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According the classical physics, the electron should radiate energy and fall to the nucleus in a short period of time. However, this was not the case. Hence, Bohr proposed his theory, suggesting that electrons existed in specific orbits, where they did not radiate energy. These orbits had quantised or discrete energies. Moving between these orbitals meant the emission of specific amounts of energy, emission of photons.

However what was so revolutionary behind this idea? It seems to me, he solved this radiation problem, by simply stating that it didn't happen, "electrons exist in specific obrits, where they don't radiate energy". Did Bohr know why this actually happened or did he just state it? Currently, I am struggling to understand what was so revolutionary about Bohr's contribution to the previous nuclear model of the atom.

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  • $\begingroup$ "First, we guess it" - Richard Feynman on the scientific method $\endgroup$ Oct 28, 2023 at 1:13
  • $\begingroup$ You have deeply misunderstood what an orbital actually is… the electron is NOT a little ball orbiting a nucleus, but a cloud of electron density arranged in space according to the solutions of the Schrödinger equation. $\endgroup$ Oct 28, 2023 at 14:01
  • $\begingroup$ Bohr did not solve the radiation problem, he provided a model of hydrogen atom which reproduced the measured emission spectra. It's just that this model is based on the idea that there are stationary orbits which do not radiate. $\endgroup$ Oct 28, 2023 at 14:36

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Of course like the egg of Columbus it seems obvious after the fact. In addition to “solving” the stability problem, Bohr’s hypothesis on the motion of the electron also provided an accurate prediction of the Rydberg constant, something that provided enormous credibility to his radical hypothesis.

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The point was that he created a model which predicted the stability of atoms and predicted the discrete spectra of atoms. Sure he didn't have an underlying explanation for why electrons could only exist in and jump between specific orbits, but the predictions of these postulates matched experiment better than any other model at the time. That's what was so special about it.

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The revolutionary idea was that microscopic particles do not behave like macroscopic bulk matter and the view that particles are small billiard balls is untenable. It took another decade to sort this idea out mathematically in the quantum mechanics of Heisenberg and in the wave mechanics of de Broglie and Schrodinger.

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Michael Fowler has written a very accessible account of the considerations underlying the Bohr atom

According to the Bohr atom there is a relation between the size of the Hydrogen atom and the Balmer series.

The Balmer series had been recognized decades before, but until the introduction of the Bohr atom there was no hypothesis as to why some of the spectral lines of the Hydrogen atom were falling into that pattern.

Bohr noticed that if it is granted that the energy levels of the nucleus-electron system come in integer increments of angular momentum, the increments in proportion to Planck's constant, then the known size of the Hydrogen atom follows.


(According to the wikipedia article: the expression for the Balmer series was generalized to cover all of Hydrogen's spectral lines by Rydberg in 1888. The Balmer series was recognized first because those spectral lines fall in the visible spectrum. Presumably: the information obtained from the Balmer series was in itself sufficient to formulate the Bohr atom.)

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Bohr was just lucky by chance.

The quantum eigenstates of the Schrödinger H-atom decompose into spherical waves, which can be labeled by the number of knots on the equator $$L_z Y_{l,m} = m Y_{l,m} $$.
The quantisation of the magnetic energy as an integer spectrum of the Bohr unit was a good starting point.

The second quantum number $l^2$ of the total angular momemtum squared, for spherical waves was known for a century already and extensively used in theory of waves in the lated 1890ties, but Bohr ignored it.

Instead he attributed Plancks energy formula $$E_n = \hbar \omega_n$$ to a series of 1-d equatorial waves concentrated on equatorial circles in a series of radius given by the energy series of the Balmer formula.

There is an accidental degeneration of the energy spectrum.

The energy depends on the sum only, of $\frac{l^2}{r^2} $ of total angular momentum squared and the radial number of knots $n_r+l$ for the H-Atom, such that the number of wave knots of the states with maximal classical equatorial angular momentum equals the total absolute momentum $\hbar m = \hbar l$.

So the completely misleading idea of waves, continuously moving on circles with length in integer multiples of wavelength, yields the observable part of the spectrum.

The states of maximal $L_z=m=l$ in Schrödinges H_Atom do not depend on $\theta$-coordinate angle at all, while waves with $m=0$ at the same total angular momentum quantum number $l$ are rotational invarient with a static wave state along meridians.

The symmetry causing this degeneracy is the same, that has all classical Kepler orbits of the same energy with their grater axis aligned along a radisu to have the same lenght of their greater axis, independent of the angular momentum. The symmetry is generated by the vector orthogonal to velocity and angular momentum named after Laplace, Runge und Lenz, that may be described as the perihel vector for any system. It is rotating in bounded systems, generally. For the e Coulomb potential its a constant of motion and has the form

$$\vec R = \vec p\times(\vec x \times \vec p) -\frac{\vec x}{|\vec x|} $$

In the infamous anthropocentric view, probably, nature created euclidean $\mathbb R^3$ and the degeneracy of the Kepler problem $V=1/r$ in order to make the break through of Kepler and Bohr possible.

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