 1977 1982 1970
1971 1962 1982 1962 1962 1979
1963 1982 1977
689 1860 1570 976
655 613 487 3668 1425
409 57 1795 1381 8439 C764 1427 1426 1429 616
1311 1263 1428 443
tered, even scattered through large angles. Rutherford reasoned that such behavior was possible only if the metal atoms that made un the foil consisted of a hiehlv " .dense nucleus surroundedby a void in which moved electrons. Stamos no. 11and 12 illustrate the deflection of aloha oarticles b;the nucleus in what has become known asthe"gold foil experiment". The conceptual development by Rutherford of a nuclear atom-an atom where all the positive charge was concentrated at the center while electrons somehowwere accommodated "outside" the nucleus paved the way for Bohr's monumental contributions to quantum theory. I t was Niels Bohr's (1885-1962) interpretation of the line soectrum of atomic hvdroeen , .. that disnelled remainine doubts surrounding the validity of the energy quantization concevt. Rohr's theoretical model. hased in oart ona nuclear atomand quantization of angular momehtum, yielded a value of the Rvdberg constant in dramatic agreement with experiment. stamp no. 13, in addition to ~ o h r ' ssignature, illustrates another facet of the theoretical model; viz. the discrete orbits in which the single electron in the hydrogen atom was required to move. The orbits can be indexed by quantum numbers 1, 2, 3.. . with electron energies El, Ez, E B . ... Stamps of common design (nos. 14 and 15) were issued by Denmark and Greenland to honor the 50th anniversary of Bohr's atomic theory, and each bears the formula hu = E1 - El. which accounts for the transition enerev ". betweedany two stationary states. Of additional interest is the elliptical orbit pictured on these stamps. Such noncircular orbits acknowledge Arnold Sommerfeld's (1868-1951) subsequent contribution to the atomic theorv of Bohr hv allowing for noncircular orbits. Such o r b i g require twb quantum numbers (a primary integer and a secondary integer) to describe their major and minor axes. Bohr became a central figure in the conceptual development of quantum mechanics and the leading proponent of its so-called "Copenhagen Interpretation". Of course there were other experimental observations that lent support to the emerging quantum theory. Two of these are of ohilatelic interest. soecificallv the Franck-Hertz experim&t and the X-ray st;dies oiilauricede Hroglie. Gustav Hertz (1887-1975; no. 161 u,as thr neoheu.of Heinrich Hertz, famous for his 19th century research on electro-
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magnetic waves. Together with James Frauck (1882-1964; no. 17) Gustav Hertz investigated electron collisions with gases and vapors with results stronelv suooortive of Bohr's .. idens regarding stationary elrctronic states in atoms. Maurice de Bwglie (1875-196U1 meanu,hile carried out some of theear1iest;esearch involving X-rays as a spectroscopic tool. Stamp no. 18, as its design shows, contains a portrait, a drawing of his spectroscopic apparatus, and the formula A W = hv. Maurice de Broglie served as a scientific secretary to the celebrated 1911 Solvay Congress convened to assess quantum development. He did much to stimulate his younger brother Louis de Broglie's (1892-1987) interest in the new ohvsics. Based on the ideas of Planck and Einstein. Louis . . developed the concept of wave-particle duality. ~ e g i n n i n ~ with Planck and Einstein, the commonlv acceoted wavelike properties of light had to he modified tb inclkde the quantum-corpuscular-particlelike nature exhibited by electromagnetic radiation in the "photoelectric effect" and in the explanation of atomic spectra. In 1923, Louis de Broglie speculated that the opposite might be true, that particuiate matter was also wavelike in nature! Specifically, he suggested that electrons in atoms nossess wavelike oronerties kith . . wavelengthsgo\,erned h y A = h rno.'l'his equation stipulates that there is a natural wavelenrth (todav called the de Hroglie wavelength), A, associated with a material hody of mass m moving at a speed u. This formula is shown on stamp no. 19. In 1927, de Broglie's speculation was dramatically confirmed independently by G. P. Thomson (1892-1975) and the team of C. P. Davisson (1881-1938) and L. H. Germer (1896-1972). In both cases electrons were used as projectiles onto elemental metallic sinele crvstal surfaces. Reflection " and diffraction were observed. The latter is a property of waves. Subseauent develonment of the electron microscone. made possible by an understanding of de Broglie waves: is also shown on stamp no. 19 along with a background of electron diffraction patterns-a pattern characteristic of waves. A key requirement of the Bohr theory of the hydrogen atom was that allowed energy states of an electron in a circular orbit have angular m&nentum around the nucleus equal toan integral multiple of h or h12a. De Broglie realized that this condition is satisfied when the orbit contains an integral number of standing wavelengths. Louis de Broglie received the 1929 Nobel Prize in Physics for work on " the wave nature of the electron" and this effort is remembered on stamp no. 20. It was the de Broglie wave idea, and the occurrence of standing waves with its analogy to acoustics, that attracted the attention of Erwin SchrBdineer (1887196lJ. He introduced a theory that he called wave'mechanics in which tht. behavior of a system is described hy a oartial differential wave equation.-Only certain solutions t o the equation are allowed within the constraints of the boundary conditions of the atomic system. These solutions are interpreted as "probabilities" or "regions" about the nucleus where there is hieh "electron densitv". Such a reeion or u ~" boundary surface is shown on stamp no. 21; the left portion reoresents the d? orbital while the rieht is aview of the same " orbital looking ciown the z axis. Meanwhile. Werner Heisenbere (1901-1976: no. 22) aoproached the same problem throu&matrix mechanics.'~& senberg's model of the atom was ourelv a mathematical one. ~ u r t h e ihe , enunciated a "principle of uncertainty", which stated that it is impossible to determine (measure) simultaneously the and momentum of a material hody. There will naturally be an uncertainty in each measurement that, when minimized, will still yield a product of value at least equal to h. This uncertainty principle challenged the deterministic ohilosoohers' notion that., eiven sufficient data, all knowlkdge was knowable. Heisenberg was a ouoil of Max Born (1882-1970: no. 17). .. who, too, wasinterested in the new quantum theory.'~esoon
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saw that the two seemingly different approaches of Schrodinger and Heisenberg were equivalent. Much of our present-day formalism in quantum mechanics is due to Born. The citation accompanvina his 1954 Nohel Prize in Physics reads "for his fuidamental work in quantum mechanics and especially for his statistical interpretation of the wave equation". Max Born is also well known to chemists and physicists for the Born-Oppenheimer approximation in qua&um mechanical calculatibns on molecules and for contributing the Born-Haher cycle to thermodynamics. Important experimental research had been reported much earlier and as such had a profound impact on the development of the new quantum theory. Pieter Zeeman (18651943) and Johannes Stark (1874-1957) reported on the influence that placing the light source in a strong magnetic or electric field had upon the lines observed in the atomic spectra, respectively. At the turn of the century, Zeeman under the direction of his teacher, Henrik Lorentz (18531928), showed that spectral lines were split into multiple field-the stroneer the field.. the ereater lines hv a maenetic " " the splitting. These observations confirmed an earlier suggestion of Lorentz's that atoms consisted of charged partiEles whose interactions could he affected by a n excernal magnetic field. Both men, student and teacher, shared the 1902 Nobel Prize in Physics, which is commemorated on stamp no. 23. Further experiments using electric fields were conducted by Stark. An explanation of the so-called "Stark splittinps" in the spectrum of atomic hydrogen (shown on stamp no. 24) provibed angular momentum assignments for atomic energy levels and supported the "correctness" of the Bohr atomicmodel. More difficult to explain was the so-called anomalous Zeeman effect exhibited by multiplet energy states. During the earliest days of the wave mechanical model and matrix mechanical model onlv three auantum numbers had been employed in its formaiism. A detailed study of the anomalous Zeeman effect led Wolfgang Pauli (1900-1958; no. 25) to propose a fourth quantum number and to announce his now famous exclusion principle: There can never he two equivalent electrons in an atom for which, in a strong field, the values of all the quantum numbers are the same. Two graduate students, Samuel Goudsmit and George Uhlenbeck soon associated the fourth quantum number with the spin of an electron. Pauli required that the fourth quantum number he restricted to one of two possible values: +1/2 or -1/2. Thus, the electron came to he viewed as spinning onlv one of two alphafbeta, etc. ways; up/down, clockwise/countercl~ckwis~, The exclusion principle made it possible to arrange electrons of various elements &to levels a i d sublevels, thereby hringing harmony between electronic structure of atoms and the periodic table. Schrodinger, in his original studies, had used a relativistic approach, which he discarded because of unsatisfactory agreement between theory and experimental data. His discrepancy was due to the neglect of electron spin. Later, Paul A. M. Dirac (1902-1984; no. 26) applied Einstein's theory of special relativity to an integrated form of matrix mechanics with wave mechanics and showed that spin arose naturally from the treatment. From this approach, Dirac was able to predict the existence of the positron two years before its discovery hv Carl Anderson (horn 1905). It was also Dirac who devised the "delta-function" and introduced it as a useful mathematical device into quantum theory. In the 50 or more years that have now passed since the events described above, scientists have witnessed the application of quantum methods to systems and problems of increasing complexity and sophistication. Many of the princ i ~ a l sin this develonment are still alive. and we cannot include their roles in'this philatelic account as it is not the normal oractice for postal authorities to honor living personalities. ?here havebeen two exceptions to this n&. One 258
Journal of Chemical Education
Figure 2. Sweden 1982 commemorative
issues recognizing Nobei prizes in
atomic physics.
individual was physicist Louis de Broglie, who only died in the early spring of 1987l and who was honoured by the nations of Nicaragua (no. 19) and Sweden (no. 20) while he still lived. The other is chemist Linu; Pauling (born 1901). He coauthored the influential textbook Introduction to Quantum Mechanics (3)and authored the treatise The ~ a t u r of e the Chemical Bond (4). In these works, Pauling significantly extended the valence bond description of molecular structure conceived by earlier workers. In this regard, benzene is worthy of particular mention. Pauling explained the experimental observation of six identical C-C bonds by postulatine- a nrocedure he called "resonance". In resonance. the . electronic situation is represented by a mathematical mixture of wave functions of the valence bond type, one for each contributing electrovalent structure. Two such structures (the Kekuli? structures) are illustrated on stamp no. 27. which also bears a portrait of Linus Pauling. It is interesting and instructional to note how various governments have perceived the importance of pure science. The nation of Sweden has been particularly cognizant of the contributions made by scientists to all of humankind. A regular program of recognizing Nobel laureates began in 1961with issues commemorating previous Nohel Prizes. Figure 2 shows the entire booklet and contents of the five prizes issued in physics for work cited primarily in quantum theory. I t is gratifying to find that such a large part of the
'
Unfortunately, several introductory textbooks erroneously report the death of Prince Louis de Broglie as occurring in the 1970's. Such reDoninQhas been observed for the last half dozen years with the most cimmonly mentioned date being 1977. nowever, the 1929 Nobei Laureate in Physics died 19 March 1987 in a Paris hospital at age 94.
quantum story is recorded on the world's postage stamps. For a further account of the application of quantum theory to spectroscopy, as told through the medium of philately, see reference 5. Note added in Proof: A stamp bearing Schrodinger's portrait was issued by Austria in August 1987 to mark the centenary of his birth.
Llterature Cited
I.
severalrecenttexts =an be ~ i t e dincluding the r o ~ ~ ~ ~(4 i nB.~OV, g: P.; B W ~ ~ D. D ,J.;
Acknowledgment
2.
The author appreciates the helpful comments from C. Marvin Lang. Photographic assistance has been provided by Karel Hartman and Gary Shulfer; for such assistance, the author is grateful.
3.
Routh, J. L. Introduction Lo the Chemistry o/Life; Saundem: New Yark. 1982. (b) Ehbing,D.D. GanerolCh~miatry,Znded.:Houghton-Miinin: Boston. 1987. (c) Kotz. J. c.; P U ~ ~ K. ~ IF.I chemlstry& , c h a m i d ~ e m i i u i t ysaunders: : N ~Y W ~ X1987. , (d) Masterton, W. L.; Slominski, E. J.; Stanitski, C. L. Chemical Principles; Saunden: New Yark. 1987. (el Seager. S. L.: Slabaugh. M. R. Chemistry lor Today, 2nd ed.; WeaL:St.Paul,MN, 1987. (02umdahl.S. S. Chemistry; Heath: Lexington,MA, 1986. N O ~ K IJ. ~ .H. physical chemistry: ~ i t t kBCOW": , N*W YO.X, 1985. Pau1ing.L.; Wi1son.E. B.,Jr.lnfmduelion foQvonium Mechonirs;MeGraw-Hill: New ~ o r k 1935. . ~ s u l i n gL. , ~ h Nolureolthe o chomieal~ond,znded.: Cornell university: Ithaea,NY. 1940. Mill..,F. A.Appl.Sp OcLl arc. L983,37, 219.225. s m t t standard postogp stornp ~ ~ tsmtt: ~ NIV ~ yark. ~ g ~ ~ :
4.
,. 6.
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