32.3

Nuclear Fission

In 1939 four German scientists, Otto Hahn, Lise Meitner, Fritz Strassmann, and Otto Frisch, made an important discovery that ushered in the atomic age. They found that a uranium nucleus, after absorbing a neutron, splits into two fragments, each with a smaller mass than the original nucleus. The splitting of a massive nucleus into two less massive fragments is known as nuclear fission.
Figure 32-4 shows a fission reaction in which a uranium nucleus is split into barium and krypton nuclei. The reaction begins when absorbs a slowly moving neutron, creating a “compound nucleus,” . The compound nucleus disintegrates quickly into , , and three neutrons according to the following reaction:

This reaction is only one of the many possible reactions that can occur when uranium fissions. For example, another reaction is

Some reactions produce as many as 5 neutrons; however, the average number produced per fission is 2.5.

Figure 32-4 A slowly moving neutron causes the uranium nucleus to fission into barium , krypton , and three neutrons.

When a neutron collides with and is absorbed by a uranium nucleus, the uranium nucleus begins to vibrate and becomes distorted. The vibration continues until the distortion becomes so severe that the attractive strong nuclear force can no longer balance the electrostatic repulsion between the nuclear protons. At this point, the nucleus bursts apart into fragments, which carry off energy, primarily in the form of kinetic energy. The energy carried off by the fragments is enormous and was stored in the original nucleus mainly in the form of electric potential energy. An average of roughly 200 MeV of energy is released per fission. This energy is approximately 108 times greater than the energy released per molecule in an ordinary chemical reaction, such as the combustion of gasoline or coal. Example 4 demonstrates how to estimate the energy released during the fission of a nucleus.

| Example 4 | | | The Energy Released During Nuclear Fission

Estimate the amount of energy released when a massive nucleus (A = 240) fissions. Reasoning Figure 31.5 shows that the binding energy of a nucleus with A = 240 is about 7.6 MeV per nucleon. We assume that this nucleus fissions into two fragments, each with . According to Figure 31-5, the binding energy of the fragments increases to about 8.5 MeV per nucleon. Consequently, when a massive nucleus fissions, there is a release of about 8.5 MeV – 7.6 MeV = 0.9 MeV of energy per nucleon.
Solution Since there are 240 nucleons involved in the fission process, the total energy released per fission is approximately .

Need more practice?

Interactive LearningWare32.1
Consider the following neutron-induced fission reaction:

(a) Determine the atomic mass number A and the atomic number Z for the unknown nucleus . What element is it? (b) Find the energy (in MeV) released by this reaction.
Related Homework: Problem 20

Virtually all naturally occurring uranium is composed of two isotopes. These isotopes and their natural abundances are (99.275%) and (0.720%). Although is by far the most abundant isotope, the probability that it will capture a neutron and fission is very small. For this reason, is not the isotope of choice for generating nuclear energy. In contrast, the isotope readily captures a neutron and fissions, provided the neutron is a thermal neutron ( or less). The probability of a thermal neutron causing to fission is about five hundred times greater than a neutron whose energy is relatively high—say, 1 MeV. Thermal neutrons can also be used to fission other nuclei, such as plutonium . Conceptual Example 5 deals with one of the reasons why thermal neutrons are useful for inducing nuclear fission.

| Conceptual Example 5 | | | Thermal Neutrons Versus Thermal Protons or Alpha Particles

Why is it possible for a thermal neutron (i.e., one with a relatively small kinetic energy) to penetrate a nucleus, whereas a proton or an particle would need a much larger amount of energy to penetrate the same nucleus? Reasoning and Solution To penetrate a nucleus, a particle such as a neutron, a proton, or an particle must have enough kinetic energy to do the work of overcoming any repulsive force that it encounters along the way. A repulsive force can arise because protons in the nucleus are electrically charged. Since a neutron is electrically neutral, however, it encounters no electrostatic force of repulsion as it approaches the nuclear protons and, hence, needs relatively little energy to reach the nucleus. In contrast, a proton and an particle both carry positive charge, and each encounters an electrostatic force of repulsion as it approaches the nuclear protons. It is true that each also experiences the attractive strong nuclear force from the nuclear protons and neutrons. But the strong nuclear force has an extremely short range of action and, therefore, comes into play only when an impinging particle reaches the nucleus. In comparison, the electrostatic force of repulsion has a long range of action and is encountered by an incoming charged particle throughout the entire journey to the target nucleus. Consequently, an impinging proton or particle needs a relatively large amount of kinetic energy to do the work of overcoming the repulsive electrostatic force.
Related Homework: Problem 40

The fact that the uranium fission reaction releases 2.5 neutrons, on the average, makes it possible for a self-sustaining series of fissions to occur. As Figure 32-5 illustrates, each neutron released can initiate another fission event, resulting in the emission of still more neutrons, followed by more fissions, and so on. A chain reaction is a series of nuclear fissions whereby some of the neutrons produced by each fission cause additional fissions. During an uncontrolled chain reaction, it would not be unusual for the number of fissions to increase a thousandfold within a few millionths of a second. With an average energy of about 200 MeV being released per fission, an uncontrolled chain reaction can generate an incredible amount of energy in a very short time, as happens in an atomic bomb (which is actually a nuclear bomb).

Figure 32-5 A chain reaction. For clarity, it is assumed that each fission generates two neutrons (2.5 neutrons are actually liberated on the average). The fission fragments are not shown.

By using a material that can absorb neutrons without fissioning, it is possible to limit the number of neutrons in the environment of the fissile nuclei. In this way, a condition can be established whereby each fission event contributes, on average, only one neutron that fissions another nucleus (see Figure 32-6). Thus, the chain reaction and the rate of energy production are controlled. The controlled fission chain reaction is the principle behind nuclear reactors used in the commercial gereration of electric power.

Figure 32-6 In a controlled chain reaction, only one neutron, on average, from each fission event causes another nucleus to fission. The “lost neutron” is absorbed by a material (not shown) that does not fission. As a result, energy is released at a steady or controlled rate.

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