electrons
Electrons
An electron is an electron, not a wavefunction, not a wave nor a particle. It is, however modeled by functions of wave equations representing waves in probability space.
An electron is partially particle-like and partially wave-like, but is really something more complex that is neither a simple wave nor a simple particle. The electron is described by a probabilistic quantum wavefunction, which spreads out through space and vibrates, but in such a way that it still has certain discrete properties such as mass. When bound in a stable state in an atom, the electron wavefunction spreads out into a certain shape called an "orbital". The orbital does not contain the electron or describe the average location of a little hard electron orbiting around. Rather, the orbital is the electron.
The electron and proton aren't like pool balls. The electron is normally considered to be pointlike, i.e. has no size, but what this really means is that any apparent size we measure is a function of our probe energy and as we take the probe energy to infinity the measured size falls without limit. The proton has a size (about 1fm) but only because it's made up of three pointlike quarks - the size is actually just the size of the quark orbits and the proton isn't solid.
Classically two pointlike particles, an electron and a quark, can never collide because if they're point-like their frontal area is zero and you can't hit a target that has a zero area.
What actually happens is that the electron and quark are quantum objects that don't have a position or a size. They are both described by some probability distribution. Quantum mechanics tells us that a reaction between the electron and quark can occur, and indeed this is what happens when you collide particles in an accelerator like the LHC.
See atomic orbitals and electron shells.
Properties of an electron
Electrons cannot be described simply as solid particles. An analogy might be that of a large and often oddly shaped "atmosphere" (the electron), distributed around a relatively tiny planet (the nucleus). Atomic orbitals exactly describe the shape of this "atmosphere" only when one electron is present. When more electrons are added, the additional electrons tend to more evenly fill in a volume of space around the nucleus so that the resulting collection (electron cloud) tends toward a generally spherical zone of probability describing the electron's location
Wave-like
Electrons do not orbit a nucleus in the manner of a planet orbiting a star, but instead exist as standing (stationary) waves. Thus the lowest possible energy an electron can take is similar to the fundamental (lowest) frequency of a wave on a string. Higher energy states are similar to harmonics (positive integer multiple) of that fundamental frequency.
The electrons are never in a single point location, though the probability of interacting with the electron at a single point can be found from the electron's wavefunction. The electron's charge acts like it is smeared out in space in a continuous distribution.
Particle-like
The number of electrons orbiting a nucleus can be only an integer. Electrons jump between orbitals like particles. For example, if one photon strikes the electrons, only one electron changes state as a result. Electrons retain particle-like properties such as: each wave state has the same electric charge as its electron particle. Each wave state has a single discrete spin (spin up or spin down)
Movement of an electron in an orbital
Opposite to contrary belief, electrons aren't particles with definite position and momentum. The Heisenberg uncertainty principle describes the limit to the precision with which certain pairs of physical properties, such as position and momentum, can be simultaneously known. In other words, the more accurately one property is measured, the less accurately the other property can be known.
Coming from everyday physics, this is commonly understood to mean that you can't measure an electron accurately. This is not right. An electron does not have a precise position or momentum. It does not have a precise trajectory. It has a collection of places it might be and speeds it might have.
This might lead you to think of an electron as like a cloud. A wavefunction describes how it is spread out over an extended region. A piece of it is at every location, and each piece has a definite momentum. Again, this is not right. The wave function describes the state of the electron. If the electron interacts with something you may be able of infer a position and momentum. You cannot predict the outcome in advance. The wave function allows you to predict probabilities.
Since you are used to a deterministic predictable universe, this would lead you to think that the wavefunction does not tell you everything you need to know about the electron. There must be hidden variables that would tell you more. If you could measure those hidden variables, you could predict outcomes. Sadly, you would still be wrong. The wave function does completely describe the electron. An electron is inherently unpredictable to a degree.
There are many possible states. All the properties of the electron can be inferred from the state it is in. Even the degree of unpredictability depends on the state. Some states allow you to predict the location reasonably well, but leave the momentum poorly defined. Orbitals are like this. The electron is confined near a nucleus.
In another more spread out state, the electron might be flying across a vacuum chamber towards a screen. There is no way to predict which spot it will hit on the screen, but its momentum is more predictable.
Will electrons fall into the nucleus?
Well, the fact that we think of electrons as little balls orbiting around the nucleus is inheretently wrong. As a matter of fact it is possible to find electrons inside the nucleus but the probability is incredibly low (it can be assumed that the probability of finding that particular electron in the nucleus is around the same as finding it on another planet lightyears away) as it is incredibly energetically unfavourable.