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Explanation
This explanation may be incomplete or incorrect: Created by a COMPLAINING EQUATION. Please mention here why this explanation isn't complete. Do NOT delete this tag too soon. 
This comic humorously describes the changing view of what an atom is.
 Small hard ball model
The first model shown, in 1810, is said to be a "small hard ball model." Around this time, John Dalton published his textbook A New System of Chemical Philosophy which linked existing ideas of atomic theory and chemical reactivity to produce a combined Law of multiple proportions which proposed that each chemical element is comprised of a single unique type of atom, and introduced the concept of molecular weight. Dalton's theories form the basis of what is known today as stoichiometry, which underpins chemical reactivity. As atoms were considered at this time to be the smallest possible division of matter the scientific community thought of them as "hard round balls" of different sizes; thus the name described here. The "small hard ball" model is still commonly used when teaching and discussing chemical molecules which do not require the level of detail provided by more advanced models, with atoms represented as small, hard, round balls connected by sticks representing chemical bonds.
 Plum pudding model
In the late 19th and early 20th centuries, the study of these "atom" things faced a crisis: where would the newly discovered "electrons" go? In 1904, physicist J. J. Thomson, who discovered electrons, had an idea: maybe the electrons were small point charges moving around in a big mass of positive charge. This was the "plum pudding model", the second model on the comic, called this because people imagined the positively charged mass as a "plum pudding". (The title text references Thomson as well, along with the humorous observation that plum puddings themselves are made of atoms.) The problem with this approach is that same charges generally repel, resulting in the more mobile or unbalanced charges forming a surface shell around the others, attempting to escape, rather than being content to being randomly distributed among them.
 Tiny bird model
There were many competing ideas in the formative years of whatareatomsmadeofology, Randall makes up a 1907 "tiny bird model."
 Rutherford model
Ultimately, the tentative winner in the battle was the model of Thomson's student Ernest Rutherford, who discovered from electrostatic scattering experiments that the positive charge seemed to be concentrated in the center of the atom, and proposed his Rutherford model, or "planetary model", in 1911, where electrons orbit a very concentrated positive charge. This model has often been compared to the orbit of the planets around the sun. This is the fourth model in the comic.
 Bohr model
The Rutherford model could not explain the discrete spectral lines in absorption and emission spectra. It also did not explain why electrons did not spiral in to the nucleus. Niels Bohr patched the model up by proposing that electrons could only exist in distinct "energy levels" at discrete distances from the nucleus. The 1913 "Bohr model", the fifth model shown here, was part of beginning quantum mechanics. Physics behaves differently at the small scale of atoms than the large scales we are more familiar with.
 Nunchuck model, Chadwick model
The next refinement was in the structure of the nucleus. Note that at this time, nobody thought of splitting up the nucleus into protons and neutrons. But pretty soon people noticed that protons and neutrons existed; Randall facetiously suggests a "nunchuck model", the sixth model shown, of a packet of protons swinging a packet of electrons around. But more seriously, James Chadwick, who discovered the neutron, figured that the atom had a nucleus of neutrons and protons, along with a bunch of electrons orbiting around it in a Bohrish manner. This is what the layman today often thinks of as an atom, and is the seventh model shown here. One can imagine a handle filled with electrons bonded by the strong nucleur force to a chain made of neutrons, bonded again by the strong nuclear force to a handle made of protons. The heavier protonic handle acts loosely as an orbital center as the electronfilled opposite handle swings wildly around it, attempting to resolve its electrostatic attraction within the restraints of its chain.
 538 Model
The eighth model shown is a made up "538 model," in 2008. 538 is a statistical analysis website that gained fame in 2008 for predicting every race but 2 correctly in the US presidential election and predicting every state and Obama's win in the 2012 election. Unlike most other media and polling institutes it saw a rather high probability of 29% for Trump to win the 2016 election by summing up the uncertainties in all the battle states. It has since been known for making mathematical models for everything; the model jokingly suggests that 538 has modeled and presumably made predictions about the atom. The pie chart shows the statistical composition of neutrons, protons and electrons, 38%, 31%, and 31% respectively. This could either be the average of a massive body with several isotopes or represent gallium69, the most abundant isotope of gallium, with 31 protons, 31 electrons and 38 neutrons. FiveThirtyEight has previously been mentioned in several xkcd comics, including in 477: Typewriter, 500: Election, 635: Locke and Demosthenes, 1130: Poll Watching, 1779: 2017, and 2002: LeBron James and Stephen Curry.
 Quantum model
But is the Chadwick model what scientists endorse today? No! The theory of electromagnetism says that accelerated charges, like the electrons circling, would lose energy emitted as electromagnetic waves and would quickly orbit into the nucleus. Bohr only postulated that this would not happen, but his model could not explain why. Another problem^{[citation needed]} is that atoms, even the hydrogen atom are not flat  which they would be, if a single electron orbited in a circular or elliptical trajectory. Today (i.e. actually since 1926, 29 years after the discovery of the electron) physicists subscribe to a quantum model, which is the ninth model shown here. Instead of electrons with definite location and momentum (~speed), the parts of the atom are described by probability fields of possible locations and momentums. The changes in momentum probability normally cancel each other out, so there is no electromagnetic radiation. This is very abstract, and in the last model, the model is postulated to get so abstract that it is just a "small hard ball surrounded by math" model, the last model shown. This then is remarkably similar to the model we started out from, the "small hard ball model" (without the math).
 “Small hard ball surrounded by math” model
The picture for the "small ball surrounded by math" depicts a circle with several numbers around it. While the numbers seem to symbolize the "surrounding math" in a general sense, some of them suggest constants used in actual mathematical equations or other numbers related to the quantum model. The shapes and densities of the atomic orbitals are calculated with the Schrödinger_equation, which is complex and difficult to solve. Or with string theory, which does not make it easier. For this reason atoms are generally precisely considered in only very simple simulations, and the details of interactions of many atoms at large scales that form our daily lives are incredibly hard to precisely understand and predict on an atomic level. It comes down to "these roundish things we call atoms are moving around in these approximate ways obeying this complex equation with too many numbers involved in most situations to accurately model, so let's use a different, empirically derived formula that describes the behavior of the system in general."
Number  Explanation 

18  Maximum number of electrons in the third (M) electron shell 
0.1  1/10th, a simple decimal 
π  The number pi ratio of circumference of a circle to half its diameter. Pi is present in many physics equations, often as its double value (2π); also in the definition of the reduced Planck constant present in quantummechanical equations. 
173  Possibly a typo (could be 137) referring to the fine structure constant which value is approximately 1/137 
√2  An irrational constant, the square root of two, which comes up frequently 
4i  A simple complex number; i is considered the square root of 1 (4i is the square root of 16) 
Transcript
This transcript is incomplete. Please help editing it! Thanks. 
 [One large panel with a caption centered on top and ten small drawings in two rows. Each drawing has a description below it.]
 Models of the Atom
 over time
 [A somewhat imperfectly drawn circle.]
 1810
Small hard ball model
 [A roundedcorners trapezoid inside which there are four small plus signs and four small circles with minus signs inside them.]
 1904
Plum pudding model
 [A bigger circle, with four birds on the surface and music notes above.]
 1907
Tiny bird model
 [A small circle with dots circling around it, drawn with paths.]
 1911
Rutherford model
 [A circle with a plus sign with three circles around it, each with a dot.]
 1913
Bohr model
 [A nunchuck swinging, with the left stick filled with circles with plus signs and the right stick filled with circles with minus signs.]
 1928
Nunchuck model
 [A nucleus with three circles around it, each with a dot.]
 1932
Chadwick model
 [A pie chart, where a part of it has a circle, a part of it has a circle with a minus sign and a part of it has a circle with a plus sign.]
 2008
538 model
 [A small circle with cloverlike orbitals around it and surrounded by two outer partly dashed circles.]
 Today
Quantum model
 [A circle surrounded with numbers.]
 Numbers: 18, 0.1, π, 173, √2, 4i
 Future
"Small hard ball surrounded by math" model
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