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After the plum-pudding model failed, physicists concluded that atoms had nuclei that were relatively dense and positively charged. But the rejection of the plum-pudding model posed many conceptual challenges for physicists of the early 20th century because it was hard to reconcile alternative models of the atom with classical mechanics and Maxwell's equations.

One challenge was with the configuration of electrons in atoms. If electrons were in orbit around the nucleus, it was logically assumed that electrons must accelerate and Maxwell's equations predict that an accelerating charge releases electromagnetic radiation. This causes the electrons to loose energy and move towards the nucleus.

Given this knowledge, why didn't physicists assume that electrons were stationary directly outside the nucleus. Is this also an unstable configuration of the atom?

mrhumanzee
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Let's imagine a stationary electron near a positively-charged nucleus. It would immediately be electrostatically attracted straight into the nucleus and you wouldn't have atoms with negatively-charged exteriors and positively-charged nuclei.

niels nielsen
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