Nuclear Fission refers to the process by which a large, unstable nucleus is split into several smaller and more stable nuclei. Consider the fission of uranium-235 which occurs via collision with a neutron:
$$^{235}_{92}U + ^{1}_{0}n → ^{139}_{56}Ba+^{94}_{36}Kr + 3^{1}_{0}n+ energy$$
Notice that the total mass of the products is the same as the mass of the reactants. A significant aspect of nuclear fission is that nuclear fission releases energy
Nuclear Fusion is just the opposite of nuclear fission. In nuclear fusion, two smaller nuclei are fused together into a single larger and more stable nucleus. For example, hydrogen can be fused together to form helium:
$$4^{1}_{1}H → ^{4}_{2}He + 2^{0}_{1}e + energy$$
Just like with nuclear fission, nuclear fusion releases energy. Both of these processes release energy because the products are more stable than the reactants.
Nuclear reactors take advantage of chain reactions in which the neutrons released in the initial fission reaction go on to cause more fission reactions.
The fission reaction is initiated by a neutron colliding with the initial atom, which then releases more neutrons. Those neutrons can then go on to initial their own fission reactions, which then release more neutrons ad nauseum.
Ideally, each fission reaction would produce one neutron that collides with another nucleus because then the chain reaction would grow at a constant rate. If the fission reaction produces less than 1 neutron that collides with another nucleus, the reaction is said to be subcritical and will die out because the number of neutrons released is insufficient to sustain a chain. On the other hand, if the fission reaction produces more than 1 neutron that collides with another nucleus, the reaction is said to be supercritical and will result in an explosion due to the rapid escalation of reaction (remember that each reaction releases heat). If the reaction produces roughly 1 neutron that collides with another nucleus per reaction, the reaction is said to be critical.
I've always found it entertaining how when nuclear reactors are portrayed in TV shows and movies, the reaction manager inevitably runs around proclaiming that the reactor is "going critical" as if it were a bad thing. In reality, that's exactly what one would want out of a reactor.
1. In nuclear fission, a large unstable nucleus is split into several smaller and more stable nuclei.
2. In nucleus fusion, several smaller nuclei are fused into one larger and more stable nucleus.
3. In both fission and fusion, energy is released because the products are more stable than the reactants.
4. When a fission reaction releases on average 1 neutron that collides with another reactant, the reaction is in a critical/self-sustaining state. If the average is lower than 1, the reaction is in a subcritical state and will die out. If the average is higher than 1, the reaction is in a supercritical state and will rapidly escalate until explosion.
#1. Problems with Fusion
The primary problem with fusion is the overcoming of the electrostatic repulsion between protons. Protons really don't want to be close to each other, which is neccessary if the nuclei are to fuse. Thus, in order to get nuclei to fuse, one has to get the protons really, really close together. This requires an immense amount of energy e.g for two H-atoms to fuse, the necessary temperature is estimated to be `4 x 10^7 K` . This is the primary reason why fusion is not currently a viable source of energy.
#2. Cold/Hot Fusion
The way fusion occurs in stars is called "hot" fusion due to the immense temperature and pressure inside the stars. Under this temperature and pressure, the protons are pushed close enough that the nuclei are able to fuse.
Cold fusion is a theoretical form of fusion that occurs at lower temperatures, ideally at room temperature. As of now we don't know whether it is actually possible, but the results of cold fusion being possible would be immense. For starters, we could generate incredible amounts of energy just by fusing hydrogen, helium, and lithium atoms which make up most of the known universe.
#3. Nuclear Power
Nuclear power is simply sustained fission reactions. While there is a stigma against nuclear power due to the association of the word nuclear, nuclear power is actually one of the safest, most efficient, and most reliable sources of energy. For example, the fission reaction of 1 mol of uranium-235 releases `10^(13) J` of energy in comparison to the combusion of methane, which only releases `10^5 J` . That's a difference of 8 magnitudes!
#4. Release of Energy
A question you may have asked while reading this is how both fission and fusion can release energy despite the two being opposite reactions. The answer is due to the stability of nuclei of elements around iron. As atoms become more and more like iron-54, they release more and more energy. All fission and fusion reactions are therefore just attempts at becoming iron-54, similar to how atoms react to gain the electron configuration of a noble gas.
The reason heavy and unstable elements exist is due to large bursts of energy that are capable of producing an unstable nucleus, such as supernova.