Audible includes a very good audiobook production of Manjit Kumar's "Quantum: Einstein, Bohr, and the Great Debate About the Nature of Reality". We have listened and relistened to this audiobook several times, and have found it extremely informative.
It is a great narrative of the chronological and biographical development of great physicists from Planck to Lorentz, Sommerfeld, Ehrenfest, Rutherford, Fermi, Bohr, Einstein, Heisenberg, and Schrodinger, etc.
The book is a very good historical review of the development of the quantum. We also find the book very useful from a technical point of view. Of course it hardly contains any formulas, but it explains the physics in basic mathematical terms. It uses words instead of formulas, and does this very well.
We have also found the book rather inspiring, recognizing that physics is a passion and that it has always involved bold proposals and visionaries. We are also reminded that physics is developed from bold proposals, and there is a very strong "cult of personality" involved. Scientists, especially "theoretical physicists" are very romantic and idealistic figures. This includes Neils Bohr, who retrospectively is one of the most revered physicists of 20th century comparable to Einstein, but whose whole career hinges on his proposed description of the constitution of atoms and the quantum discontinuity.
We enjoy the descriptions of Rutherford, as extremely energetic and engaged in his laboratory, and having many fundamental questions for Bohr. Rutherford argues that an electron moving in a circle is an oscillating system with a frequency. But "what is the relation between the frequency of the photon ejected by energy transitions, and the frequency of oscillation of the electron orbit?". We would expect the oscillating system to radiate energy at the frequency of its oscillation. But two energy levels have two different frequencies, and what is the relation between these two frequencies?
Moreover if there is no continuous motion between energy levels, Rutherford asks "How does the electron know where to go? to which energy levels will it jump?"
A decisive stumbling block in the approach to the atom is Larmor's formula, a prediction from Maxwell field theory that any accelerated electric charge must radiate energy. Fundamentally, the quanum was invented to evade this problem. Evidently the hydrogen atom is, yet the Maxwell prediction is that it cannot be. It appears impossible problem. All the "theory" predicted radiation instability. At some point "Bohr decided that ' the quantum of stability must therefore be treated from a different point of view.'" Bohr determined a "radical change" was needed...
And this is the essence, we think, of what Bohr is trying to express when he says "Anybody who isn't shocked when they come to learn quantum theory, cannot possibly have understood it." This is a very revealing metalogic statement. As we understand it, Bohr is admitting that to understand quantum theory, is to understand that it does not answer the fundamental question, and in contrast to all classical expectations, simply posits quantum discontinuous transitions. It is shocking once it's understood, because it is a huge leap and logical non sequitur. The quantum does not follow from anything previous.
What about Planck's formula?
The quantum was introduced by Max Planck, in his formula for blackbody radiation. This is technical issue, relating the temperature of a body to the emission spectrum of the body. The proper treatment depends on Gustav Kirchoff's proposed universal law of radiation. Kirchoff proposed without any experimental evidence, that the radiation of a cavity at thermal equilibrium was independant of the shape and material of the cavity. This universal radiation of Kirchoff is, however, not correct. And this is one of the main issues plaguing physics ever since. This is subject of much discussion by Prof. P.M. Robitaille, and not something we can elaborate at the moment.
In memoriam, I'll just remember Michael Craig Robinson, who was a very generous man who died in tragic wilderness plane crash doing what he loved, backcountry white water rafting. He was a PhD in physics, he was the first to tell me that electronics operate very well in the cold, and that a glass box which contained light radiation was a type of "blackbody", and i was only 17-18 years old at that time, but it made an impression on me.