An atom with stationary electrons positioned around a positive nucleus would be unstable, because the electrons with their negative charge would be irresistibly pulled towards it. If they moved around the nucleus, like planets orbiting the sun, the atom would still collapse. Newton had shown long ago that any object moving in a circle undergoes acceleration. According to Maxwell’s theory of electromagnetism, if it is a charged particle, like an electron, it will continuously lose energy in the form of electromagnetic radiation as it accelerates. An orbiting electron would spiral into the nucleus within a thousandth of a billionth of a second. The very existence of the material world was compelling evidence against Rutherford’s nuclear atom.That's (p. 81) from Quantum, an exceptionally good account of the revolution in physics in the first half of the last century (the physics is nicely explained (the author studied philosophy as well as physics) and most importantly, the biography is as engaging as in a novel (if a literary one))... I quoted the paragraph above because of its combination of logical clarity, scientific support and falsity. The resolution begins to emerge in 1913 (p. 96):
Whereas others had interpreted these problems of instability as damning evidence against Rutherford’s nuclear atom, for Bohr they signalled the limitations of the underlying physics that predicted its demise. His identification of radioactivity as a ‘nuclear’ and not an ‘atomic’ phenomenon, his pioneering work on radioelements, what Soddy later called isotopes, and on nuclear charge convinced Bohr that Rutherford’s atom was indeed stable. Although it could not bear the weight of established physics, it did not suffer the predicted collapse. The question that Bohr had to answer was: why not?Bohr’s electron shell model of the atom was ready to explain chemistry by 1922, and in 1923 it was physically justified by a French prince who had earlier failed his physics exams (p. 149):
If viewed as a standing wave around the nucleus instead of a particle in orbit, an electron would experience no acceleration and therefore no continual loss of radiation sending it crashing into the nucleus as the atom collapsed. What Bohr had introduced simply to save his quantum atom, found its justification in de Broglie’s wave-particle duality. When he did the calculations, de Broglie found that Bohr’s principal quantum number, n, labelled only those orbits in which electron standing waves could exist around the nucleus of the hydrogen atom. It was the reason why all other electron orbits were forbidden in the Bohr model.In late 1925 Schrodinger read of de Broglie’s idea in a footnote to one of Einstein’s papers, and by early 1926 he had obtained his famous wave equation (p. 206):
Schrodinger knew exactly where to start and what he had to do. De Broglie had tested his idea of wave-particle duality by reproducing the allowed electron orbits in the Bohr atom as those in which only a whole number of standing electron wavelengths could fit. Schrodinger knew that the elusive wave equation he sought would have to reproduce the three-dimensional model of the hydrogen atom with three-dimensional standing waves. The hydrogen atom would be the litmus test for the wave equation he needed to find.Schrodinger disagreed with the probabilistic interpretation of his wave equation introduced by Max Born that same year; but Bohr was more perceptive (p. 219):
Niels Bohr would soon argue that until an observation or measurement is made, a microphysical object like an electron does not exist anywhere. Between one measurement and the next it has no existence outside the abstract possibilities of the wave function. It is only when an observation or measurement is made that the ‘wave function collapses’ as one of the ‘possible states of the electron becomes the ‘actual’ state and the probability of all the other possibilities becomes zero.