| ν = N²K |  | 1 | - | 1 |  |
| n″ ² | n′ 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.
The Introduction of more than one Quantum Number.
During the first years after 1913, Bohr was practically alone in working out his theory, at that time still assailed by many, and in showing its application to many problems. In 1916, however, the theorists in other countries, led by the well-known Munich professor, Sommerfeld, began to associate themselves with the Bohr theory, and their investigations gave rise to much essential progress. We shall here mention some of the most important contributions.
In the theory for the hydrogen spectrum propounded above, it was assumed that we had to do with a single series of stationary orbits, each characterized by its quantum number. But as shown by theoretical investigations each of the stationary orbits must, when more detail is asked for, also be indicated by an additional quantum number.
Fig. 26.—A compound electron motion produced
by the very rapid rotation of an elliptical orbit.