37.2.2 Discrete Spectra
Michael Faraday wanted to know whether an electric current could pass through a gas. To find out, he sealed metal electrodes into a glass tube, lowered the pressure with a primitive vacuum pump, and then attached an electrostatic generator. When he started the generator, the gas inside the tube began to glow with a bright purple color! Faraday’s device, called a gas discharge tube, is shown in FIGURE 37.4.
FIGURE 37.4 Faraday’s gas discharge tube.
The purple color Faraday saw is characteristic of nitrogen, the primary component of air. You are more likely familiar with the reddish-orange color of a neon discharge tube. If light from a neon discharge tube is sent through a spectrometer, it produces the spectrum seen in FIGURE 37.5. This is called a discrete spectrum because it contains only discrete, individual wavelengths. Further, each kind of gas emits a unique spectrum—a spectral fingerprint—that distinguishes it from every other gas.
FIGURE 37.5 The discrete spectrum of a neon discharge tube.
The discrete emission spectrum of a hot, low-density gas stands in sharp contrast to the continuous blackbody spectrum of a glowing solid. Not only do gases emit discrete wavelengths, but it was soon discovered that they also absorb discrete wavelengths. FIGURE 37.6a shows an absorption experiment in which white light passes through a sample of gas. Without the gas, the white light would expose the film with a continuous rainbow spectrum. Any wavelengths absorbed by the gas are missing, and the film is dark at that wavelength. FIGURE 37.6b shows, for sodium vapor, that only certain discrete wavelengths are absorbed.
FIGURE 37.6 Measuring an absorption spectrum.
Although the emission and absorption spectra of a gas are both discrete, Figure 37.6b shows an important difference: Every wavelength absorbed by the gas is also emitted, but not every emitted wavelength is absorbed. All the absorption wavelengths are prominent in the emission spectrum, but there are many emission wavelengths for which no absorption occurs.
What causes atoms to emit or absorb light? Why a discrete spectrum? Why are some wavelengths emitted but not absorbed? Why is each element different? Nineteenth-century physicists struggled with these questions but could not answer them. Classical physics was incapable of providing an understanding of atoms.
The only encouraging sign came from an unlikely source. While the spectra of other atoms have dozens or even hundreds of wavelengths, the emission spectrum of hydrogen, seen in FIGURE 37.7, is very simple and regular. If any spectrum could be understood, it should be that of the first element in the periodic table. The breakthrough came in 1885, not by an established and recognized scientist but by a Swiss schoolteacher, Johann Balmer. Balmer showed that the wavelengths in the hydrogen spectrum could be represented by the simple formula
FIGURE 37.7 The hydrogen emission spectrum.
This formula predicts a series of spectral lines of gradually decreasing wavelength, converging to the series limit wavelength of 364.7 nm as . This series of spectral lines is now called the Balmer series.
Later experimental evidence, as ultraviolet and infrared spectroscopy developed, showed that Balmer’s result could be generalized to
We now refer to Equation 37.4 as the Balmer formula, although Balmer himself suggested only the original version of Equation 37.3 in which . Other than at the highest levels of resolution, where new details appear that need not concern us in this text, the Balmer formula accurately describes every wavelength in the emission spectrum of hydrogen.
The Balmer formula is what we call empirical knowledge. It is an accurate mathematical representation found empirically—that is, through experimental evidence—but it does not rest on any physical principles or physical laws. Yet the formula was so simple that it must, everyone agreed, have a simple explanation. It would take 30 years to find it.