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Why Don’t Electrons Crash into the Nucleus in Atoms?

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If one describes atoms using only the Coulomb forces, the electron and the nucleus will attract each other and no stable atoms could exist. Obviously this is not the case. Niels Bohr was the first (1913) to propose a better model, which consisted of electrons moving around the nucleus in circular orbits. Each orbit corresponds to a certain discrete energy level. This model is based upon the quantisation of the angular momentum.

Unfortunately, electrons moving in a circular orbit have an acceleration due to the centripetal force. In classical electromagnetic theory, an accelerated charged particle must emit EM-radiation due to energy conservation. Hence, the electron would lose energy and spiral down towards the nucleus. Again stable atoms could not exist. What is wrong now?

It turns out that the picture of electrons moving in circular orbits around the nucleus isn’t correct either(*). The solution here is the implementation of Quantum Mechanics via the Schrödinger Equation and the concept of wavefunction. By applying such formalism, the “electron” occupies a volume of space simultaneously, so that it is “smeared” in a particular geometry around the nucleus. While there are no more “orbits”, we do use the term “orbitals” to indicate the shape of such geometry. However, this term should not be confused to mean an orbiting electron similar to our planets in the solar system. By describing the system in terms of the QM wavefunction, it creates stable states for the nucleus+electrons system that matches very well with experimental observation of standard atomic spectra.

Since there are no more “orbits” in the conventional sense, the problem of electrons radiating due to an accelerated motion is no longer meaningful. It explains why we have stable atoms.

To read more in detail: http://scienceworld.wolfram.com/physics/HydrogenAtom.html

(*) By saying that “an electron orbits the nucleus”, one is already implicitly assuming that one can track the position and momentum of that electron in an atom over a period of time. We have no such ability, and for those who know a bit about the Heisenberg Uncertainty Principle (HUP), one can already tell that such a statement violates this principle.

Contributed by Marlon and edited by ZapperZ

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  1. Alex Klotz
    Alex Klotz says:

    And sometimes it *does* crash into the nucleus, and it's not the end of the world. An electron can interact with the nucleus and turn a proton into a neutron. It's called electron capture.

  2. Jeff Rosenbury
    Jeff Rosenbury says:

    Yes, it's obvious they don't (regularly) crash into the nucleus. But why don't they? My understanding is that electrons and some other particles exist in a phase (more generally guage) space. So adding two such particles (with identical quantum properties) gives us zero particles, not two particles. (Other particles such as photons can add.) Oh, and an electron and a proton have slightly less energy than a combined neutron — usually. So electron capture is somewhat rare.

  3. JBA
    JBA says:

    Any electron fired at an atom must penetrate the atom's electron shell(s) in order to reach the nucleus. So what are the energy exchanges that occur during those penetrations?

  4. Jano L.
    Jano L. says:

    *If one describes atoms using only the Coulomb forces, the electron and the nucleus will attract each other and no stable atoms could exist.*This is wrong, Coulomb interaction is essentially the same as Newtonian gravity, which allows stable elliptical orbits.What Bohr was pointing out is that if we take Larmor formula for energy radiated per unit time by accelerated charge, the system radiates energy away and if we assume this energy comes from the potential energy of the two charged particles forming the system, the potential energy should decrease in time and hence average distance of the particles should decrease in time.Larmor's and similar formulae for radiated power in point-particle theories are based on the assumption that the fields are purely retarded fields of the particles in the system. However, realistically the EM field contains additional contributions due to distant sources (background radiation), which invalidate this simplistic argument.

  5. jtbell
    jtbell says:

    Oh, and an electron and a proton have slightly less energy than a combined neutron — usually. So electron capture is somewhat rare.

    In ordinary hydrogen, where the nucleus is a proton, electron capture is impossible, for the reason you give.

    However, an electron and a [SUP]26[/SUP]Al nucleus have a greater energy (mass) than a [SUP]26[/SUP]Mg nucleus. Therefore electron capture is possible in [SUP]26[/SUP]Al.

    The two nuclei differ in that [SUP]26[/SUP]Mg has a neutron in place of one of the protons in [SUP]26[/SUP]Al; but the difference between the binding energies of the two nuclei is enough to “overcome” the mass difference between the proton and neutron.

  6. Jim Hasty
    Jim Hasty says:

    I have read somewhere that the electrons inhabit orbital shells around the nucleus; each shell a different radius. When an electron drops to a lower shell closer to the nucleus it must give up a quanta of energy – and vice-versa when moving to higher shells. Quanta come in only discrete units. The electrons in the orbitals closest to the nucleus are unable to emit the last quanta of energy which would allow them to drop to the nucleus. In this way atoms are very stable unless disturbed by outside particles.

  7. edguy99
    edguy99 says:

    One model of what happens when you shoot a free electron at a proton, and it’s fun too! This model does not run into infinities as the electron gets very close to the proton since it assumes the force between an electron and a proton never exceeds the ionization energy of hydrogen which is 13.6 eVolts.

    [URL=’http://www.animatedphysics.com/games/shoottheelectron.htm’]http://www.animatedphysics.com/games/shoottheelectron.htm [/URL]

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  8. Funley
    Funley says:

    An electron in an S state actually spends some time inside the nucleus, thus affecting the nuclear energy levels a bit. This is known as the isomer effect and is observed in nuclear magnetic resonance and the Mössbauer effect.

    • Bernhard Kup
      Bernhard Kup says:

      The comments above are all lacking a very essential aspect:The kinetic energy of the electron which never will become zero,is the reason for some sort of repulsive force near the nucleus.This is very often overlooked and may also be explained by thethe De Broglie wavelength.By the way: The old Bohr model of orbits is getting correct again forso-called Rydberg atoms of hight quantum numbers n = 40 to 100.So never think that only one model can explain everything!

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