Quantum Physics

28.2 Atomic Spectra 905l(nm) 400 500 600 700(a)HHgNeHl(nm) 400 500 600 700(b)Figure 28.3 Visible spectra. (a) Line spectra produced by emission in the visible range for the elementshydrogen, mercury, and neon. (b) The absorption spectrum for hydrogen. The dark absorptionlines occur at the same wavelengths as the emission lines for hydrogen shown in (a).K. W. Whitten, R. E. Davis, M. L. Peck, and G. G. Stanley, General Chemistry,7th ed., Belmont, CA, Brooks/Cole, 2004.ions such as He and Li 2 . Further, a thorough understanding of the physics underlyingthe hydrogen atom can then be used to describe more complex atomsand the periodic table of the elements.Suppose an evacuated glass tube is filled with hydrogen (or some other gas) atlow pressure. If a voltage applied between metal electrodes in the tube is greatenough to produce an electric current in the gas, the tube emits light having acolor that depends on the gas inside. (This is how a neon sign works.) When theemitted light is analyzed with a spectrometer, discrete bright lines are observed,each having a different wavelength, or color. Such a series of spectral lines is commonlycalled an emission spectrum. The wavelengths contained in such a spectrumare characteristic of the element emitting the light (Fig. 28.3). Because notwo elements emit the same line spectrum, this phenomenon represents a marvelousand reliable technique for identifying elements in a gaseous substance.The emission spectrum of hydrogen shown in Figure 28.4 includes four prominentlines that occur at wavelengths of 656.3 nm, 486.1 nm, 434.1 nm, and410.2 nm, respectively. In 1885 Johann Balmer (1825–1898) found that the wavelengthsof these and less prominent lines can be described by the simple empiricalequation1 R H 1 [28.1]2 2 1 2 nwhere n may have integral values of 3, 4, 5, . . . , and R H is a constant, called theRydberg constant. If the wavelength is in meters, R H has the valueR H 1.097 373 2 10 7 m 1 [28.2]The first line in the Balmer series, at 656.3 nm, corresponds to n 3 in Equation28.1, the line at 486.1 nm corresponds to n 4, and so on. In addition to theBalmer series of spectral lines, a Lyman series was subsequently discovered in thefar ultraviolet, with the radiated wavelengths described by a similar equation.In addition to emitting light at specific wavelengths, an element can absorblight at specific wavelengths. The spectral lines corresponding to this process formwhat is known as an absorption spectrum. An absorption spectrum can be obtainedby passing a continuous radiation spectrum (one containing all wavelengths)through a vapor of the element being analyzed. The absorption spectrumconsists of a series of dark lines superimposed on the otherwise bright continuousspectrum. Each line in the absorption spectrum of a given element coincides witha line in the emission spectrum of the element. This means that if hydrogen is theλ(nm)364.6410.2 434.1486.1 656.3Figure 28.4 The Balmer series ofspectral lines for atomic hydrogen,with several lines marked with thewavelength in nanometers. The linelabeled 346.6 is the shortest-wavelengthline and is in the ultravioletregion of the electromagneticspectrum. The other labeled lines arein the visible region. Balmer series Rydberg constant