There is a popular image of the atom that shows the nucleus as a collection of balls, with ball-like electrons following circular orbits around them. The parallels to our own solar system, to the orbits of the moon around the earth and the earth around the sun, strike a chord with most people, but the depiction is inaccurate. It is based on the ideas of several prominent early twentieth century physicists, developed after the discovery of the electron in 1897 showed that atoms were not the smallest building block of nature. There are two serious mistakes in this image, and the actual structure of the atom is a lot more interesting.
The first problem is that the proton itself is not an indivisible particle: it’s composed of three quarks, subatomic particles which were hypothesized in the early sixties and observed in experiments beginning in the late sixties. The same is true of the neutron: it’s also composed of three quarks, though the flavor composition is different than that of the proton. (“Flavor composition”? Yes, quarks come in different flavors.) So those giant balls in the nucleus are actually comprised of smaller particles. At this point we believe quarks to be themselves indivisible, not composed of another even smaller particle.
But the second reason this picture is incorrect is that the electron doesn’t follow a linear orbit around the proton, the way gravitationally orbiting bodies do. In fact, due to the small mass of the nucleus and the even smaller mass of the electron, gravity is the least important force in an atom. The electromagnetic force, between the oppositely charged proton and electron, is much larger than the gravitational force between these tiny objects. But wait, you might say, if there’s such a large attractive force, shouldn’t the electron just spiral into the proton? This quandary illustrates perfectly why we can’t rely on classical physics, which was built up for objects comprised of billions of atoms, for the particles within a single atom. Because yes, if we had two oppositely charged billiard balls that have a weak gravitational interaction and a strong electromagnetic interaction, they will crash into each other! But, the electron is so small and so light that we cannot treat it as a classical object.
Here is where quantum mechanics come into play. Quantum mechanics as a whole is a set of mathematical constructions used to describe quantum objects, and it’s quite different than what’s used for classical, large-scale physics. There are all sorts of interesting consequences of quantum mechanics, such as the Heisenberg Uncertainty Principle, which states that for some pairs of variables, such as energy and time or position and momentum (mass times velocity), how precisely you can measure one depends on how precisely you are measuring the other. For each variable pair, there is a basic uncertainty in the measurement of both, which is very small but becomes relevant at the quantum scale. This shared minimum uncertainty between related variables is a fundamental property of nature. For momentum and position, this leads to that old joke about Heisenberg being pulled over for speeding: the police officer asks, “Do you know how fast you were going?” and Heisenberg responds, “No, but I know exactly where I am!”
What the uncertainty principle means here is that the electron is actually incapable of staying in the nucleus. Imagine a moment in time where the electron is within the nucleus: now its position is very well known, so there is a large uncertainty in its momentum. Thus the velocity may be quite high, which means that a moment later the electron will have moved far from the nucleus. In fact, because of the uncertainty in position, we cannot ever really say where in space the electron is. It is more accurate to talk about its position as determined by a probability cloud, which is denser in places that the electron is more likely to be (near the nucleus) and less dense where it is less likely to be (far from the nucleus). This also takes into account the wave nature of the electron as a quantum object, which we’ll get into another time.
With this knowledge, we can discard that old image of an electron orbiting a nucleus. A single electron, even though it is measurable as an individual, indivisible particle, exists as a cloud around the nucleus. The shape of the cloud is described by quantum mechanics, and as we add more electrons to the atom, we will find a whole gallery of electron cloud shapes. These shapes are the heart of interatomic bonding, as we will see.