Problems

Note to Instructors: Most of the homework problems in this chapter are available for assignment via an online homework management program such as WileyPLUS or WebAssign, and those marked with the icon are presented in a guided tutorial format that provides enhanced interactivity. See Preface for additional details.
ssm Solution is in the Student Solutions Manual.
This icon represents a biomedical application.
Section 32.1 Biological Effects of Ionizing Radiation

| 1 | ssm www A 75-kg person is exposed to 45 mrem of particles (RBE = 12). How much energy has this person absorbed?

| 2 | Neutrons (RBE = 2.0) and particles have the same biologically equivalent dose. However, the absorbed dose of the neutrons is six times the absorbed dose of the particles. What is the RBE for the a particles?

| 3 | A film badge worn by a radiologist indicates that she has received an absorbed dose of 2.5 × 10−5 Gy. The mass of the radiologist is 65 kg. How much energy has she absorbed?

| 4 | A person receives a single whole-body dose of particles. The absorbed dose is 38 rad, and the RBE of the particles is 12. (a) Determine the biologically equivalent dose received by this person, (b) With this dose, which one of the following would you expect to happen: no short-term ill effects, the onset of radiation sickness, a 50% chance of dying, or almost certain death?

| 5 | ssm A beam of particles is directed at a 0.015-kg tumor. There are 1.6 × 1010 particles per second reaching the tumor, and the energy of each particle is 4.0 MeV. The RBE for the radiation is 14. Find the biologically equivalent dose given to the tumor in 25 s.

| 6 | Multiple-Concept Example 1 discusses the concepts that are relevant to this problem. A person undergoing radiation treatment for a cancerous growth receives an absorbed dose of 2.1 Gy. All the radiation is absorbed by the growth. If the growth has a specific heat capacity of 4200 J/(kg · C°), determine the rise in its temperature.

* | 7 | A 2.0-kg tumor is being irradiated by a radioactive source. The tumor receives an absorbed dose of 12 Gy in a time of 850 s. Each disintegration of the radioactive source produces a particle that enters the tumor and delivers an energy of 0.40 MeV. What is the activity (see Section 31.6) of the radioactive source?

* | 8 | Multiple-Concept Example 1 uses an approach similar to that needed in this problem, except here the temperature remains constant while a phase change occurs. A sample of liquid water at 100 °C and 1 atm pressure boils into steam at 100 °C because it is irradiated with a large dose of ionizing radiation. What is the absorbed dose of the radiation in rads?

* | 9 | ssm A beam of nuclei is used for cancer therapy. Each nucleus has an energy of 130 MeV, and the relative biological effectiveness (RBE) of this type of radiation is 16. The beam is directed onto a 0.17-kg tumor, which receives a biologically equivalent dose of 180 rem. How many nuclei are in the beam?
Section 32.2 Induced Nuclear Reactions

| 10 | What is the atomic number Z, the atomic mass number A, and the element X in the reaction (, p)?

| 11 | ssm www Write the equation for the reaction (γ, αn) . The notation “n” means that an particle and a neutron are produced by the reaction.

| 12 | A neutron causes to change according to the reaction

(a) Identify the unknown nucleus , giving its atomic mass number A, its atomic number Z, and the symbol X for the element. (b) The nucleus subsequently undergoes decay, and its daughter does too. Identify the final nucleus, giving its atomic mass number, atomic number, and name.

| 13 | Complete the following nuclear reactions, assuming that the unknown quantity signified by the question mark is a single entity:

a. |
b. |
c. |
d. |
e. |

| 14 | Write the reactions below in the shorthand form discussed in the text.

a. |
b. |
c. |

* | 15 | ssm Consider the induced nuclear reaction . The atomic masses are (2.014 102 u), (14.003 074 u), (12.000 000 u), and (4.002 603 u). Determine the energy (in MeV) released when the and nuclei are formed in this manner.

* | 16 | During a nuclear reaction, an unknown particle is absorbed by a copper nucleus, and the reaction products are , a neutron, and a proton. What is the name, atomic number, and nucleon number of the nucleus formed temporarily when the copper nucleus absorbs the unknown particle?
Section 32.3 Nuclear Fission, Section 32.4 Nuclear Reactors

| 17 | absorbs a thermal neutron and fissions into rubidium and cesium . What nucleons are produced by the fission, and how many are there?

| 18 | How many neutrons are produced when fissions in the following way: ?

| 19 | ssm When a (235.043 924 u) nucleus fissions, about 200 MeV of energy is released. What is the ratio of this energy to the rest energy of the uranium nucleus?

| 20 | Interactive LearningWare 32.1 at reviews the concepts that lie at the heart of this problem. What energy (in MeV) is released by the following fission reaction?

| 21 | Neutrons released by a fission reaction must be slowed by collisions with the moderator nuclei before the neutrons can cause further fissions. Suppose a 1.5-MeV neutron leaves each collision with 65% of its incident energy. How many collisions are required to reduce the neutron’s energy to at least 0.040 eV, which is the energy of a thermal neutron?

| 22 | Uranium fissions into two fragments plus three neutrons: . The mass of a neutron is 1.008 665 u and that of is 235.043 924 u. If 225.0 MeV of energy is released during the fission, what is the combined mass of the two fragments?

* | 23 | ssm When 1.0 kg of coal is burned, about 3.0 × 107 J of energy is released. If the energy released during each fission is 2.0 × 102 MeV, how many kilograms of coal must be burned to produce the same energy as 1.0 kg of ?

* | 24 | The energy consumed in one year in the United States is about 9.3 × 1019 J. With each fission, about 2.0 × 102 MeV of energy is released. How many kilograms of would be needed to generate this energy if all the nuclei fissioned?

* | 25 | The water that cools a reactor core enters the reactor at 216 °C and leaves at 287 °C. (The water is pressurized, so it does not turn to steam.) The core is generating 5.6 × 109 W of power. Assume that the specific heat capacity of water is 4420 J/(kg · C°) over the temperature range stated above, and find the mass of water that passes through the core each second.

** | 26 | A 20.0 kiloton atomic bomb releases as much energy as 20.0 kilotons of TNT (1.0 kiloton of TNT releases about 5.0 × 1012 J of energy). Recall that about 2.0 × 102 MeV of energy is released when each nucleus fissions. (a) How many nuclei are fissioned to produce the bomb’s energy? (b) How many grams of uranium are fissioned? (c) What is the equivalent mass (in grams) of the bomb’s energy?

** | 27 | ssm www A nuclear power plant is 25% efficient, meaning that only 25% of the power it generates goes into producing electricity. The remaining 75% is wasted as heat. The plant generates 8.0 × 108 watts of electric power. If each fission releases 2.0 × 102 MeV of energy, how many kilograms of are fissioned per year?
Section 32.5 Nuclear Fusion

| 28 | Two deuterium atoms () react to produce tritium () and hydrogen () according to the reaction

What is the energy (in MeV) released by this deuterium-deuterium reaction?

| 29 | Interactive solution 32.29 at illustrates one way to approach problems of this type. The fusion of two deuterium nuclei (, mass = 2.0141 u) can yield a helium nucleus (, mass = 3.0160 u) and a neutron (, mass = 1.0087 u). What is the energy (in MeV) released in this reaction?

| 30 | Tritium () is a rare isotope of hydrogen that can be produced by the fusion reaction

(a) Determine the atomic mass number A, the atomic number Z, and the names X and Y of the unknown particles. (b) Using the masses given in the reaction, determine how much energy (in MeV) is released by this reaction.

* | 31 | ssm One proposed fusion reaction combines lithium (6.015 u) with deuterium (2.014 u) to give helium (4.003 u): . How many kilograms of lithium would be needed to supply the energy needs of one household for a year, estimated to be 3.8 × 1010 J?

* | 32 | Deuterium () is an attractive fuel for fusion reactions because it is abundant in the waters of the oceans. In the oceans, about 0.015% of the hydrogen atoms in the water (H2O) are deuterium atoms. (a) How many deuterium atoms are there in one kilogram of water? (b) If each deuterium nucleus produces about 7.2 MeV in a fusion reaction, how many kilograms of ocean water would be needed to supply the energy needs of the United States for one year, estimated to be 9.3 × 1019 J?

** | 33 | The proton–proton cycle thought to occur in the sun consists of the following sequence of reactions:

1. |
2. |
3. |

In these reactions is a positron (mass = 0.000 549 u), v is a neutrino (), and is a gamma ray photon (mass = 0 u). Note that reaction (3) uses two nuclei, which are formed by two reactions of type (1) and two reactions of type (2). Verify that the proton-proton cycle generates about 25 MeV of energy. The atomic masses are (1.007 825 u), (2.014 102 u), (3.016 030 u), and (4.002 603 u). Be sure to account for the fact that there are two electrons in two hydrogen atoms, whereas there is one electron in a single deuterium () atom. The mass of one electron is 0.000 549 u.
Section 32.6 Elementary Particles

| 34 | The main decay mode for the negative pion is . Find the energy (in MeV) released in this decay. Consult Table 32-3 as needed.

| 35 | A collision between two protons produces three new particles: . The rest energies of the new particles are (139.6 MeV), (1116 MeV), and K0 (497.7 MeV). Note that one proton disappears during the reaction. How much of the protons’ incident energy (in MeV) is transformed into matter during this reaction?

| 36 | A particle (see Table 32-3) decays into a particle and a proton: . Ignore the kinetic energy of the particle, and determine how much energy (in MeV) is released during this process.

| 37 | The K− particle has a charge of −e and contains one quark and one antiquark. (a) Which quarks can the particle not contain? (b) Which antiquarks can the particle not contain?

| 38 | Review Conceptual Example 7 as background for this problem. An electron and its antiparticle annihilate each other, producing two -ray photons. The kinetic energies of the particles are negligible. For each photon, determine (a) its energy (in MeV), (b) its wavelength, and (c) the magnitude of its momentum.

* | 39 | ssm www Suppose a neutrino is created and has an energy of 35 MeV. (a) Assuming the neutrino, like the photon, has no mass and travels at the speed of light, find the momentum of the neutrino. (b) Determine the de Broglie wavelength of the neutrino.

* | 40 | Review Conceptual Example 5 as background for this problem. An energetic proton is fired at a stationary proton. For the reaction to produce new particles, the two protons must approach each other to within a distance of about 8.0 × 10−15 m. The moving proton must have a sufficient speed to overcome the repulsive Coulomb force. What must be the minimum initial kinetic energy (in MeV) of the proton?

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