The False Hydrogen Spectrum.

In 1897 the American astronomer, Pickering, discovered in the spectrum of a star, in addition to the usual lines given by the Balmer series, a series of lines each of which lay about midway between two lines of the Balmer series; the frequencies of these lines could be represented by a formula which was very similar to the Balmer formula; it was necessary merely to substitute n = 3½, 4½, 5½, etc., in the formula on [p. 57] instead of n = 3, 4, 5, etc. It was later discovered that in many stars there was a line corresponding to n″ = ³/₂ or n′ = 2 in the usual Balmer-Ritz formula ([p. 59]). It was considered that these must be hydrogen lines, and that the spectral formula for this element should properly be written

ν = K 1 - 1
(n″/2) ²(n′/2) ²

where n″ and n′ can assume integral values. This was done since it was not to be believed that the spectral properties of chemically different elements could be so similar. This view was very much strengthened when Fowler, in 1912, discovered the Pickering lines in the light from a vacuum tube containing a mixture of hydrogen and helium. It could not quite be understood, however, why the new lines did not in general appear in the hydrogen spectrum.

According to the Bohr theory for the hydrogen spectrum it was impossible—except by giving up the agreement ([cf. p. 129]) with electrodynamics in the region of high orbit numbers—to attribute to the hydrogen atom the emission of lines corresponding to a formula where the whole numbers were halved. The formula given above might, however, also be written as

ν = 4K 1 - 1
n″ ²n′ ²

If the earlier calculations had been carried out a little more generally, i.e., if instead of equating the nuclear charge with 1 elementary electric quantum e, as in hydrogen, it had been equated with Ne where N is an integer, then the frequency might have been written as

ν = N²K 1 - 1
n″ ²n′ ²

This formula is evidently the same as that just given when N equals 2. Now we know that helium has the atomic number and nuclear charge 2 ([cf. p. 90]); a normal neutral helium atom has two electrons and it is, therefore, very different from a hydrogen atom. If, however, a helium atom has lost one electron and therefore has become a positive ion with one charge, it is a system like the hydrogen atom with only one single electron moving about the nucleus. It differs in its “outer” characteristics from the hydrogen atom only in having a nuclear charge twice as great, i.e. its spectral formula must be given with N = 2, or N² = 4. The formula for the supposed hydrogen lines would consequently fit the case of a helium atom which has lost an electron. Bohr was aware of this, and he therefore suggested that the lines in question were due, not to hydrogen, but to helium.

At first all the authorities in the field of spectroscopy were against this view; but most of the doubt was dispelled when Evans showed that the lines could be produced in a vacuum tube where there was only helium with not a trace of hydrogen.

In a letter to Nature in September 1913, Fowler objected to the Bohr theory on the ground that the disputed line-formula did not exactly correspond to the formula with 4K, but that there was a slight disagreement. Bohr’s answer was immediate. He called attention to the fact that—since temporarily he had sought only a first approximation—in his calculations he had taken the mass of the nucleus to be infinite in comparison to the mass of the electron, so that the nucleus could be considered exactly at the focus of the ellipse described by the electron. In reality, he said, it must be assumed that nucleus and electron move about their common centre of gravity, just as in the motion in the solar system it must be assumed that not the centre of the sun, but the centre of gravity of the entire system remains fixed. This motion of the nucleus leads to the introduction of a factor M/(M + m) in the expression for the constant K given on [p. 129], where M is the mass of the nucleus and m that of the electron, which in hydrogen is ¹/₁₈₃₅ that of the nucleus. In helium, M is four times as large as in hydrogen, so that the given factor here has a slightly different value. The difference in the values for K for the hydrogen and for the helium spectrum which was found by Fowler, is 0·04 per cent., which agrees exactly with the theoretical difference.

Bohr thus turned Fowler’s objection into a strong argument in favour of the theory.