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Unformatted text preview: Hydrogen-Deuterium Mass Ratio 1 Background 1.1 Balmer and Rydberg Formulas By the middle of the 19th century it was well established that atoms emitted light at discrete wavelengths. This is in contrast to a heated solid which emits light over a continuous range of wavelengths. The difference between continuous and discrete spectra can be readily observed by viewing both incandescent and fluorescent lamps through a diffraction grating; hand held gratings are available for you to do this in the laboratory. Around 1860 Kirchoff and Bunsen discovered that each element has its own characteristic spec- trum. The next several decades saw the accumulation of a wealth of spectroscopic data from many elements. What was lacking though, was a mathematical relation between the various spectral lines from a given element. The visible spectrum of hydrogen, being relatively simple compared to the spectra of other elements, was a particular focus of attempts to find an empirical relation between the wavelengths of its spectral lines. In 1885 Balmer discovered that the wavelengths n of the then nine known lines in the hydrogen spectrum were described to better than one part in a thousand by the formula n = 3646 n 2 / ( n 2- 4) A (angstrom) , (1) where n = 3 , 4 , 5 , . . . for the various lines in this series, now known as the Balmer series. (1 angstrom = 10- 10 m.) The more commonly used unit of length on this scale is the nm (10- 9 m), but since the monochromator readout is in angstroms, we will use the latter unit throughout this write-up. In 1890 Rydberg recast the Balmer formula in more general form as 1 / n = R (1 / 2 2- 1 /n 2 ) (2) where again n = 3 , 4 , 5 , . . . and R is known as the Rydberg constant. For reasons to be explained later, its value depends on the mass of the nucleus of the particular isotope of the atom under consideration. The value for hydrogen from current spectroscopic data is R H = 109677 . 5810 cm- 1  , and the current value for an infinitely heavy nucleus is R = 109737 . 31568525(73) cm- 1  . A generalization of the Rydberg formula to 1 / = R H 1 n 2 1- 1 n 2 2 (3) suggested that other series may exist with n 1 taking on the values 1 , 3 , 4 , 5 , . . . , subject to the restriction that n 2 > n 1 . This proved to indeed be the case. In 1906 Lyman measured the ultraviolet spectrum of hydrogen and found the series, now bearing his name, corresponding to n 1 = 1. In 1908 Paschen measured the infrared spectrum of hydrogen and discovered the series, now bearing his name, corresponding to n 1 = 3. Figure 1 shows some of the lines in these series. 1 Figure 1: Energy level diagram of atomic hydrogen showing the transitions giving rise to the Lyman (IR), Balmer (visible) and Paschen (UV) spectra....
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