MadSci Network: Chemistry

Re: Why don't atoms collapse?

Date: Fri Feb 5 16:51:59 1999
Posted By: Dan Berger, Faculty Chemistry/Science, Bluffton College
Area of science: Chemistry
ID: 917651020.Ch

Why don't atoms collapse?

A hydrogen atom as one electron and one proton, why doesn't collapse since they are "pulling" on each other. I know that it isn't because the electron "orbits" around the proton as in classical physics. I have also heard that electrons behave more like waves nearer they are to the nucleus, does this relate to why atom doesn't collapse? I hope you will be fairly explicit or lead me to some good material on this.

This is not a trivial question. Ernest Rutherford, when he discovered the atomic nucleus in 1911-1912, proposed that electrons don't fall into the nucleus for the same reason that planets don't fall into the sun: their velocity is sufficient to exactly balance the attraction exerted, and so they maintain orbits. This proposal was called the solar system model of the atom.

Keeping a planet or an electron in an orbit involves a continuous acceleration: the object's velocity is constantly changed (in direction) in order to maintain the orbital curve. Unfortunately, Maxwell's Equations say that accelerating an electric charge results in the emission of electromagnetic radiation (light energy). An orbiting electron would radiate its orbital energy away, and fall into the nucleus in something like a picosecond.

The key assumption here, though, is that energy is a continuous function. Max Planck (1900) and Albert Einstein (1905) showed that energy is quantized, having only certain possible values. In 1919 Niels Bohr proposed a modification of the solar system model, in which electronic orbital energies are quantized. In Bohr's model, electrons can occupy only certain orbits, because they can radiate only certain quantities of energy. This saved the nuclear atom -- or rather saved atomic physics, because the nuclear atom was established by experiment -- and even allowed an interpretation in terms of the wave nature of the electron: electron orbits had to be such that a non-zero, integral number of half-wavelengths would fit around the circumference.

Today we have abandoned the solar system model of the atom in favor of the Schrödinger model: electrons are standing waves distributed through the spherical volume of the atom. Nevertheless, we still understand electronic energy levels as being quantized. Electrons are not permitted to fall into the nucleus because this would involve a violation of quantization.

Finding the electron in the nucleus would also be a violation of the Uncertainty Relation: we would know the electron's position and momentum simultaneously! In fact, the electron's velocity can be approximated by solving the expression for the uncertainty in velocity, using the electron's rest mass and the mean distance of the electron from the nucleus (which can be calculated from the expression for the atomic orbital -- a wave equation! -- in which the electron is located).

Electrons are inherently fuzzy particles, especially when they are in atoms -- and the "fuzz" is on the order of the size of the atom. This means that, while the electron has a certain probability of being "in" the nucleus, the probability can never be 100%.

Probably the best reference for more information on this (though it is pretty tough sledding) is PW Atkins' "Molecular Quantum Mechanics."

  Dan Berger
  Bluffton College

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