nuclear binding energy - where fusion and fission come from

This is a graph of the nuclear binding energy.

In this curve, you can see the variation of the binding energy per nucleon with respect to the atomic mass number.

Beginning with introducing some terminology like nucleon and binding energy which appear on the y-axis here, I will explain what the configuration of the curve tells us and, eventually, how and why we can utilize the atomic energy in two different ways: nuclear fission and nuclear fusion.

As most of you know, the famous formula of Albert Einstein, E = mc², tells us that mass is equivalent to energy. The nucleus of an atom is composed of some tiny particles called nucleons. What is interesting is that the mass of a nucleus is always less than the sum of the individual masses of its nucleons.  This is because a nucleus consumes more energy to bind its nucleons together, and according to Einstein's formula, the reduced mass of the nucleus is expressed by this consumed energy. This difference of energy is called the binding energy. The y-axis of the graph is the binding energy of a nucleus divided by the number of its nucleons and the x-axis indicates the mass number of an atom, which is equal to the number of the nucleons in the atom, representing all the elements on the earth.

Now that you are introduced to the definition of the components of the x and y axes in this curve, I'd like to explain what the configuration of the curve indicates and what physical meanings this diagram has in terms of energy production.

First, noting that the higher binding energy per nucleon an element has, the more stable it is because it is difficult to divide the nucleus due to its strong binding energy per nucleon.  In this respect, the element that has the highest binding energy per nucleon in this region is the most stable substance on the earth and the mass number, in this case, is 56, which is iron! This explains why there is an abundant amount of iron in the universe.

More importantly, as we observe this diagram, we can see there are two possibilities to produce energy. The left part of the curve from the peak indicates that, by combining two light elements, say hydrogen nuclei, into one heavier nucleus, we can produce energy by this difference in the binding energy per nucleon. On the other hand, if we split a heavy nucleus, such as uranium, into lighter nuclei, a certain amount of energy is produced by this difference. These two mechanisms are nuclear fusion and fission, respectively.

There is also a big difference between nuclear fusion and fission besides their apparently opposite ways to produce energy; the amount of the produced energy is much greater in nuclear fusion than in fission. However, which mechanism do you think we are using today to generate electricity, fusion or fission? (waiting for any response..^^) Right, it’s fission. Even though the nuclear fusion has some conspicuous advantages such as huge amount of energy production, abundance in fuel, or friendliness with environment, there are also technical difficulties to make fusion reactions take place in an artificial and controlled manner. Therefore, the already well-established technology to utilize this binding energy, nuclear fission, is being commercially used today. At the same time, however, many institutions and universities in many countries, including MIT, are doing research and development to harness this fascinating, but challenging, energy source, nuclear fusion.