It is here that most elementary science textbooks stop. Most people have a mental image of an atom something akin to this: (Click image to enlarge.)

From the get-go there are two things wrong with this image, both of which were known to the scientists of the early 1900's (well before images like the one above made their way into science textbooks worldwide). First is a factor of scale: if the nucleus were the size of a fly in the middle of a stadium, the electrons would never be any nearer than the stands. Second is the fact that atomic-scale particles such as the proton and electron do not actually behave like solid particles; they rather behave like waves of energy. They don't really have a well-defined "position," as they appear to have above. Of course, both of these properties of the atom are difficult to draw in an economic fashion, so compromises must be made and the above representation must suffice. Unfortunately, few teachers explain this to students, and as a result people incorrectly imagine the atom to look something like the picture above.
There is, however, more to the story. By the 1970's, scientists had learned that there are more than three basic parts to an atom. It was discovered that not only are there particles such as photons, pions, and gluons that hold the atom together, there are particles called up quarks and down quarks that make up each proton and neutron. As a result, our simple atom has become an atomic zoo, as illustrated below: (The image below has the same shortcomings as those described for the previous image; Click image to enlarge.)

As you can see, it seems there's quite the mess to be had within the atom. It turns out, though, that this scheme actually simplifies our greater understanding of the subatomic realm, which contains hundreds of other types of "hadrons" in addition to the proton and neutron. Amazingly, these other entities are found to be made of the same basic particles as those found in the atom, such as quarks, further underpinning the apparent correctness of the model above.
So what's the point of knowing the true fundamental constituents of the atom? Well, our understanding of the basic "electron and nucleus" structure of the atom gave us our mastery over chemistry and molecules; an understanding of the true structure of the atom will perhaps someday provide us the tools for mastering the atom itself.
And yet most people are stuck somewhere between here and the ancient Greeks.
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