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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
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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 wholebody,
single dose of 460 rem has a 50% chance of dying .
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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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