Chapter Review
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Chapter 32: Nuclear Physics and Nuclear Radiation Chapter Review |
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Chapter Review
This final chapter primarily deals with nuclear and subnuclear physics. In this chapter we touch on topics at the very forefront of human understanding. Nuclear physics is very important in everyday life from the standpoint of energy generation and even medical applications. The chapter concludes with a brief discussion on gravity waves.
32-1 The Constituents and Structure of Nuclei
The nuclei of atoms consist of protons and neutrons; collectively these particles are called nucleons. The number of protons in a nucleus is called the atomic number, Z; the number of neutrons is called the neutron number, N. The total number of nucleons is called the mass number, A. Clearly,
A = Z + N.
The chemical element to which a nucleus belongs is determined by the value of Z. Both Appendices D and E in your textbook list the atomic number of the chemical elements.
The notation used to specify the composition of the nucleus of a chemical element X is
AZX.
Sometimes Z is omitted because the value of Z is specified by the chemical element X. Even though Z is the same for every nucleus of a certain chemical element, the number of neutrons may not be the same. Nuclei having the same Z but different values of N are said to be different isotopes of the same nucleus. For example, 11H and 31H are different isotopes of the hydrogen nucleus with 0 neutrons (A = 1) and 2 neutrons (A = 3), respectively.
The masses of nuclei are often quoted in terms of the atomic mass unit, u. By definition,
1 u = 1.660540 x 10-27 kg.
The mass of an atom, quoted in this unit, is often called its atomic mass. Appendix E in your textbook gives the atomic masses of many common isotopes. Because of the equivalence between mass and energy, E = mc2, the mass of a nucleus is sometimes given in units of E/c2: 1 u = 931.494 MeV/c2. The size of a nucleus can be estimated by an empirical relationship
r = (1.2 x 10-15 m)A1/3,
where A is the mass number. As this relationship shows, the radius of a nucleus is typical on the order of 10-15 m; this distance is called the fermi (fm).
A nucleus may contain many protons a very small distance apart. This situation leads to large electrostatic repulsion between the protons. Holding the nucleus together, against this repulsive force, is the strong nuclear force. This force is a fundamental force of nature that (a) is short range, acting only over a distance of a couple of fermi, and (b) is attractive, acting with nearly equal strength between all nucleons. Since neutrons experience the strong nuclear force, but do not experience electrostatic repulsion (being electrically neutral) their presence in a nucleus helps to stabilize the nucleus (hold it together). The most stable nuclei are those with nearly equal numbers of protons and neutrons (N 
Z). The more protons in a nucleus, the less stable it is; no nucleus with more than Z = 83 protons is stable.
Exercise 32.1 A Lithium Isotope: Estimate the mass, in u, and the radius, in fm, of the isotope 73Li.
Solution:
Appendix E in the textbook gives the atomic mass of a neutral lithium-7 atom to be 7.016005 u. To estimate the mass of the nucleus we must subtract the mass of the Z = 3 electrons surrounding it. The mass of an electron is
Therefore,
MLi-7 = 7.016005 u - 3(5.4858 x 10-4 u) = 7.0144 u.
The given lithium isotope has A = 7. Therefore,
rLi-7 = (1.2 x 10-15 m)A1/3 = (1.2 x 10-15 m)71/3 = 2.3 x 10-15 m = 2.3 fm.
Practice Quiz
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32-2 Radioactivity
An unstable nucleus will disintegrate into a different nucleus; when it does it will emit one of more particles. Also, a nucleus in an excited state can make a transition to a lower energy state and emit a high-energy photon. Both of these processes are referred to as nuclear decay and the emission that occurs is called radioactivity. Therefore, nuclear decay is often called radioactive decay.
The main types of particles emitted during radioactive decay are:
Radioactive decay that emits an alpha particle is called alpha decay. The initial unstable nucleus is called the parent nucleus and the final nucleus is called the daughter nucleus. The daughter nucleus will have two less protons and two less neutrons than the parent nucleus. If the X represents the unstable parent and Y is the daughter, we can write this process as
.
Notice that the atomic number and mass numbers on the left-hand side equals the sum of the corresponding atomic and mass numbers on the right-hand side.
Radioactive decay that emits a b-ray (either b+ or b-) is called beta decay. In the beta decay emission of an electron, the basic process is that a neutron decays into a proton and an electron. Hence, the mass number remains the same, but the atomic number changes (increases) by one
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The process of b+ decay is more complicated to explain, but a similar result applies except that the atomic number decreases by one,
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When radioactive decay occurs, the total mass of the decay products (the final nucleus + emitted particles) is less than the mass of the initial nucleus. The difference in mass, Dm, results in a release of energy in the amount
E = |Dm|c2.
This fact can be used to predict how much kinetic energy the electron or positron should have as a result of beta decay. When the measured kinetic energies of the decay products in beta decay did not satisfy the conservation of energy, it was determined that another particle must be given off. This particle is called a neutrino. Neutrinos are very weakly interacting particles. A neutrino (
) is given off in b+ decay, and an antineutrion (
) is given off during b- decay.
Physlet Illustration: Alpha Decay |
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| In this simulation, a uranium nucleus undergoes alpha decay. Each square on the grid corresponds to 2 femtometers and the clock is in microseconds . How much energy is released in this decay? | ||
Hints:
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Radioactive decay that emits a gamma ray photon (g) is called gamma decay. This process occurs when a nucleus in an excited state decays to a lower energy state. An excited nucleus is indicated by placing an asterisk by the symbol. Thus we have
.
Both A and Z remain the same during gamma decay.
The rate at which nuclear decay takes place is called the activity, R. A common unit of measure for activity is the curie (Ci) which is defined as
1 Ci = 3.7 x 1010 decays/s.
The Si unit of activity is the becquerel (Bq), which is defined as 1 Bq = 1 decay/s. Most commonly, activities are measured in millicuries (mCi) and microcuries (mCi).
Exercise 32.2 The Beta Decay of Carbon: Estimate the energy released when carbon-14 undergoes b- decay.
Picture the Problem In the picture, the completely filled circles represent neutrons and the others are protons. The picture shows the beta decay of a carbon-14 isotope.
Strategy By comparing the masses of carbon-14 to that of nitrogen-14 + and electron we can estimate the energy released from the mass difference.
Solution
| 1. We can get the mass of a carbon-14 nucleus from appendix E in the text: | MC = 14.003242u - 6(5.4858 x 10-4u) = 13.999951u |
| 2. We can get the mass of a nitrogen-14 nucleus from appendix E in the text: | MN = 14.003074u - 7(5.458 x 10-4u) = 13.999234u |
| 3. The mass difference is: | |
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| 4. The energy released is: |  |
Insight Notice how many digits we had to keep in order to see the mass difference. Despite having to keep all these decimal places, the amount of energy is considerable. Another approach to doing this type of calculation is sometimes used. If you add the mass of 6 electrons to that of the carbon-14 nucleus you have the mass of the carbon-14 atom. Also add the mass of 6 electrons to that of the nitrogen-14 nucleus, then, when you add the mass of the emitted electron, you get a total of 7 electrons, making the mass on the right-hand side that of the nitrogen-14 atom. Hence, the mass difference could be determined just from the differences in the atomic masses. It allows you to do the problem in fewer calculations but the logic is less direct.
Practice Quiz
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