La modernización como proceso de transformación socio-espacial

The final quantum conjectures I will address come out of Bohr’s model of the hydrogen atom.11 _{Bohr motivates his 1913 paper by noting that certain} experimental results on α-ray scattering seem to support Rutherford’s atomic model, but that this model comes up against conceptual and theoretical problems not encountered in alternative atomic models such as Thompson’s. One important issue is that Rutherford’s model requires the existence of stable states that cannot be determined based on classical electrodynamics. Furthermore, the quantities present in the Rutherford model do not provide enough information to determine a characteristic length for the radius of the atom. Bohr notes that the introduction of

h provides this information, since its units and dimensions make it possible to calculate the length of the atom which turns out to be of the expected order of magnitude based on other experiments. Thus, Bohr’s use of the quantum postulate is directed towards providing a preliminary theory of the structure of the atom, in contrast to the work on radiation that came before. However, his quantum

conjecture is again notably different from Planck’s, even though the fundamental idea of quantization comes directly from Planck’s work.

In the first section of the paper, Bohr shows how applying assumptions found in Planck’s theory of radiation to ideas on the atomic structure of hydrogen results in an account of how electrons might be bound to a positive nucleus in stable states. He first considers an atomic model in the style of Rutherford, consisting of a system of a positively charged nucleus with an electron orbiting this nucleus. He describes how a classical treatment of energy radiation by the electron would result in a continuously shrinking orbit, with large, continuous quantities of emitted radiation, such as are not observed in experiments. Here is where Bohr brings in assumptions from Planck’s work, which he phrases as follows.

Now the essential point in Planck’s theory of radiation is that the energy radiation from an atomic system does not take place in the continuous

way assumed in the ordinary electrodynamics, but that it, on the contrary, takes place in distinctly separated emissions, the amount of energy radiated out from an atomic vibrator of frequency ν in a single emission being equal toτ hν, whereτ is an entire number, and h is a universal constant. (Bohr, 1913, p. 4)

It is crucial that Bohr had to determine how he might apply something like Planck’s quantum conjecture to an atomic system. In order to do so, he posited the existence of stable states, with electrons orbiting the nucleus in definite orbits. He initially considered the emission process from an atomic system as taking place in quantized amounts, dependent on the parameter h. He assumed that the radiation is monochromatic, and that the amount of energy emitted is equal to hν, whereν is the frequency of the emitted radiation (p. 8). More importantly, Bohr then goes on to show how a modification of this conjecture can be used to recover the same results. Rather than assuming that the stationary states correspond to emissions of integral quanta, Bohr assumes “that the frequency of the energy emitted during the passing of the system from a state in which no energy is yet radiated out to one of the different stationary states, is equal to different multiples of ω/2, where ω is the frequency of revolution of the electron in the state considered” (p. 14). Thus, he eliminates the reference to actual quanta of energy, and relates instead the

frequency of emitted radiation to the frequency of revolution of an electron in one of the stable states. Bohr’s ultimate statement of his conjecture is the following.

If we therefore assume that the orbit of the electron in the stationary states is circular, the result . . . can be expressed by the simple condition: that the angular momentum of the electron round the nucleus in a stationary state of the system is equal to an entire multiple of a universal value, independent of the charge on the nucleus. (Bohr, 1913, p. 15)

Using this conjecture along with his elementary atomic model, Bohr was able to account for the Balmer formula, which described the discrete spectral lines observed when hydrogen gas is heated.12

Although Bohr explicitly references Planck’s quantization conjecture, Bohr’s interpretation of quantization is a novel one. First, it is clearly the case that his quantum conjecture differs from those of Planck and Einstein. Several quotes from Bohr emphasize the fact that this application is different from what has come before. For instance,

It is readily seen that there can be no question of a direct application of Planck’s theory. This theory is concerned with the emission and

absorption of energy in a system of electrical particles, which oscillate with a given frequency per second, dependent only on the nature of the system and independent of the amount of energy contained in the system. (Bohr, 1922, 10)

This is in contrast to an atomic system, where the frequency depends on the energy of the system. Therefore, despite the reference to the emission of discrete amounts of energy, this is not a straightforward application of Planck’s idea. This difference is unsurprising. While quantum hypotheses raised in the context of blackbody radiation and light quanta were dealing with thermodynamical phenomena, and thus evaluating behaviour on a large scale, Bohr was using a quantum hypothesis in the investigation of individual atomic structure. Unlike Einstein’s conjecture of light quanta, Bohr does not hypothesize about the constitution of electromagnetic radiation itself.