# How was Bohr's third postulate later found to be wrong?

Why does the Bohr's third postulate was later found to be wrong? I read it in a note but don't know why is it?

The third postulate is:

The orbits of electronic motion are circular and well defined and are such that angular momentum $mvr$ of the electron is quantized in units of $h/2\pi$.

Around 1927, there was a transition from the "old" quantum mechanics to the "new" quantum mechanics. There were lots of problems with the old quantum mechanics, and the shortcomings of the Bohr model were just one such problem. In the new quantum mechanics, the idea of classical trajectories for particles is completely abandoned. They propagate as waves instead.

Ultimately, the reason for preferring the new quantum mechanics is that it is in better agreement with experiment. One decisive experiment was the 1926 Bothe-Geiger experiment, which disproved Bohr's idea that light could still be described classically, and only the atom needed to be quantized. The old quantum mechanics also got various things wrong in its description of the atom, e.g., it predicted the hydrogen atom to have an orbital angular momentum of $1\hbar$ in its ground state, rather than the correct value of zero.

So in summary, Bohr's third postulate was not one isolated problem with the old quantum mechanics that needed to be fixed for one specific reason.

Bohr's stipulation that the orbits are circular and quantized in units of $\hbar$ was expanded by Sommerfeld to elliptical orbits and the condition $$\oint pdq=n\hbar$$ The (relativistic) semi-classical Bohr-Sommerfeld theory of the hydrogen atom could explain the observed spectrum of hydrogen as well as the solutions of the Dirac equation but failed in describing higher order perturbation effects of the Stark effect correctly and the Lamb shift.

• Some good points here but the Lamb shift was measured in 1947, well after Bohr’s theory had been abandoned. – ZeroTheHero May 12 '18 at 14:44
• @ZeroTheHero- You are, of course, right, neither the Bohr-Sommerfeld nor the Dirac theory explains the Lamb- shift. Still, the agreement of this "wrong" semi-classical Bohr-Sommerfeld theory with advanced QM theory in describing the H-spectrum is rather astounding. – freecharly May 12 '18 at 17:53

The reason why this is wrong is because :

1. If the orbit of an electron is well defined, then it must mean that it is rotating around the nucleus ( like a planetary system ).

$\implies$ They are accelerating ( since rotation changes the velocity vector at every instant ) and from electrodynamics, we have that an accelerating charge should radiate.

$\implies$ All electrons would gradually lose energy to radiation, spiral into the nucleus and atoms would be impossible.

1. With the advent of the probabilistic nature of physics ( Born's rule and the Uncertainty Principle ), orbits just went out of the picture because they would represent definite positions of the electron, which is impossible via the Uncertainty Principle. So, the postulate utterly fails at this point too...
• I don't think this is a very good explanation. Radiation is a secondary issue. The main issue is just how quantum mechanics really is found to work. Bohr was fully aware of the radiation issue, and he simply postulated that there was no radiation except in a transition between allowed states. – user4552 May 12 '18 at 13:19
• Maybe it's not complete, we can't say it's wrong. Even if Bohr postulated that quantised orbits won't radiate, it goes straight against electrodynamics. – Yuzuriha Inori May 12 '18 at 13:57
• A body emitting synchrotron radiation loses energy continuously, but the energy of an electron in a Bohr orbit is forbidden to change its energy continuously, any energy changes must be discrete. Thus the model explains the discrete spectra of atoms and the non-emission of synchrotron radiation; pity about the other empirical properties of atoms which it fails abysmally with. ;) – PM 2Ring May 12 '18 at 20:39