Quantum_ Einstein, Bohr and the Great Debate About the Nature of Reality - Manjit Kumar [54]
'I hope very soon to be able to send you my paper on the atoms,' Bohr wrote to Rutherford on 31 January 1913, 'it has taken far more time than I had thought; I think, however, that I have made some progress in it in the latest time.'19 He had stabilised the nuclear atom by quantising the angular momentum of the orbiting electrons, and thereby explained why
Figure 6: Some of the stationary states and the corresponding energy levels of the hydrogen atom (not drawn to scale)
they could occupy only a certain number, the stationary states, of all possible orbits. Within days of writing to Rutherford, Bohr came across the third and final clue that allowed him to complete the construction of his quantum atomic model.
Hans Hansen, a year younger and a friend of Bohr's from their student days in Copenhagen, had just returned to the Danish capital after completing his studies in Göttingen. When they met, Bohr told him about his latest ideas on atomic structure. Having conducted research in Germany in spectroscopy, the study of the absorption and emission of radiation by atoms and molecules, Hansen asked Bohr if his work shed any light on the production of spectral lines. It had long been known that the appearance of a naked flame changed colour depending upon which metal was being vaporised: bright yellow with sodium, deep red with lithium, and violet with potassium. In the nineteenth century it had been discovered that each element produced a unique set of spectral lines, spikes in the spectrum of light. The number, spacing and wavelengths of the spectral lines produced by the atoms of any given element are unique, a fingerprint of light that can be used to identify it.
Spectra appeared far too complicated, given the enormous variety of patterns displayed by the spectral lines of the different elements, for anyone to seriously believe that they could be the key to unlocking the inner workings of the atom. The beautiful array of colours on a butterfly's wing were all very interesting, Bohr said later, 'but nobody thought that one could get the basis of biology from the colouring of the wing of a butterfly'.20 There was obviously a link between an atom and its spectral lines, but at the beginning of February 1913 Bohr had no inkling what it could be. Hansen suggested that he take a look at Balmer's formula for the spectral lines of hydrogen. As far as Bohr could remember, he had never heard of it. More likely he had simply forgotten it. Hanson outlined the formula and pointed out that no one knew why it worked.
Johann Balmer was a Swiss mathematics teacher at a girls' school in Basel and a part-time lecturer at the local university. Knowing that he was interested in numerology, a colleague told Balmer about the four spectral lines of hydrogen after he had complained about having nothing interesting to do. Intrigued, he set out to find a mathematical relationship between the lines where none appeared to exist. The Swedish physicist, Anders Ångström, had in the 1850s measured the wavelengths of the four lines in the red, green, blue and violet regions of the visible spectrum of hydrogen with remarkable accuracy. Labelling them alpha, beta, gamma and delta respectively, he found their wavelengths to be: 656.210, 486.074, 434.01 and 410.12nm.21 In June 1884, as he approached 60, Balmer found a formula that reproduced the wavelengths () of the four spectral lines: = b[m2/(m2–n2)] in which m and n are integers and b is a constant, a number determined by experiment as 364.56nm.
Balmer discovered that if n was fixed as 2 but m set equal to 3, 4, 5 or 6, then his formula gave an almost exact