# Atomic Spectra

We have already seen the colors of a continuous spectrum -- such as the white light from a hot filament in a lamp or bulb. When this white light passes through a prism the different wavelengths of light are bent through different angles and the colorful spectrum results. However, the spectrum from a gas that is heated is somewhat different. Only certain, particular, discrete wavelengths (or colors) are present. Each element has a "fingerprint" in the particular lines, colors, or wavelengths in its spectrum.

Hydrogen is the lightest and simplest element. In 1885, J J Balmer, a Swiss high school teacher, found that the wavelengths of the four visible lines produced by hydrogen are described by  n = 3, 4, 5, 6

where R = 1.097 x 107 m-1 is called the Rydberg constant. These spectral lines are known as the Balmer series. To explain the four visible wavelengths n takes on only the values n = 3, 4, 5, or 6. Use Balmer's equation to determine the first three wavelengths in the Balmer series. , n = 3, 4, 5, 6

with R = 1.097 x 107 m-1.

Solution: For n = 3,  1.524 x 106 m-1 = 6.563 x 10-7 m = 656.3 nm (red)

For n = 4,  = 486.2 nm (blue-green)

For n = 5,  = 434.1 nm (violet)

Further experiments determined that there were additional, similar series of spectral lines produced by hydrogen in the infrared and ultraviolet regions. These series of lines could be described by equations similar to Balmer's. In the UV region, the Lyman series was found and could be described by  n = 2, 3, . . .

These lines in the Lyman series have wavelengths from 91 nm to 122 nm. In the IR region, the Paschen series could be fit by  n = 4, 5, . . .

Further into the IR region lay another series of lines, the Brackett series, whose wavelengths could be calculated from  n = 5, 6, . . .

These may be generalized to  n2 = 1, 2, 3; n1 = (n2 + 1), (n2 + 2), . . .

Any detailed model of the atom's structure ought to be able to predict these wavelengths of the light given off by hydrogen, the simplest atom.  