THE HYDROGEN SPECTRUM The Balmer Series.—As a general rule the spectrum of an element presents no obvious regularity of structure. It appears to be a miscellaneous collection of lines with no element of order in their positions or intensities. The spectrum of hydrogen, how ever, furnishes a conspicuous exception to this rule. In the visible and near ultra-violet regions, this spectrum consists entirely of a regular succession of lines which occur at continuously dimin ishing intervals as the shorter wave-lengths are approached, and at the same time show a steady falling off of intensity. (Plate II., No. 6.) Such a succession is known as a series of lines. It should be remarked that hydrogen has two distinct spectra, produced under different conditions of excitation. Under weak stimulus it yields a "blue" open band spectrum with no evidence of simple structure; a stronger stimulus, however, produces a much simpler "red" spectrum. It is the latter which contains the series here referred to.
The regularity of the hydrogen spectrum led in the early days of spectroscopy to many attempts to interpret the lines as ana logous to the fundamental and harmonic vibrations in acoustics. They failed because the wave-lengths or frequencies of the lines were not in the ordinary harmonic ratios and could be expressed by no formula in any way consistent with such an interpretation. It was not until 1885, in fact, that any reasonably accurate formula was suggested. In that year Balmer pointed out that the wave-lengths of the four lines of the series then known were accurately represented by the expression: = 3645.6 4) if m were given the respective integral values, 3, 4, 5 and 6. All doubt as to the significance of this relationship was removed by the fact that several further prominent lines, photographed by Sir William Huggins in the ultra-violet spectra of the stars, were found to be represented by the same formula when the value of m was increased successively by steps of unity. The series has con sequently come to be known as the Balmer series of hydrogen.
It is of advantage in theoretical discussions to express results in frequency, or wave-number, instead of wave-length. In these terms, if v,,, represents the wave-number of a line of the series, the Balmer formula becomes—adopting later and more accurate measurements:— where R=109678.3.
One or two important conclusions at once follow from this formula. In the first place, the strong red line at v15233.22 (X6562.793), corresponding to m=3, is actually the first line of the series, for if m= o, 1, 2, we obtain infinite, negative, and zero values for the wave-numbers, and these can have no physical significance. Secondly, no line of the series can occur further
in the ultra-violet than v27419.67 (X3645.982), corresponding to m= infinity. The series is therefore wholly contained between the limits of wave-length, 6562.793 and 3645.982.
Other Series of Hydrogen.—The Balmer series is not, how ever, the complete "red" spectrum of hydrogen. In the extreme ultra-violet a similar series has been found (the Lyman series), and in the infra-red, yet another (the Ritz-Paschen series). The wave-numbers of the lines in these series respectively obey the equally simple formulae— v.= (m= 2, 3, • • • ) v.= (m=4, 5, • • • )• The natural deduction that a series, might exist has been confirmed by F. S. Brackett, who has observed the first lines of such a series in the far infra-red. The difficulties of observation in this region are such as to prohibit the detection of further series of the same form.
It appears, therefore, that the wave-number of any line in the hydrogen spectrum can be expressed as the difference of two quantities. In any one series the larger of these quantities is con stant, and represents the wave-number of the line of shortest wave-length that the series can theoretically contain. It is known as the limit of the series. The other quantity varies from line to line, and is known as the term. Clearly there is no fundamental difference between a limit and a term, for the limit of the Balmer series is a term of the Lyman series; the limit of the Ritz Paschen series is a term of both the Balmer and the Lyman series ; and so on. We can, therefore, generalize our results by say ing that the hydrogen spectrum is associated with a number of terms of the form where is any integer, and that the difference between any two of these terms corresponds to a possible line in the spectrum. The classification of the lines into separate series is thus somewhat arbitrary, and owes more to the visible appearance of the spectrum than to ultimate distinc tions. In considering the nature of the spectrum, attention must naturally be concentrated on the terms, the lines being regarded as rather complex, derivative expressions of these simple f unda mental quantities. From this point of view we may say that the whole of the hydrogen spectrum is expressed by the symbol where m ranges from one to infinity.