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4-2: The Atomic Spectra

The lights from discharge tubes or arcs across various kinds of electrodes with a high voltage potential being applied represent line spectra which consist of a numbers of bright sharp lines characteristic of the gases involved in the tube or the matters of the electrodes. Some examples are shown in the pictures below.

Examples of Atomic Spectra
The sun light has a continuous spectrum, in which there are some absorption lines named the Fraunhofer lines of which detailed explanations are omitted here. The spectra of hydrogen and mercury show some characteristic lines, but the pictures here are not so good to look them clearly.

[Balmer's Formula]
The group of lines of the hydrogen spectrum named the Balmer series which are observed in the part from visible to ultraviolet region is shown in the following picture. (Other series than the Balmer one, e.g. the Lymann, Paschen and Brackett series, are found in the hydrogen spectrum as well.)
A line spectra of hydrogen atom (the Balmer series)
A high school teacher, J. J. Balmer (Switzerland, 1825 - 98) discovered in 1885 that the wavelengths of the spectral lines, , , and , in the Balmer series shown in the above picture are respectively written

and these are represented by a simple formula

This is called Balmer's formula. It has been confirmed that the other lines in the Balmer series than the above , , and also obey Balmer's formula mentioned above.

[Rydberg's Formula]
In 1890, Rydberg (Sweden) found a very simple formula which can represent the wavelengths , not only in the hydrogen spectrum but also in the spectra of alkali atoms. This is Rydberg's formula

where m and n are integers, and a and b are different for each series of spectra but constant within a series. The constant R is called the Rydberg constant whose value was obtained from the experimental data for hydrogen as

Balmer's formula is one of the special cases in Rydberg's formula. Putting a = b = 0 and m = 2 in Rydberg's formula, we can obtain

which is equivalent to Balmer's formula.
We cannot explain these Balmer's and Rydberg's formulae with the classical theory. At this point people necessitated making a big jump to a new revolutionary theory.
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