2. Productive ambiguity

‘Productive ambiguity’ begins with Bohr’s move to Cambridge in 1911 to work with J. J. Thompson on the electron theory and to publish an English translation of his thesis. He did not flourish in Cambridge, however, and moved to Manchester in early 1912 to study under Ernest Rutherford. He soon took an interest in the work of another researcher in the laboratory, Charles Galton Darwin, who was wrestling with the problem of how electrons in a nuclear atom interact with passing alpha particles. Consideration of Darwin’s problem prompted Bohr to discover the radical mechanical instability of the nuclear atom, a result for which his thesis and his philosophy had prepared him. He exploited the instability to develop his quantum atom. His several attempts to ground his invention in existing physics give a precious insight into his mind at work, into his way of entertaining several contradictory formulations of his thought at the same time.

Bohr’s Derivation of the Rydberg Formula

Atoms evolved from hypothetical entities into the objects of detailed laboratory study. The discovery of the negatively charged electron by Thomson in 1897 implied that atoms, indivisible for more than 2000 years, now had to be recognized as having some kind of internal structure. In 1911 Rutherford interpreted the latest experimental results in terms of a ‘nuclear atom’, in which most of the atom’s mass is concentrated in a small central nucleus, surrounded by electrons which account for much of the volume. In 1913, Bohr presented a theory of atomic structure which combined a model of classical mechanical ‘orbits’ and transitions between these orbits governed by quantum rules. Although he made some unjustified (and incorrect) assuptions regarding the quantization of orbital angular momentum, he successfully predicted the Rydberg formula and showed that the Rydberg constant is a composite of fundamental physical constants.

The Nuclear Atom

Chapter 5 describes how the concept of quantization (discretization) was first applied to atoms. This was done in 1913 by Niels Bohr, using Ernest Rutherford’s paradigm-changing, solar-system model of atomic structure, wherein the positively charged nucleus occupies a tiny central space, much smaller than the known sizes of atoms. Bohr, postulating a quantized version of this model for hydrogen, was able to explain previously inexplicable experimental features of that atom. He did so via an ad hoc quantization procedure that discretized the single electron’s energy, its angular momentum, and the radii of the orbits it could be in around the nucleus, formulas forwhich are presented, along with a diagram displaying the quantized energies. Despite this success, Bohr’s model failed not only for helium, with its two electrons, but for all other neutral atoms. It left some physicists hopeful, ready for whatever the next step might be.

1. The fly in the cathedral

‘The fly in the cathedral’ charts the discovery of the nuclear atom and the start of modern atomic and nuclear physics. It began in 1895 with the discovery of X-rays by Wilhelm Roentgen and radioactivity by Henri Becquerel. In 1897, J.J. Thomson discovered the electron and realised they were common to all atoms, which implied that atoms have an internal structure. Negatively-charged electrons are bound to positively-charged entities within the atom, but what carries this positive charge and how is it distributed? It was Ernest Rutherford, in 1911, who announced his solution: all of an atom’s positive charge and most of its mass are contained in a compact nucleus at the centre.

The Strange Case of Helium and the Nuclear Atom

It is often taken as a matter of established fact that the difference between a good scientist and a great scientist is the ability to distinguish in advance which problems are going to be the important ones. I think this belief is a reflection of the fact that history is written by the winners: Professor X chooses a problem and with much hard work solves it, but it turns out not to have important consequences, so it and he are forgotten; Professor Y does the same, but this time the result spurs further work or even opens new and unforeseeable regions of science, so he naturally feels that his “intuition” was correct. But how do you distinguish his intuition from a lucky guess? I suggest that a study of the history of science tells us that luck plays a significant part. Consider, for example, Lord Rutherford’s discovery of the nuclear atom—perhaps the most important experimental discovery of the twentieth century, in that it led to quantum theory and the whole of nuclear physics. To set the stage: By the first few years of the twentieth century it had been determined that there were three kinds of radioactive emissions, termed alpha, beta, and gamma rays. The gamma rays were electromagnetic in nature, the beta rays were electrons, and Rutherford had just shown that the alpha rays were in fact helium; or rather, as he put it, the alpha rays were a stream of particles zipping along at roughly 10,000 miles per second which, after they slowed down and lost their electric charge, became helium atoms. (He didn’t realize at the time that they “lost” their positive electric charge by picking up negatively charged electrons.) What next? Well, the natural thing to do was to see how these radioactive emissions interacted with matter. This had already been done with the beta and gamma radiations: a stream of these radiations had been directed at various targets, and such parameters as their depth of penetration and ionizing capabilities had been measured, with no particular insights gained (an example of Professor X’s work).