24. The Nucleus atomic number nucleons mass number Protons and Neutrons isotopes

Transcription

1 4. The Nucleus The last several chapters have shown that an understanding of the behavior of atomic electrons can lead to an understanding of the regularities associated with chemical reactions as well as the structure and function of materials. However, in all of the chemistry that we have studied, even in the most violent of chemical reactions, the nucleus remains untouched and unaffected at the center of the atoms. Nevertheless, most of the mass-energy of the atom is locked in the nucleus, and an understanding of its structure leads us to practical applications which have become very important to the well-being of human beings. Nuclear weapons, nuclear power plants, cancer treatments, and radioactive dating methods have all sprung from the study of the nucleus. Protons and Neutrons Chapter 7 explained that each neutral atom is characterized by a number of electrons that occupy orbitals about the atomic nucleus, and that the number of protons is the atomic number of the atom. This determines the chemical element that the atom represents and, hence, its chemical properties. The positive charge in each atom comes from the protons in the atomic nucleus. The amount of positive charge is balanced by the negative charge of the electrons so that the atom as a whole is electrically neutral. Each nucleus may also contain neutrons particles that are electrically neutral, and have about the same mass as protons. The nuclei corresponding to a particular element, such as fluorine, may all have the same mass. However, most elements can have more than one kind of nucleus; the different nuclei of an element are called isotopes, some of which are shown in Table 4.. There are three kinds of hydrogen nuclei. Most helium nuclei have the mass of four protons, but some have only that of three. There are three kinds of carbon nuclei, two kinds of copper, five of zinc, eight of tin, and nine of xenon. The nuclei of different isotopes of an element have the same number of protons, but different numbers of neutrons. The structure of atomic nuclei can be summarized as follows:. The number of protons in a nucleus is the same as the atomic number of the atom. This determines the number of electrons in the neutral atom and, thus, the chemical properties of the atom. All nuclei of a particular chemical element have the same number of protons.. Most nuclei contain one or more neutrons in addition to the protons. The neutrons add mass to the nucleus, but not electric charge. 3. Both protons and neutrons are called nucleons. 4. The total number of nucleons (protons and neutrons) in a nucleus is called its mass number. 5. Different isotopes of a particular element have the same number of protons in each nucleus, but different numbers of neutrons. For example, all oxygen nuclei have eight protons, but some have eight neutrons, others have nine neutrons, and still others have ten neutrons. The mass numbers of these isotopes are, 7, and, respectively.. The different isotopes of a particular element are usually designated by adding the mass number as a superscript to the element s symbol. The atomic number may also be designated by a subscript. For example, the oxygen isotopes described above would be designated as O, 7 O, and O. Naturally occurring elements usually contain several isotopes, all of which have the same chemical properties. The chemical atomic mass of an element is the average atomic mass of the isotopes that make up the element. In the case of copper, which has two isotopes, 9 percent of the copper atoms have a mass number of 3, and 3 percent have a mass number of 5. All have 9 protons, but some have 34 neutrons and others have 3. The average mass of copper atoms, taking the relative abundances of the two isotopes into account, is This is the number published as the atomic mass of copper, since both kinds of copper atoms are 3

2 Table 4.. Some isotopes of the elements. ATOMIC NUMBER ISOTOPE NUMBER OF PROTONS NUMBER OF NEUTRONS MASS NUMBER H H H He He C C C O O O F Cu 9Cu U 3 9U present in all chemical reactions. Radioactivity Most of the atomic nuclei in nature are stable; they do not change if left to themselves. They are not even affected by violent chemical reactions such as explosions or combustion. These reactions involve rearrangements of atomic electrons, but not changes in the nuclei themselves. However, some naturally occurring nuclei spontaneously undergo changes that result in rearrangement of the nuclear constituents and the release of significant amounts of energy. Such nuclei are said to be radioactive. The situation seems to be something like that which occurs when atomic electrons are in high-energy states. Such excited electrons can return to the lower energy states only if their excess energy can be released, perhaps by creating and emitting a photon. Radioactive nuclei are also in states with more energy than necessary. They can become more stable if the excess energy can be released. However, the difference between nuclei and atoms is that nuclei have more ways to release energy, some of which are discussed below. Alpha Decay The nucleus may emit a fast, massive particle that contains two protons and two neutrons (Fig. 4.). When first discovered these particles were called alpha rays, but they have since been found to be identical to the nuclei of 4 He atoms. Even today, such nuclei when produced in nuclear processes are called alpha particles. Rutherford used these naturally occurring alpha particles as the bullets in his early experiments on atomic nuclei discussed in Chapter 5. Since the nucleus loses two protons in alpha decay, the resulting nucleus ( daughter ) has a lower atomic number than before and thus belongs to a different chemical element. Its mass number is reduced by four. An example is the radioactive decay of radium. Ra Rn + 4 He. Note that both charge and mass number are conserved 4

3 Figure 4.. Alpha decay. Figure 4.. Beta decay. in this transformation. Beta Decay The nucleus may emit a fast electron (Fig. 4.). Since there is reason to believe that electrons cannot be confined in the nucleus (using the Uncertainty Principle, for example), a neutron within the nucleus appears to create and immediately emit the electron, much as orbital electrons create and emit photons as an energy release mechanism. Neutrons isolated outside of atomic nuclei always decay by beta emission after a short time. The neutrons become protons, emitting energy and negative charge in the form of fast electrons 0n p + 0 e. This is the basic beta-decay reaction. It sometimes occurs with neutrons inside nuclei. The resulting nucleus will have one fewer neutron and one more proton than before. Again, it will belong to a new chemical element. An important example is the beta decay of carbon-4. 4 C 4 7N + 0 e. Once again note that mass number and electric charge are both conserved. Subsequent research has shown that another particle, called a neutrino, is also emitted with each electron in beta decay. Neutrinos have little or no rest mass, no electric charge, and travel at or near the speed of light. They interact weakly and only with nuclear particles. As a result they are able to penetrate large thicknesses of material, such as the entire diameter of the earth, with only a small probability of interacting with anything. Neutrinos are created and emitted in beta decay and carry away some of the excess energy of the decaying nucleus. Gamma Decay Gamma decay is most like the emission of light by atomic electrons (Fig. 4.3). Alpha and beta decay usually leave the particles of the daughter nucleus in excited states. The daughter nucleus can move to lower-energy states by emitting a photon. However, nuclear states usually involve greater energy changes than electron states in atoms, so the resulting photons from nuclei have higher energy than those emitted by atoms. These high-energy photons are called gamma rays. Neither the atomic number (number of protons) nor the mass number (total number of nucleons) of nuclei changes during gamma decay, although mass does change because energy is released. Gamma decay usually follows all the other radioactive decays, because the residual nuclei are almost always left in an excited condition. Electron Capture Sometimes the nucleons could have a lower energy if one of the protons could become a neutron (Fig. 4.4). One mechanism by which this can occur is for 5

4 Figure 4.3. Gamma decay. the nucleus to capture one of the orbiting atomic electrons, combining the electron with a proton to make a neutron. The excess energy is emitted in the form of a neutrino and, sometimes, one or more gamma rays. The result of electron capture is a decrease in the atomic number, since the nucleus now has less charge than before. As with beta decay, the nuclear mass number does not change; there are the same total number of nucleons as before. An important example of electron capture occurs in the decay of potassium K + 0 e 40 Ar + 0 0neutrino. Note once again that total mass number and electric charge are both conserved in this reaction. Positron Decay Nature provides one other mechanism to convert protons in nuclei into neutrons. If the available energy is large enough, nuclei will sometimes emit a particle that has all the properties of an electron except that it carries a positive rather than a negative charge. Such a particle is called a positron. Positron decay (Fig. 4.5) is like beta decay in every way, except that the emitted particle has positive charge and the resulting nucleus has an atomic number that is one lower, rather than one higher, than before the decay took place. For example, C 5B + 0 +e neutrino. Positrons, which are produced by naturally occurring gamma rays in the atmosphere and in matter, have an interesting history. As they gradually slow down, they transfer their kinetic energy to atomic electrons and cause ionization. When they are slow enough, they attract an electron, and the two of them form a little atom called positronium. (However, it is a strange kind of atom because the electron and positron have the same mass. Positronium is an atom without a nucleus.) After a short time the positron and electron annihilate each other, emitting their total mass-energy in the form of two gamma rays. Fission Some nuclei, usually the heaviest ones, have so much excess energy that they break apart into two large fragments in a process called spontaneous nuclear fission (Figure 4.). The products of such fission are always neutron rich they have too many neutrons and are always radioactive. They begin emitting energy, usually by beta emission. In addition, some of the neutrons of the original fissioning nucleus are not included in either of the major fragments. These become free neutrons, which we will study in the next chapter. Some nuclei that do not spontaneously decay by fission can be made unstable by absorbing a neutron. Important examples of such induced nuclear fission is Figure 4.4. Electron capture. The nucleus captures an orbital electron, changing one proton to a neutron.

5 Figure 4.5. Positron decay and annihilation. A proton inside a nucleus becomes a neutron by emitting a positive electron. The positron later combines with a normal electron and annihilates. Figure 4.. Spontaneous fission. 35 9U + 0n 90 3Sr Xe + 0n + 0n or 35 9U + 0n 3Sr Xe + 0n + 0n. Exactly how the unstable nucleus breaks up is somewhat a matter of chance. Application of Radioactive Materials Radioactivity represents significant energy release from the nuclei of atoms. Not surprisingly, such energy has important effects in nature and is used in several important devices. The energy released by radioactive processes appears as the kinetic energy of the emerging charged particles. These transfer their kinetic energy to the matter through which they pass by interacting via the electrical interaction. Most often these fast, charged particles interact with electrons in matter, dislodging them from the atoms to which they are attached. These atoms then become ionized (Fig. 4.7). All the effects caused by radioactivity can be traced to either the ionized atoms or the free electrons that are produced in this way. (Gamma rays also cause ionization through the highenergy version of the photoelectric removal of electrons from atoms and, indirectly, through the production of high-energy positron-electron pairs.) Radioactive emissions are sometimes called ionizing radiation because of the ionization they cause. The oldest practical application of radioactivity is in the making of radium-dial watches. Radioactive material is mixed with a luminescent powder and painted on watch dials. The charged particles released by the radioactivity separate electrons from atoms in the powder. As the electrons return to their equilibrium states, they emit light. Another early application was in the treatment of cancer (Fig. 4.). The radioactive emissions cause ionization in biological materials as well as in nonliving substances. Such ionization disrupts a cell s normal Figure 4.7. Radioactive emissions transfer energy to matter by causing ionization. Which of the fundamental interactions is responsible? 7

6 function. Rapidly reproducing cells like cancer cells seem particularly susceptible to this kind of damage. If there is enough disruption, individual cells lose their ability to function and die. This possibility makes ionizing radiation one of the most important weapons against certain diseases, particularly cancer. Radiation treatment alone has changed cancer of the uterine cervix from one of the principal causes of death in women to one of the most curable of all cancers. On the other hand, ionizing radiation can also cause undesirable biological effects. Figure 4.. Gamma radiation from radioactive materials can kill cancer cells inside the body. In more recent years radioactivity has been used to run small power cells in applications that require small amounts of energy over a long time, and for which it is inconvenient to change batteries. For example, implanted heart-pacemakers and some applications in space probes use radioactive power cells. Finally, radioactivity in the materials of which the earth is composed provides the energy that keeps the interior of the earth at a higher temperature than its surface. If there were no such source of energy, the earth would have cooled long ago to a uniform temperature. Processes that occur on the surface of the earth would be different if this significant energy source were not operating. Radioactive Half-life The decay of radioactive nuclei is a statistical process. The decays are governed by waves of probability, just as atomic processes are governed by orbitals of probability. Predicting the instant that a particular nucleus will decay is impossible. It may wait several thousand years in its excited state, or it may decay in the next instant. However, if there is a large collection of similar nuclei the average behavior of the group can be predicted and measured with considerable accuracy. Some of the nuclei will decay almost immediately, others will decay after a short time, and still others will wait a long time before their radioactive decay. One way to describe the decay of a particular sample of radioactive nuclei is to specify its half-life, the time required for half of the nuclei to decay. The halflife is a characteristic of particular species of radioactive nuclei and varies from a fraction of a second to many billions of years for different species of nuclei. For example, the half-life of a sample of carbon-4 nuclei is 5,730 years, whereas that of a sample of potassium-40 nuclei is.3 billion years. The statistical nature of radioactive decay has an interesting consequence we will need to know about. Suppose we have a certain sample of radioactive material and measure its decay as time passes (Fig. 4.9). After a time equal to the half-life of the material, half of the original nuclei would have decayed. At the end of a second half-life, half of the remaining nuclei would have decayed. In total, three-fourths of the original material would have decayed, leaving one-fourth as it was at the beginning. During a third half-life, half of these would decay leaving one-eighth in the original Figure 4.9. The random decay of radioactive nuclei. Each frame represents the passage of one half-life.

7 form. As each half-life passes, one-half of the material present at the beginning of the interval decays. For example, suppose that we start with billion atoms of carbon-4. (This is a small number for any real sample.) After 5,730 years (the half-life of carbon- 4), 500 million atoms would remain. After the next 5,730 years, 50 million would survive; 5 million would be around after a third 5,730 years. The decay would continue in this way, the number of survivors being halved every 5,730 years, as long as significant numbers of nuclei remain in the sample. (When the numbers become small, the laws of probability are no longer adequate to give an accurate prediction of when the last few nuclei will decay.) The half-lives of radioactive nuclei depend on processes that take place inside nuclei themselves, but seem not to depend on ordinary processes in which the outer atom might be involved. Events such as chemical reactions and ambient physical conditions such as temperature and pressure do not alter the decay of unstable atomic nuclei. Radioactive Dating The rates at which radioactive materials decay provide a set of clocks, which can be used to estimate time intervals under certain circumstances. For example, the age of the earth and its materials has been debated for hundreds of years. Radioactive dating of the earth s materials has finally given some reliable data from which such estimates can be made. The first observation is that the earth s materials cannot be infinitely old. There are many radioactive isotopes present in the earth s crust. In fact, all the elements with atomic numbers greater than 3 (bismuth) are radioactive. If the earth were infinitely old, these would all have decayed; yet many of them are still present. The second important observation is that the earth is probably more than several million years old. Radioactive materials in the earth s crust all have halflives exceeding about billion years. Several other isotopes, with half-lives in the range of a few million years, are not present. It is argued that many of these must have been formed at the same time as other earth materials, but they have all decayed since that time. Thus, the minimum age of the earth is several million years and the maximum age is several billion years. Some radioactive isotopes permit a more precise estimate. Potassium-40, for example, has a half-life of.3 billion years. When it decays by electron capture, the product is argon, which is normally a gas. When potassium decays inside a rock, the argon atoms are trapped. The method is applied to rocks which begin in the hot, molten state. The high temperatures boil off any existing gases from the molten rock, including argon. Since argon is a noble gas, we also know that no argon is trapped in the rock as a compound or mineral. Thus, when it is cooled to solid form, we begin with a rock that is free of argon. If we subsequently analyze a rock containing potassium-40, the amount of argon-40 reveals the number of potassium-40 nuclei that have decayed since the rock solidified. This, together with a measurement of the number of potassium-40 nuclei that remain, allows a calculation of the number of half-lives that have elapsed. The method assumes that the amounts of potassium-40 and argon-40 found remaining in the rock are related by radioactive decay. It also assumes that once the original rock has cooled and solidified, it is not again melted or subjected to nearmelting temperatures that would drive off accumulated argon. The method is limited to measuring the ages of rocks that had a molten origin at least some tens of millions of years ago or more. There are several radioactive materials in the earth s crust that permit this same kind of calculation. In each case it is possible to estimate or measure the number of nuclei that have decayed and the number that remain. The fraction of nuclei that have decayed reveals the number of half-lives that have elapsed and this, in turn, allows a calculation of the time interval since the formation of the material. All of these calculations indicate that the earth is about 4. billion years old. Another important isotope used for dating is carbon-4. Unlike the radioactive materials in the earth s crust, carbon-4 is continuously being formed in the earth s atmosphere as cosmic rays (mostly protons ejected by the sun) bombard atmospheric nitrogen atoms. After their formation, carbon-4 atoms combine with atmospheric oxygen to form carbon dioxide. They may then become part of living material through the normal carbon cycle, being incorporated by plants into biologically important materials. Most carbon in living things is not carbon-4 at all, but rather carbon-. Unlike carbon-4, carbon- is a stable isotope of carbon and does not decay. For every carbon-4 atom in the atmosphere, there are about 0 carbon- atoms. The activity of the sun keeps this fractional ratio of carbon-4 to carbon- constant by generating new carbon-4 to replace that which decays. The method assumes that the sun has produced the carbon-4 at about the same rate for the past 70,000 years, i.e., the sun has shone with about the same intensity over that short portion of the sun s lifetime. Since all living things are continuously exchanging their carbon with the atmosphere, the fraction of radioactive carbon- 4 to stable carbon- atoms in living plants and animals also remains relatively constant. However, when an organism dies it no longer exchanges carbon with the atmosphere. The carbon-4 is no longer replenished as it decays, and so the fraction 9

8 of undecayed but unstable carbon-4 nuclei relative to the stable carbon- nuclei decreases at a predictable rate. Measurement of this slowly changing fraction permits an estimate of the time that has elapsed since the death of the organism. The 5,730-year half-life of carbon-4 limits the maximum time interval for which this method is useful to about 70,000 years (about half-lives). By this time the carbon-4 is down to about /409 of its original concentration, and the uncertainties in the resulting time estimates increase. Summary The nucleus of each atom is a small, dense core containing one or more protons and, with the exception of H, one or more neutrons. The number of protons (the atomic number) determines the chemical element to which the atom belongs. Each element usually has several isotopes atoms with the same number of protons but different numbers of neutrons. Some of these are unstable, or radioactive, and become more stable by emitting ionizing radiation (an alpha particle, electron, or electromagnetic radiation) or by fissioning. These processes all release energy from atomic nuclei. The rate at which radioactive nuclei decay is measured by their half-life and can be used to estimate how much time has elapsed since certain kinds of events took place. Much of our knowledge of the history of the earth and its life forms comes from the study of radioactive materials and their by-products. STUDY GUIDE Chapter 4: The Nucleus A. FUNDAMENTAL PRINCIPLES. The Electromagnetic Interaction: See Chapter 4.. The Strong Interaction: See Chapter. 3. The Wave-Particle Duality of Matter and Electromagnetic Radiation: See Chapters 4 and. 4. The Conservation of Mass-Energy: See Chapter The Conservation of Electric Charge: See Chapter 7.. The Conservation of Mass Number: In radioactive decays, the number of nucleons (mass number) is conserved. B. MODELS, IDEAS, QUESTIONS, OR APPLICA- TIONS. What are the parts of a nucleus and how is a nucleus described?. How does a nucleus spontaneously adjust to lower energy arrangements? 3. Why must ionizing radiation be carefully controlled? 4. How can radioactive isotopes be used to determine the date of an event? C. GLOSSARY. Alpha Decay: A mode of radioactive decay in which a cluster of two protons and two neutrons (alpha particle) is emitted.. Atomic Number: See Chapter Beta Decay: A mode of radioactive decay in which a high-energy electron (beta particle) and a neutrino (technically, an antineutrino) are emitted. 4. Electron Capture: A mode of radioactive decay in which an orbital electron combines with a nuclear proton to form a neutron and emit a neutrino. 5. Fission: A mode of radioactive decay in which a nucleus of high mass number splits into two roughly equal and separate parts and, often, one or more free neutrons.. Gamma Decay: A mode of radioactive decay in which a high-energy photon (gamma ray) is emitted. 7. Ionizing Radiation: High-energy emission products of radioactive decay which ionize matter as they pass through.. Isotope: Atoms having the same number of protons but different numbers of neutrons are isotopes of one another. Deuterium is an isotope of hydrogen. 9. Mass Number: See Chapter Neutrino: An elementary (pointlike) particle emitted in beta decay. The neutrino is notable because it lacks both a strong and an electromagnetic interaction with matter but interacts instead through the weak interaction.. Neutron: A substructure of the nucleus of the atom. Neutrons do not have an electrical charge. A neutrons consist of three quarks. Protons and neutrons are both referred to as nucleons.. Proton: A substructure of the nucleus of the atom. Protons are positively charged and consist of three quarks. 3. Radioactive Dating: A method for measuring the age of a sample by measuring the relative amounts of radioactive elements and decay products in the sample and accounting for the ratio in terms of the number of half-lives that must have elapsed. 4. Radioactive Half-Life: A period of time in which half the nuclei of a species of radioactive substance would decay. 5. Radioactivity: Spontaneous changes in a nucleus accompanied by the emission of energy from the nucleus as a radiation. 30

9 D. FOCUS QUESTIONS. Consider radioactivity: a. Name and state the fundamental conservation principle that accounts for the energy released in a nuclear reaction. What is the source of the energy released? b. Write the equation describing beta decay in the decay of carbon-4. Explain the meaning of the equation. c. What does half-life mean and what is the halflife of carbon-4? d. Explain how carbon-4 is used to date events. What assumptions are made and what limitations are there in the analysis?. Consider radioactivity: a. Name and state the fundamental conservation principle that accounts for the energy released in a nuclear reaction. What is the source of the energy released? b. Write the equation describing electron capture in the decay of potassium-40. Explain the meaning of the equation. c. What does half-life mean and what is the halflife of potassium-40? d. Explain how potassium-40 is used to date events. What assumptions are made and what limitations are there in the analysis? E. EXERCISES 4.. A certain atom has a mass number of 40 and an atomic number of 9. How many neutrons does it have? 4.. How are the atoms of carbon-4 (radioactive carbon) and carbon- (the usual form of stable carbon) different from one another? How are they alike? 4.3. Describe Rutherford s evidence for the existence of the nucleus Describe two kinds of particles of which atomic nuclei are composed What is meant by the atomic number of a particular nucleus? 4.. What is meant by the mass number of a particular nucleus? 4.7. What is the difference between the various isotopes of a given element? 4.. Radium- is radioactive and emits alpha rays. What would be the atomic number and mass number of the resulting nuclei? To which element would these belong? 4.9. Iodine-3 is radioactive and emits beta rays. What would be the atomic number and mass number of the resulting nuclei? To which element would these belong? 4.0. What is a positron? What happens to the positrons that occur in nature? 4.. What is radioactivity? 4.. Mercury-95 is radioactive through the process of electron capture. What would be the atomic number, the chemical element, and the mass number of the resulting nuclei? 4.3. Why would you expect fast-moving charged particles from radioactive decay to cause ionization? 4.4. Why would you expect ions to behave differently from other atoms? 4.5. Suppose there are 00,000 radioactive atoms in a sample of material. How many would be left after one half-life has elapsed? Two half-lives? Three half-lives? 4.. Explain what is meant by ionization What is an ion? 4.. Why would you expect radioactive decay to be harmful to living systems? 4.9. What is meant by the term half-life? 4.0. How can 4 C be used to date an object? 4.. Explain how radioactive potassium can be used to date a rock. What date or age is revealed by this method? 4.. Review the description of carbon-4 dating. What assumptions are being made that might affect the precision of the method? What experiments could be performed to reassure oneself that the assumptions are valid? 4.3. List and describe three practical uses of ionizing radiation. What is a danger associated with ionizing radiation? 4.4. Skeletal remains of a humanlike creature were discovered in Olduvai Gorge in Tanzania in 9. The discoverers claim that the bones were found in a geologic formation that is about. million years old. 3

10 Would carbon-4 dating be useful for establishing age in this instance? Why? 4.5. Which of the following is true regarding the isotopes of an element? (a) They are equally radioactive. (b) They have the same atomic mass. (c) They have the same number of neutrons. (d) They have the same number of protons. (e) They have different numbers of protons. 4.. In which of the decay processes is the atomic number of the final nucleus the same as that of the original nucleus? (a) alpha decay (b) beta decay (c) gamma deca (d) electron capture (e) fission 3