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.
Answered by: Paul Walorski, B.A., Part-time Physics Instructor
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.
Answered by: Sally Riordan, M.A., Management Consultant, London
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
Answered by: Stuart Taylor, Chemistry graduate student, Oxford