Bohr replaced it by a model that combined the classical theory with the Planck quantum theory. Using this hybrid theory, Bohr derived a general formula for the emission of radiation by the hydrogen atom that not only gives the observed wavelengths of the Balmer lines (the Balmer formula given above being a special case of the Bohr formula) but correctly predicts other series of lines in the ultraviolet and the infrared part of the hydrogen spectrum that were subsequently observed. Bohr reasoned that the very existence of an atom such as hydrogen, consisting of a positively charged proton and a negatively charged electron revolving in a definite orbit around the proton, can be understood only in terms of some basic length that can account for the stable dimensions of the atom (in other words, why the atom does not collapse). Because dimensional considerations show that such a length cannot be constructed by some mathematical combination of the electric charge e on the electron, and the mass m of the electron alone, Bohr argued that one must introduce into atomic theory another basic physical constant that, when properly combined with the constants e and m, gives this required length. He found that Planck's constant h served this purpose well, and he proposed for this basic length the mathematical combination
Because the numerical value of the length is 10-8 cm, it equals the so-called radius of the hydrogen atom. This value is also referred to as the Bohr radius of the hydrogen atom, or the radius of the first Bohr orbit. Using a revolutionary and completely anticlassical concept, introduced by the quantum theory, that action is quantised in indivisible units of h (meaning that there can be no action less than h), Bohr accounted for the stability of the hydrogen atom by assigning a single unit of action to the first so-called Bohr orbit. He thus eliminated any possible smaller orbit, because such an orbit would then have an action less than h, contrary to the quantum hypothesis. Bohr next assumed that each succeeding higher permissible orbit of the electron, as one moves away from the proton, differs from the one immediately below it by a single unit of action h. Thus, the action of the second orbit must be 2h, the action of the third orbit 3h, and so on.