Editing Hydrogen atom (section)

=== Failed classical description ===
[[Rutherford model|Experiments]] by [[Ernest Rutherford]] in 1909 showed the structure of the atom to be a dense, positive nucleus with a tenuous negative charge cloud around it. This immediately raised questions about how such a system could be stable. [[Classical electromagnetism]] had shown that any accelerating charge radiates energy, as shown by the [[Larmor formula]]. If the electron is assumed to orbit in a perfect circle and radiates energy continuously, the electron would rapidly spiral into the nucleus with a fall time of:<ref>{{Cite web|url = http://www.physics.princeton.edu/~mcdonald/examples/orbitdecay.pdf|title = Classical Lifetime of a Bohr Atom|date = 7 March 2005|publisher = Joseph Henry Laboratories, Princeton University|last1 = Olsen|first1 = James|last2 = McDonald|first2 = Kirk|access-date = 11 December 2015|archive-date = 9 September 2019|archive-url = https://web.archive.org/web/20190909221112/http://www.physics.princeton.edu/~mcdonald/examples/orbitdecay.pdf|url-status = dead}}</ref>
<math display="block">t_\text{fall} \approx \frac{ a_0^3}{4 r_0^2 c} \approx 1.6 \times 10^{-11} \text{ s} ,</math>
where <math>a_0</math> is the [[Bohr radius]] and <math>r_0</math> is the [[classical electron radius]]. If this were true, all atoms would instantly collapse. However, atoms seem to be stable. Furthermore, the spiral inward would release a smear of electromagnetic frequencies as the orbit got smaller. Instead, atoms were observed to emit only discrete frequencies of radiation. The resolution would lie in the development of [[quantum mechanics]].