Physics Solution Manual for 1100 and 2101

Therefore the initial total momentum before the

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Unformatted text preview: oton carries a charge of −e, which is opposite the charge of +e that a proton carries. Only 2 2 possibility D shows a charge of −e + 1 e − 3 e − 3 e . 3 ( ) 11. (e) Hubble’s law indicates that a galaxy located at a distance d from the earth is moving away from the earth at a speed that is directly (not inversely) proportional to d. 1626 IONIZING RADIATION, NUCLEAR ENERGY, AND ELEMENTARY PARTICLES CHAPTER 32 IONIZING RADIATION, NUCLEAR ENERGY, AND ELEMENTARY PARTICLES PROBLEMS ______________________________________________________________________________ 1. SSM WWW REASONING The biologically equivalent dose (in rems) is the product of the absorbed dose (in rads) and the relative biological effectiveness (RBE), according to Equation 32.4. We can apply this equation to each type of radiation. Since the biologically equivalent doses of the neutrons and α particles are equal, we can solve for the unknown RBE. SOLUTION Applying Equation 32.4 to each type of particle and using the fact that the biological equivalent doses are equal, we find that ( Absorbed dose )α RBEα = ( Absorbed dose )neutrons RBE neutrons 14444 24444 3 1444444 2444444 3 Biologically equivalent dose of α particles Biologically equivalent dose of neutrons Solving for RBEα and noting that (Absorbed dose)neutrons = 6(Absorbed dose)α, we have RBEα = 6 ( Absorbed dose ) ( Absorbed dose )neutrons ( RBE neutrons ) = ( Absorbed dose ) α ( 2.0 ) = 12 ( Absorbed dose )α α ______________________________________________________________________________ 2. REASONING The absorbed dose (AD) in grays (Gy) is the energy absorbed divided by the Energy absorbed tumor mass: AD = (Equation 32.2). Because both tumors receive the same Mass absorbed dose, the absorbed dose found in (a) will allow us to determine the energy absorbed by the second tumor, again via Equation 32.2. SOLUTION a. Substituting the given values into Equation 32.2, we obtain AD = Energy absorbed 1.7 J = = 14 Gy Mass 0.12 kg b. For the second tumor, the absorbed dose is still AD = 14 Gy, but the mass is now 0.15 kg. Solving Equation 32.2 for the energy absorbed, we obtain Energy absorbed = ( AD ) Mass = (14 Gy ) ( 0.15 kg ) = 2.1 J Chapter 32 Problems 3. 1627 REASONING AND SOLUTION a. The biologically equivalent dose is equal to the product of the absorbed dose and the RBE (see Equation 32.4): Biologically equivalent dose = (Absorbed dose)(RBE) = ( 38 rad ) (12 ) = 460 rem b. According to the discussion at the end of Section 32.1, a person exposed to a whole-body, single dose of 460 rem has a 50% chance of dying . ______________________________________________________________________________ 4. REASONING a. The absorbed dose (AD) and the biologically equivalent dose (BED) are related by Equation 32.4: BED = AD × RBE (32.4) where AD is the absorbed dose measured in rads, and RBE is the relative biological effectiveness of the cosmic rays. The cosmic rays are protons, for which the RBE is 10. We note that the biologically equivalent dose is given in millirems, where 1 mrem = 10−3 rem. b. The absorbed dose is related to the energy absorbed and the mass of the person by Equation 32.2: AD = Energy absorbed Mass (32.2) If the energy is measured in joules, and the mass in kilograms, the absorbed dose is given in grays (Gy), where 1 Gy = 1 J/kg. To convert the absorbed dose found in (a) from rads to grays, we will use the equivalence 1 rad = 0.01 Gy = 0.01 J/kg. SOLUTION a. Solving Equation (32.4) for the absorbed dose (AD), we find that AD = BED 24 ×10−3 rem = = 2.4 × 10−3 rad RBE 10 b. Solving Equation (32.2) for the mass and using 1 rad = 0.01 Gy = 0.01 J/kg, we find that Mass = Energy absorbed = AD ( 1.9 ×10−3 J = 79 kg 0.01 J/kg −3 2.4 ×10 rad ) 1 rad 1628 5. IONIZING RADIATION, NUCLEAR ENERGY, AND ELEMENTARY PARTICLES SSM REASONING AND SOLUTION According to Equation 32.2, the absorbed dose (AD) is equal to the energy absorbed by the tumor divided by its mass: AD = Energy absorbed = Mass 1.60 × 10 –19 J 1 eV ( 25 s ) (1.6 × 1010 s –1 )( 4.0 × 106 eV ) 0.015 kg = 1.7 × 101 Gy = 1.7 × 103 rad The biologically equivalent dose (BED) is equal to the product of the absorbed dose (AD) and the RBE (see Equation 32.4): BED = AD × RBE = (1.7 × 103 rad)(14) = 2.4 × 10 4 rem (32.4) ______________________________________________________________________________ 6. REASONING According to Equation 32.4, the biologically equivalent dose is equal to the product of the absorbed dose and the RBE (relative biological effectiveness). If the absorbed doses are the same, then the radiation with the larger RBE produces the greater biological effect. If the two types of radiation have the same RBE, then the radiation that produces the greater absorbed dose produces the greater biological effect. SOLUTION Using Equation 32.4, the biologically equivalent dose can be determined for each type of radiation. The rankings are given in the last column of the table. Radiation Biologically Equivalent Dose = (Absorbed dose)(RBE) γ rays (20 × 10 Elect...
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