Welcome to week 9 of Science Friday! For the last two weeks, we have discussed some basic differential calculus. This week, we’re going to talk about a close companion to the field of mathematics—physics. More specifically, the atomic nucleus and the epic power it holds. The atom is a spectacular entity. While it is not the most fundamental unit of organization particle physicists have identified, it underlies everything we understand about the chemicals we use commercially and industrially. The actual structure of the atom has been revised multiple times over the course of history—so much so that it warrants its own Science Friday in the future—but one experiment worth nothing here verified the existence of a positively charged nucleus. This experiment was the famous gold foil experiment directed by the legendary physicist Ernest Rutherford. In short, the experiment involved shooting alpha particles (helium nuclei) at a gold foil. Since alpha particles are positively charged, the experimenters expected some degree of deflection when they hit the foil. The actual observations, however, showed a number of alpha particles that were deflected straight back to the source. These results hearkened a rethinking of the atom in the early twentieth century. The center, it was postulated, is composed of positive charge since alpha particles were deflected. Furthermore, the center of the atom must be extremely small in comparison to the rest of the atom since the frequency of deflections was small. Indeed, the great majority of the entity we call the atom is empty space, with only a tiny fraction occupied by protons, neutrons (discovered later), and electrons (discovered earlier). The nucleus as we understand it today is composed of protons and neutrons, the latter of which have no electric charge. One question that is obvious is what causes the protons (positive charges) to [i]not[/i] repel one another? The answer is the [b]strong nuclear force[/b], which is many orders of magnitude stronger than the electromagnetic forces at the distances involved in small atomic nuclei. To put this into perspective, the electromagnetic force itself is astronomically stronger than gravity. However, as nuclei get larger, the electrostatic repulsions between protons begin competing with the weakening strong force, which is the principal reason why almost all large nuclei are [b]radioactive[/b]—they decay into more stable nuclei. But what is the strong nuclear force exactly? Here is where our notions of macroscopic logic breaks down. It turns out that, if you took the mass of every single proton and and every single neutron in a given nucleus and added it all together, the total mass you would get would be [i]greater than[/i] than the mass of the nucleus that contains those very numbers of protons and neutrons! This seems to be a blatant violation of the conservation of mass principle that underlies all of chemistry. So where does this lost mass go? The answer is that it is turned into energy. By Einstein’s famous equation, E = mc^2, we can calculate precisely how much energy if we know the difference in mass between the nucleus we end up with and the protons and neutrons we started with. This energy is called the [b]nuclear binding energy[/b] and is used to bind the nucleus. The greater the binding energy [i]per nucleon[/i] (nucleon is the general term for the particles in the nucleus), the more stable the nucleus. Considering these facts, we can now understand what drives the devastating force of nuclear explosions and the spectacular lives of stars. When uranium is fissioned (split) by a neutron into two lighter nuclei, energy is released. The products of uranium fission are two nuclei which always have a higher binding energy per nucleon. This means that the nuclei are more stable and therefore energy is released. This may seem counterintuitive at first. After all, how does greater binding energy lead to more stability? The answer lies in the fact that, as binding energy increases, the mass deficit increases, which means that there is more mass converted into energy. The difference in the mass deficits is released. The products of hydrogen fusion also have greater binding energies than the starting nuclei. The reason why hydrogen fusion yields much more energy than fission is simply because the difference in binding energy between the reactant nuclei and product nuclei is greater than in uranium/plutonium fission. However, to fuse atoms together, it requires astronomically high temperatures and pressures—conditions only naturally met at the core of stars. For this reason, hydrogen bombs are actually triggered by fission (atomic) bombs and nuclear fusion reactors are currently infeasible. In contrast, fission requires the destabilization of nuclei by the introduction of neutrons into a critical mass (material that contains enough fissile material to initiate the chain reaction). I hope this long session of SciFri a) makes up for last week’s short one and b) was informative and fun to read. If you have any questions about my post contents, please comment. If you have any other insights, do the same. I look forward to reading the responses I receive to my weekly postings. As always, you can check out my previous work by clicking the #sciencefriday tag on the thread and changing the filter settings.