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Why don't the proton and the electron in a hydrogen atom collapse?
Asked by: J. Viranga Perera
That was the question on physicists' minds early in the 20th century prior to the development of quantum theory. It was not understood why an orbiting electron, since it is accelerating, wouldn't lose energy in the form of electromagnetic radiation and collapse into the proton.
Quantum theory posits that energy must be "packaged" in finite amounts, analagous to money. You can spend 25 cents or 26 cents, but not 25 1/2 cents. Under quantum rules, electrons cannot "spend" (lose) enough energy to collapse into the proton, so happily stay where they are. They can, however, gain a finite amount of energy and rise to a specific higher energy level. Because specific energy translates into a specific electromagentic frequecy, this behavior gives rise to dark "Fraunhaufer lines" in the Sun's spectrum. The loss of that same finite amount of energy by energetic electrons explains the bright line spectra emitted by glowing gases, such as neon.
This question was one of those which sparked off the quantum mechanics revolution at the beginning of the twentieth century. Rutherford had discovered that the atom was made of positively and negatively charged particles and immediately everyone asked, "How on Earth can they just sit there together?" Rutherford himself proposed that electrons were held in orbit by their velocity around the nucleus in the same way that the Earth is held in orbit around the Sun. It soon became clear however that electrons would radiate their energy away and therefore it was a mystery why they didn't fall into the nucleus.
The answer came from Pauli, Dirac and other physicists working on quantum theory in the 1910s and 1920s. Ultimately it involved a change in the way we think of particles. Instead of being a dot of mass, we think now of electrons being a fuzzy cloud spread over the entire atom (and even further.) The cloud represents the probablity of finding an electron at any particular point. So the electron doesn't orbit the nucleus at all but is in some sense distributed throughout the atom at every moment. Heisenberg figured out that the more you squash the electron cloud into a small space the less you know how fast it is travelling. Working with this image of the electron, it is impossible to find the electron in the nucleus permanently - you would know its speed and its position exactly. So it would violate quantum laws of physics.
Mass of proton : 1.6726 x 10-27 kg
Mass of neutron: 1.6749 x 10-27 kg
Mass of electron: 0.00091 x 10-27 kg
Since the mass of a proton plus the mass of an electron is less than that of a neutron, a large amount of energy (E=mc2) is required to combine them. The electrostatic potential energy is not suffcient to do this. However sometimes gravitation energy can be.
When stars run out of fuel, they cool down and eventually contract due to their own gravity. Stars like our sun form white dwarfs, but those about 1.5 times heavier become supernovas and collapse to form a neutron star. The gravitation force actually converts potential energy into mass by forcing protons and electrons to combine into neutrons. All light elements like unfused hydrogen will have been lost during the red giant stage, but the principle is still the same