The Spectrum of Atomic Hydrogen For almost a century light emitted by the simplest of atoms has been the chief experimental basis for theories of the structure of matter. Exploration of the hydrogen spectrum continues, now aided by lasers by Theodor W. Hansch, Arthur L. Schawlow and George W. Series he spectrum of the hydrogen atom sorbed. glvmg rise to dark lines on a that he could account for the positions has proved to be the Rosetta stone bright background. of all the known lines by applying a sim­ Tof modern physics: once this pat­ Hydrogen is the simplest of atoms. be­ ple empirical formula. The entire set of tern of lines had been deciphered much ing made up of a single electron and a lines has since come to be known as the else could also be understood. Most no­ nucleus that consists of a single proton. Balmer series. Another group of lines. tably. it was largely the effort to explain and so it can be expected to have the the Lyman series. lies in the far ultravio­ the spectrum of light emitted by the hy­ simplest spectrum. The spectrum is not. let. and there are other series at longer drogen atom that inspired the laws of however. an easy one to record. The wavelengths. Within each series the in­ quantum mechanics. Those laws have most prominent line was detected in dividual lines are designated by Greek since been found to apply not only to 1853 by Anders Jonas Angstrom. (The letters. starting with the line of longest the hydrogen atom but also to other common unit for measuring wave­ wavelength. Thus the bright red line first atoms. to molecules and to matter in lengths of light is named for Angstrom; seen by Angstrom is the Balmer-alpha bulk. They are the ultimate foundation one angstrom unit is equal to 10.8 centi­ line. the next is the Balmer-beta line and of modern chemistry. of solid-state meter.) In the next two decades three so on. Because of the prominence of the physics and even of applied sciences more lines were observed. but the first Balmer-alpha line it is sometimes called such as electronics. extended series of atomic-hydrogen The central position of the hydrogen lines was found not in the laboratory but atom in the history of 20th-century in the spectra of stars. In 1881. working physics might seem to suggest that the with the first photographs of stellar spectrum has long been known in all its spectra. Sir William Huggins identified BALMER-ALPHA 6.563 details. That is not so. Only in the past 10 lines as being emissions of atomic few years have some of the subtler fea­ hydrogen. tures of the spectrum been resolved. and It may seem surprising that lines of many others have not yet been observed the hydrogen spectrum were seen in directly. Measuring the positions of the astronomical observations before they spectral lines remains today a significant were seen in terrestrial experiments. The test of the' predictions of the quantum difficulty in measuring the spectrum in theory. the laboratory is not in detecting the The most recent advances in the anal­ lines but in preparing pure atomic hy­ ysis of the spectrum can be attributed to drogen. Ordinary hydrogen gas consists a new tool of spectroscopy: the laser. of diatomic molecules (H2). which have Beca use the finest details of the spec­ a spectrum that is much more compli­ trum are closely spaced they can be dis-I cated than the spectrum of the isolated tinguished only by light that is highly hydrogen atom. Splitting the molecules monochromatic. or confined to a nar­ requires more energy than can be sup­ row range of wavelengths. The laser is a plied by most thermal excitations. such source of such light. As a result of some as a flame. One device that furnishes ingenious laboratory technology it has the energy very effectively is the gas­ become a spectroscopic instrument of discharge tube. where electrons accel­ unprecedented resolution. erated by an applied voltage dissociate the molecules. Over the years means The Line Spectrum have been discovered for enhancing the atomic spectrum and suppressing When light from a hot filament is dis­ the molecular one. persed according to wavelength by a The spectral lines detected by Hug­ prism or a diffraction grating. the result gins range in wavelength from the red is a continuous fan of colors. but the portion of the visible spectrum to the spectrum from a pure. rarefied gas of near ultraviolet. The first two lines are PATTERN OF DISTINCT LINES is formed atoms or molecules consists of discrete quite far apart. but the subsequent ones when the light emitted by hydrogen atoms is lines. If the spectrum is recorded from come at smoothly decreasing intervals. dispersed according to wavelength. The lines are those of the Balmer series, and their ap­ light emitted by the gas. it appears as a and those at the shortest wavelengths proximate wavelengths are given in angstrom sequence of bright lines against a dark are bunched closely together. In 1885. units (one angstrom is equal to 10.8 centime­ background. If light is passed through working from the astronomical mea­ ter). The color photograph was made by Jon the gas. discrete wavelengths are ab- surements. Johann Jakob Balmer found Brenneis and one of the authors (Schawlow) 94 © 1979 SCIENTIFIC AMERICAN, INC simply the hydrogen-alpha, or H-alpha, hydrogen atom the equation has a sim­ of. he said, as being like the notes of a line. pler form: piano, whose tones depend in a compli­ In 1889 Johannes Rydberg discovered cated way on the structure of the instru­ that the line spectra of many elements, ment as a whole. most notably those of the alkali metals, The reference to musical notes was could be fitted by a single empirical for­ not an idle one. In the 19th century mula. A later version of the formula, When the appropriate values of m and n many investigators had speculated that which is equivalent to Rydberg's equa­ are substituted in this formula, it yields the light emitted by atoms might be un­ tion but more explicit, has the form the wavelengths of all the lines in the derstood by some analogy to the modes hydrogen spectrum. of vibration of a solid body. The pres­ 1 1 ence of multiple lines in each series R r - I-j . X = L(m + b)2 (n + C)2 Atomic Struc;:ture could then be explained by assuming that the first line was the fundamental Here A (the Greek letter lambda) is the In 1912 Niels Bohr spent most of the mode and the rest were overtones, or wavelength of a particular line in an year at the University of Manchester harmonics. No optical spectrum could atomic spectrum, m and n are numbers working in the laboratory of Ernest be resolved into a fundamental frequen­ that take on successive integer values (1, Rutherford, who had just made a vi­ cy and its overtones, however, and so 2, 3 and so on) and R, band c are con­ tal contribution to the understanding of more direct examination of the atom it­ stants. The values of band c depend on atomic structure. By then the Balmer self was undertaken. what series of lines is being measured, and the Rydberg formulas were well Rutherford's contribution was the but R is the same for all lines of all the known to spectroscopists, and they had demonstration that the atom is not a elements. R is now called the Rydberg been thoroughly tested, but Bohr had solid body but rather consists of a constant; if the wavelength is expressed never heard of either of them. When he small, dense, positively charged nucleus in meters, R has the value (097 X 107 was told of Balmer's equation, he was and the requisite number of negatively and the dimensions of reciprocal me­ able to derive it almost immediately charged electrons to form a stable and ters. After Rydberg had checked his for­ from the properties of the hydrogen electrically neutral system. Bohr under­ mula against a number of spectra he atom. Abraham Pais and T. D. Lee have took to explain the spectra of atoms in wrote: "I had just finished testing vari­ reported that Bohr was asked late in his the context of this model. In doing so he ous forms of the function when I heard life how he could have escaped knowing risked the ridicule of his contemporaries of Mr. Balmer's communication on the of the Balmer formula. He explained by hypothesizing that within the atom spectral lines of atomic hydrogen. I was that in those days most physicists re­ the established laws of physics do not delighted to find that his formula is a garded atomic spectra as being so com­ apply. Those laws predicted that any special case of mine, with the same val­ plicated they were hardly a part of fun­ bound electron would radiate away all ue of R, and with c = 0." Hence for the damental physics. They were thought its energy and fall into the nucleus. Bohr WAVELENGTH (ANGSTROM UNITS) BALMER-BETA BALMER-GAMMA BALMER-DELTA 4,861 4,340 4,102 in the latter's laboratory at Stanford University, The black-and­ charge tube in which hydrogen molecules (H2) are dissociated into white spectrnm was recorded in 1927 by Gerhard Herzberg, who was atoms by an electric potential, In the color photograph the yellow and then at the Darmstadt Technical University in Germany, The inter­ green bands and the continuous blue background at the right are not vals between the lines are different in the two photographs because part of the atomic-hydrogen spectrum but result from molecular con­ Brenneis and Schawlow dispersed the light with a diffraction grating, taminants in the discharge tube.