THE HYDROGEN SPECTRUM The Nucleus Atom.—From the earliest days of spectroscopy the question of the origin of spectra has engaged the attention of theoretical physicists, but it was not until 1913 that the line of investigation which has since proved so fruitful was inaugurated by Bohr. The earlier work can be summed up very briefly. The fact that a spectrum was characteristic of the emitting substance showed that it was an atomic or molecular phenomenon, and a theory of spectra therefore involved at least a partial theory of atomic and molecular structure. The fact that both sound and light were conceived as trains of waves naturally suggested that the like the former, might originate in periodic vibrations of material bodies, and the atoms of luminous substances were consequently looked upon as vibrating systems. But in those days there was no evidence of structure in the atom, and the character of the vibrations could be little more than guessed at. Furthermore, as already stated, the frequencies of the radiations in even the simplest known spectrum—that of hydrogen—bore no relation to one another which could be reconciled with the har monic ratios known in acoustics. It is not surprising, therefore, that no progress was made.
But by the year 1913 the developments of general physics had created a much more favourable situation for the solution of the problem. In the first place, a definite model of the atom, proposed by Sir Ernest Rutherford, was available, which con sisted of a central nucleus positively charged with electricity, surrounded by a number of revolving electrons whose total (nega tive) charge balanced the charge of the nucleus. One element differed from another in the nuclear charge, and consequently in the number of revolving electrons, this number being equal to the atomic number of the element. Thus, hydrogen had one re volving electron, helium, two, and so on. Secondly, other physi cal phenomena seemed to point to the conclusion that atoms could radiate energy only in definite unit quantities, known as quanta, the amount of which depended on the frequency of the radiation and was, in fact, equal to the product of the frequency and a constant quantity, h (Planck's constant). The application of this idea to the Rutherford atomic model enabled Bohr to give a quantitative explanation of the hydrogen spectrum and lay the foundations of the whole modern theory of spectra.
Bohr's Theory.—The physical conceptions of the Bohr theory
will be described here only in so far as is necessary to interpret the facts of spectroscopy. Their wider aspects are dealt with elsewhere. (See ATOM, QUANTUM THEORY.) In order to explain the hydrogen spectrum, Bohr assumed that the single electron of hydrogen could revolve round the nucleus according to the ordinary mechanical laws, but only in any one of a series of discrete orbits, determined by the condition that the angular momentum must be an integral multiple of h/27r. The atom was, therefore, capable of existing in a number of states, known as stationary states, corresponding to the different possible orbit. of the electron. The energy of the atom depended on the orbit of the electron, and was regarded as proportional to a term of the spectrum, each orbit thus being associated with a particular spectrum term. In the ordinary, non-radiating state of the gas, the electrons were in their innermost orbits, where their energy was less than that required for revolution in any other orbit, but on being stimulated to radiate, the atoms absorbed energy from the exciting source in just the amounts necessary to remove the electrons to outer orbits. An atom so excited, however, re turned to its normal state at the earliest opportunity, either by a single jump or by successive transitions to intermediate per missible orbits. At each transition it radiated the difference of energy corresponding to revolution in the two orbits concerned as a spectrum line of frequency v, where hv was the energy radiated. An inward passage between each pair of orbits thus resulted in the radiation of a particular line in the spectrum, whose wave-number was equal to the difference of the corresponding terms, and the whole spectrum consisted of the sum of the radia tions of all the atoms in the radiating source.
Treating these conceptions mathematically, Bohr was able to deduce the Balmer and other formulae for the hydrogen series, and further, to show that the Rydberg constant, R, was given by where e, m are respectively the charge and mass of an electron, E, M, are the corresponding quantities for the nucleus, and c is the velocity of light. For hydrogen, with only one electron, e=E, but 1V1 is nearly 2,000 times m. The spectroscopic determination of R, in fact, now appears to be one of the most accurate methods of determining the ratio of M to m, and gives a value, 1,845.