32.5

Nuclear Fusion

In Example 4 in Section 32.3, the plot of binding energy per nucleon in Figure 31.5 is used to estimate the amount of energy released in the fission process. As summarized in Figure 32-9, the massive nuclei at the right end of the curve have a binding energy of about 7.6 MeV per nucleon. The less massive fission fragments are near the center of the curve and have a binding energy of approximately 8.5 MeV per nucleon. The energy released per nucleon by fission is the difference between these two values, or about 0.9 MeV per nucleon.

Figure 32-9 When fission occurs, a massive nucleus divides into two fragments whose binding energy per nucleon is greater than that of the original nucleus. When fusion occurs, two low-mass nuclei combine to form a more massive nucleus whose binding energy per nucleon is greater than that of the original nuclei.

A glance at the far left end of the diagram in Figure 32-9 suggests another means of generating energy. Two nuclei with very low mass and relatively small binding energies per nucleon could be combined or “fused” into a single, more massive nucleus that has a greater binding energy per nucleon. This process is called nuclear fusion. A substantial amount of energy can be released during a fusion reaction, as Example 6 shows.

| Example 6 | | | The Energy Released During Nuclear Fusion

Two isotopes of hydrogen, (deuterium, D) and (tritium, T), fuse to form and a neutron according to the following reaction:

Determine the energy released by this fusion reaction, which is illustrated in Figure 32-10.

Figure 32-10 Deuterium and tritium are fused together to form a helium nucleus (). The result is the release of an enormous amount of energy, mainly carried by a single high-energy neutron ().

Reasoning Energy is released, so the total mass of the final nuclei is less than the total mass of the initial nuclei. To determine the energy released, we find the amount (in atomic mass units u) by which the total mass has decreased. Then, we use the fact that 1 u is equivalent to 931.5 MeV of energy, as determined in Section 31.3. This approach is the same as that used in Section 31.4 for radioactive decay.
Solution The masses of the initial and final nuclei in this reaction, as well as that of the neutron, are

Initial Masses | Final Masses
| 2.0141 u |  | 4.0026 u
| 3.0161 u |  | 1.0087 u
Total: | 5.0302 u | Total: | 5.0113 u

The decrease in mass, or the mass defect, is . Since 1 u is equivalent to 931.5 MeV, the energy released is .
The deuterium nucleus contains 2 nucleons, and the tritium nucleus contains 3. Thus, there are 5 nucleons that participate in the fusion, so the energy released per nucleon is about 3.5 MeV. This energy per nucleon is greater than that released in a fission process ( per nucleon). Thus, for a given mass of fuel, a fusion reaction yields more energy than a fission reaction.

Because fusion reactions release so much energy, there is considerable interest in fusion reactors, although to date no commercial units have been constructed. The difficulties in building a fusion reactor arise mainly because the two low-mass nuclei must be brought sufficiently near each other so that the short-range strong nuclear force can pull them together, leading to fusion. But each nucleus has a positive charge and repels the other electrically. For the nuclei to get sufficiently close in the presence of the repulsive electric force, they must have large kinetic energies, and hence large temperatures, to start with. For example, a temperature of around a hundred million °C is needed to start the deuterium–tritium reaction discussed in Example 6.
Reactions that require such extremely high temperatures are called thermonuclear reactions. The most important thermonuclear reactions occur in stars, such as our own sun. The energy radiated by the sun comes from deep within its core, where the temperature is high enough to initiate the fusion process. One group of reactions thought to occur in the sun is the proton–proton cycle, which is a series of reactions whereby six protons form a helium nucleus, two positrons, two rays, two protons, and two neutrinos. The energy released by the proton–proton cycle is about 25 MeV (see problem 33).
Man-made fusion reactions have been carried out in a fusion-type nuclear bomb—commonly called a hydrogen bomb. In a hydrogen bomb, the fusion reaction is ignited by a fission bomb using uranium or plutonium. The temperature produced by the fission bomb is sufficiently high to initiate a thermonuclear reaction where, for example, hydrogen isotopes are fused into helium, releasing even more energy. For fusion to be useful as a commercial energy source, the energy must be released in a steady, controlled manner—unlike that in a bomb. To date, scientists have not succeeded in constructing a fusion device that produces more energy on a continual basis than is expended in operating the device. A fusion device uses a high temperature to start a reaction, and under such a condition, all the atoms are completely ionized to form a plasma (a gas composed of charged particles, like + and e−). The problem is to confine the hot plasma for a long enough time so that collisions among the ions can lead to fusion.
One ingenious method of confining the plasma is called magnetic confinement because it uses a magnetic field to contain and compress the charges in the plasma. Charges moving in the magnetic field are subject to magnetic forces. As the forces increase, the associated pressure builds, and the temperature rises. The gas becomes a superheated plasma, ultimately fusing when the pressure and temperature are high enough.

The physics of nuclear fusion using magnetic confinement.

Another type of confinement scheme, known as inertial confinement, is also being developed. Tiny, solid pellets of fuel are dropped into a container. As each pellet reaches the center of the container, a number of high-intensity laser beams strike the pellet simultaneously. The heating causes the exterior of the pellet to vaporize almost instantaneously. However, the inertia of the vaporized atoms keeps them from expanding outward as fast as the vapor is being formed. As a result, high pressures, high densities, and high temperatures are achieved at the center of the pellet, thus causing fusion. A variant of inertial confinement fusion, called “Z pinch,” is under development at Sandia National Laboratories in New Mexico. This device would also implode tiny fuel pellets, but without using lasers. Instead, scientists are using a cylindrical array of fine tungsten wires that are connected to a gigantic capacitor. When the capacitor is discharged, a huge current is sent through the wires. The heated wires vaporize almost instantly, generating a hot gas of ions, or plasma. The plasma is driven inward upon itself by the huge magnetic field produced by the current. The compressed plasma becomes superhot and generates a gigantic X-ray pulse. This pulse, it is hoped, would implode the solid fuel pellets to temperatures and pressures at which fusion would occur.

The physics of nuclear fusion using inertial confinement.

When compared to fission, fusion has some attractive features as an energy source. As we have seen in Example 6, fusion yields more energy than fission, for a given mass of fuel. Moreover, one type of fuel, (deuterium), is found in the waters of the oceans and is plentiful, cheap, and relatively easy to separate from the common isotope of hydrogen. Fissile materials like naturally occurring uranium are much less available, and supplies could be depleted within a century or two. However, the commercial use of fusion to provide cheap energy remains in the future.

Check Your Understanding 3

Which one or more of the following statements concerning fission and fusion are true? (a) Both fission and fusion reactions are characterized by a mass defect. (b) Both fission and fusion reactions always obey the conservation laws of physics. (c) Both fission and fusion take advantage of the fact that the binding energy per nucleon varies with the nucleon number of the nucleus. (The answer is given at the end of the book.)
Background: In nuclear fission, a massive nucleus splits into less massive fragments. In nuclear fusion, two nuclei with smaller masses combine to form a single nucleus with a larger mass.
For similar questions (including calculational counterparts), consult Self-Assessment Test 32.1, which is described at the end of Section 32.7.

Copyright © 2007 John Wiley & Sons, Inc. All rights reserved.