QUESTION #265

# Since oppositely charged particles attract, and gravity is a phenomenon common to all particles, how come the electron is not 'sucked' into the nucleus?

Asked by: Tim Silverstein

### Answer

First of all you can neglect gravity in your question. As an exercise you might try computing the electrostatic attraction between an electron and a proton and compare it with the gravitational attraction. You'll see that gravity is many millions of times weaker.

Still, why doesn't the electron end up in the nucleus with the proton? Well, first think about the solar system. Why doesn't the earth end up in the sun? The answer is angular momentum conservation. The earth has some large amount of angular momentum because we have velocity perpendicular to the line from the sun to us. Since angular momentum is conserved we stay in a stable orbit.

Now, what about the atom? Early models of the atom treated the atom as a solar system and used the idea of angular momentum conservation to explain its stability. Then it was realized that if the electron is moving in a circle then it must be accelerating (even though the magnitude of its velocity may be constant, the fact that its velocity changes direction means it's accelerating). But all accelerated charges radiate energy. As it loses energy it loses angular momentum -- so it should spiral into the nucleus. The fact that there are any atoms at all was a great mystery at the turn of the last century -- it was one of the great problems that led to the development of quantum mechanics.

In quantum mechanics angular momentum is not a continuous variable but it is quantized: it comes in integer multiples of a fundamental unit given by Planck's constant. Now if you're familiar with chemistry then you know about s-orbitals, p-orbitals, and so on. These are quantum-mechanical states of an orbiting electron, each with a different integer value of angular momentum. The 's' is for zero angular momentum, 'p' is for one unit and so on. Now if you have any angular momentum then you're safe because your wavefunction does not overlap the nucleus very much. That means it's pretty unlikely you'll ever find yourself in the nucleus to encounter a positively charged proton. The 's'-orbital states, however, actually do spend time in the nucleus! Why don't they annihilate with the protons?

The answer is...they do! But very, very rarely. The process by which a proton absorbs an electron and becomes a neutron and a neutrino is known as 'inverse beta decay' and it does happen in some atoms occasionally. Fortunately, the force that governs this process is the weak force -- which got its name by being very, very weak. That means that despite the fact that some 's'-orbital electrons occasionally end up in the nucleus they rarely get absorbed by protons. Thus most atoms are stable and chemistry (and life) is possible.
Answered by: Brent Nelson, M.A. Physics, Ph.D. Student, UC Berkeley