Nuclear changes occur with a simultaneous release of energy. Where does this energy come from? If we could precisely measure the masses of the reactants and the products of a nuclear reaction, we would notice that the amount of mass drops slightly in the conversion from reactants to products. Consider the following nuclear reaction:

[latex]_{92}^{235}\textrm{U}\rightarrow[/latex] [latex]_{56}^{139}\textrm{Ba}+_{36}^{94}\textrm{Kr}+2_{0}^{1}\textrm{n}[/latex]

The mass of the reactant, to four decimal places, is 235.0439.  The masses of the two products are 138.9088 and 1.0087, which must be multiplied by two. Comparing the mass of the reactant (235.0439) to the total mass of the products (234.8605), we notice a mass difference of −0.1834 g, or −0.0001834 kg. Where did this mass go?

According to Albert Einstein’s theory of relativity, energy (E) and mass (m) are related by the following equation:

E = mc²

where c is the speed of light, or 3.00 × 10⁸ m/s. In the course of the uranium nuclear chemical reaction, the mass difference is converted to energy, which is given off by the reaction:

E = (−0.0001834 kg)(3.00 × 10⁸ m/s)² = −1.65 × 10¹³ J = −1.65 × 10¹⁰ kJ

That is, 16.5 billion kJ of energy are given off every time 1 mol of uranium-235 undergoes this nuclear reaction. This is an extraordinary amount of energy. Compare it to combustion reactions of hydrocarbons, which give off about 650 kJ/mol of energy for every CH₂ unit in the hydrocarbon—on the order of hundreds of kilojoules per mole. Nuclear reactions give off billions of kilojoules per mole.

If this energy could be properly harvested, it would be a significant source of energy for our society. Nuclear energy involves the controlled harvesting of energy from fission reactions. The reaction can be controlled because the fission of uranium-235 (and a few other isotopes, such as plutonium-239) can be artificially initiated by injecting a neutron into a uranium nucleus. The overall nuclear equation, with energy included as a product, is then as follows:

²³⁵U + ¹n → ¹³⁹Ba + ⁹⁴Kr + 3¹n + energy

Thus, by the careful addition of extra neutrons into a sample of uranium, we can control the fission process and obtain energy that can be used for other purposes.

A nuclear reactor is an apparatus designed to control the progress of a nuclear reaction and extract the resulting energy for useful purposes. iFigure 11.5 “A Diagram of a Nuclear Power Plant for Generating Electricity” shows a simplified diagram of a nuclear reactor. The energy from the controlled nuclear reaction converts liquid water into high-pressure steam, which is used to run turbines that generate electricity.

Figure 11.5 A Diagram of a Nuclear Power Plant for Generating Electricity.The two main components of the power plant are the nuclear reactor itself and the steam-driven turbine and electricity generator.

Notice that the fission of uranium produces two more free neutrons than were present to begin with. These neutrons can themselves stimulate other uranium nuclei to undergo fission, releasing yet more energy and even more neutrons, which can in turn induce even more uranium fission. A single neutron can thus begin a process that grows exponentially in a phenomenon called a chain reaction:

1 → 2 → 4 → 8 → 16 → 32 → 64 → 128 → 256 → 512 → 1,024 → 2,048 → 4,096 → 8,192 → 16,384 →…

Because energy is produced with each fission event, energy is also produced exponentially and in an uncontrolled fashion. The quick production of energy creates an explosion. This is the mechanism behind the atomic bomb. 

Fusion is another nuclear process that can be used to produce energy. In this process, smaller nuclei are combined to make larger nuclei, with an accompanying release of energy. One example is the hydrogen fusion, which makes helium. While the steps of the process are complicated, the net reaction is:

4¹H → ⁴He + 2.58 × 10¹² J

Notice that the amount of energy given off per mole of reactant is only a fraction of the amount given off by the fission of 1 mol of uranium-235. On a mass (per gram) basis, however, the hydrogen fusion emits many times more energy than fission does. In addition, the product of fission is helium gas, not a wide range of isotopes (some of which are also radioactive) produced by fission.

The practical problem is that to perform fusion, extremely high pressures and temperatures are necessary. Currently, the only known stable systems undergoing fusion are the interiors of stars. The conditions necessary for fusion can be created using an atomic bomb, but the resulting fusion is uncontrollable and is the basis for the hydrogen bomb. Currently, researchers are looking for safe, controlled ways of producing useful energy using fusion.