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Why electron does not fall into nucleus from orbit of an atom? As accelerated charged particle radiates energy, it should lose energy.

mpv
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user171486
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  • See https://physics.stackexchange.com/questions/68381/where-did-schr%C3%B6dinger-solve-the-radiating-problem-of-bohrs-model https://physics.stackexchange.com/questions/130936/why-do-the-electron-in-bohrs-principal-quantum-levels-or-ground-state-do-not-em https://physics.stackexchange.com/questions/72588/why-electron-clouds-in-atoms-dont-radiate and links therein. – Omry Oct 11 '17 at 18:14
  • Electrons "rotating" around the nucleus do lose energy and jump to a"lower orbit", if it is not taken. Once all "lower orbits" (energy levels) are filled up, electrons have nowhere to fall. According to the Pauli exclusion principle, two electrons cannot share the same energy level (same reason why we can't go thorough a wall). – safesphere Oct 11 '17 at 18:23

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When we talk about this problem, we implicitly assume that there is a continuum of energy states into which the charged particle can "fall" into, as it keeps radiating away energy.

Quantum Mechanics provides a refinement to this idea; for the lowest energy states inside the Hydrogen atom, the energy states simply aren't continuous. They go like $E_{n}=-k/n^{2}$, for positive integers $n$. So the electron cannot "continuously" lose energy; when it does gain or lose energy, it transiently gains or loses photons to move from one discrete energy level to another.

When the electron is momentarily in a very large $n$ Hydrogen atom state, it may emit photons each of very small spurts of energy $ k(\frac{1}{n^{2}}-\frac{1}{(n+1)^{2}})\propto \frac{1}{n^{3}}$, and almost continuously "fall" in the ladder of energy states, till it reaches the $n=1$ energy state. This is where you get the approximate classical behaviour.

Aritro Pathak
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