 College Physics for AP® Courses

# Chapter 32

1.

5.701 MeV

3.

$42 99 Mo 57 → 43 99 Tc 56 + β − + v ¯ e 42 99 Mo 57 → 43 99 Tc 56 + β − + v ¯ e$

5.

$1 . 43 × 10 − 9 g 1 . 43 × 10 − 9 g size 12{1 "." "43" times "10" rSup { size 8{ - 9} } g} {}$

7.

(a) 6.958 MeV

(b) $5.7×10−10g5.7×10−10g size 12{5 "." 7 times "10" rSup { size 8{ - "10"} } g} {}$

8.

(a) 100 mSv

(b) 80 mSv

(c) ~30 mSv

10.

~2 Gy

12.

1.69 mm

14.

1.24 MeV

16.

$7.44 × 10 8 7.44 × 10 8 size 12{7 "." "44" times "10" rSup { size 8{8} } } {}$

18.

$4.92×10–4Sv4.92×10–4Sv$

20.

4.43 g

22.

0.010 g

24.

95%

26.

(a) $A=1+1=2A=1+1=2 size 12{A"=1+1=2"} {}$, $Z=1+1=1+1Z=1+1=1+1 size 12{Z"=1+1=1+1"} {}$, $efn=0=−1+1efn=0=−1+1 size 12{"efn"=0= - 1+1} {}$

(b) $A=1+2=3A=1+2=3 size 12{A"=1+2=3"} {}$, $Z=1+1=2Z=1+1=2 size 12{Z"=1+1=2"} {}$, $efn=0=0efn=0=0 size 12{"efn=0=0"} {}$

(c) $A=3+3=4+1+1A=3+3=4+1+1 size 12{A"=3+3=4+1+1"} {}$, $Z=2+2=2+1+1Z=2+2=2+1+1 size 12{Z"=2+2=2+1+1"} {}$, $efn=0=0efn=0=0 size 12{"efn=0=0"} {}$

28.

$E = m i − m f c 2 = 4m 1 H − m 4 He c 2 = 4 ( 1.007825 ) − 4 . 002603 ( 931.5 MeV ) = 26.73 MeV E = m i − m f c 2 = 4m 1 H − m 4 He c 2 = 4 ( 1.007825 ) − 4 . 002603 ( 931.5 MeV ) = 26.73 MeV$

30.

$3.12×105kg3.12×105kg size 12{2 times "10" rSup { size 8{5} } "kg"} {}$ (about 200 tons)

32.

$E = m i − m f c 2 E 1 = 1.008665 + 3.016030 − 4.002603 ( 931.5 MeV ) = 20.58 MeV E 2 = 1 . 008665 + 1 . 007825 − 2 . 014102 ( 931.5 MeV ) = 2.224 MeV E = m i − m f c 2 E 1 = 1.008665 + 3.016030 − 4.002603 ( 931.5 MeV ) = 20.58 MeV E 2 = 1 . 008665 + 1 . 007825 − 2 . 014102 ( 931.5 MeV ) = 2.224 MeV$

$4 He is more tightly bound, since this reaction gives off more energy per nucleon. 4 He is more tightly bound, since this reaction gives off more energy per nucleon. size 12{"" lSup { size 8{4} } "He"} {}$

34.

$1 . 19 × 10 4 kg 1 . 19 × 10 4 kg size 12{1 "." "19" times "10" rSup { size 8{4} } "kg"} {}$

36.

$2 e − + 4 1 H → 4 He + 7γ + 2v e 2 e − + 4 1 H → 4 He + 7γ + 2v e$

38.

(a) $A=12+1=13A=12+1=13 size 12{A"=12+1=13"} {}$, $Z=6+1=7Z=6+1=7 size 12{Z"=6+1=7"} {}$, $efn=0=0efn=0=0 size 12{"efn"=0=0} {}$

(b) $A=13=13A=13=13 size 12{A"=13=13"} {}$, $Z=7=6+1Z=7=6+1 size 12{Z"=7=6+1"} {}$, $efn=0=−1+1efn=0=−1+1 size 12{"efn"=0= - 1+1} {}$

(c) $A=13+1=14A=13+1=14 size 12{A"=13"+"1=14"} {}$, $Z=6+1=7Z=6+1=7 size 12{Z"=6+1=7"} {}$, $efn=0=0efn=0=0 size 12{"efn"=0=0} {}$

(d) $A=14+1=15A=14+1=15 size 12{A"=14"+"1=15"} {}$, $Z=7+1=8Z=7+1=8 size 12{Z"=7+1=8"} {}$, $efn=0=0efn=0=0 size 12{"efn"=0=0} {}$

(e) $A=15=15A=15=15 size 12{A"=1"5"=15"} {}$, $Z=8=7+1Z=8=7+1 size 12{Z"=8=7+1"} {}$, $efn=0=−1+1efn=0=−1+1 size 12{"efn"=0= - 1+1} {}$

(f) $A=15+1=12+4A=15+1=12+4 size 12{A"=15"+"1=12"+4} {}$, $Z=7+1=6+2Z=7+1=6+2 size 12{Z"=7+1=6"+2} {}$, $efn=0=0efn=0=0 size 12{"efn"=0=0} {}$

40.

$E γ = 20.6 MeV E γ = 20.6 MeV$

$E 4 He = 5.68 × 10-2 MeV E 4 He = 5.68 × 10-2 MeV$

42.

(a) $3×109y3×109y size 12{3 times "10" rSup { size 8{9} } } {}$

(b) This is approximately half the lifetime of the Earth.

43.

(a) 177.1 MeV

(b) Because the gain of an external neutron yields about 6 MeV, which is the average $BE/ABE/A$ for heavy nuclei.

(c) $A=1+238=96+140+1+1+1,Z=92=38+53,efn=0=0A=1+238=96+140+1+1+1,Z=92=38+53,efn=0=0 size 12{A=1+"238"="96"+"140"+1+1+1,Z="92"="38"+"53","efn"=0=0} {}$

45.

(a) 180.6 MeV

(b) $A=1+239=96+140+1+1+1+1,Z=94=38+56,efn=0=0A=1+239=96+140+1+1+1+1,Z=94=38+56,efn=0=0 size 12{A=1+"239"="96"+"140"+1+1+1+1,Z="94"="38"+"56","efn"=0=0} {}$

47.

$238U+n→239U+γ238U+n→239U+γ$ 4.81 MeV

$239U→239Np+β−+ve239U→239Np+β−+ve$ 0.753 MeV

$239Np→239Pu+β−+ve239Np→239Pu+β−+ve size 12{"" lSup { size 8{"239"} } "Np" rightarrow "" lSup { size 8{"239"} } "Pu"+β rSup { size 8{ - {}} } +v rSub { size 8{e} } } {}$ 0.211 MeV

49.

(a) $2.57×103MW2.57×103MW size 12{2 "." "57" times "10" rSup { size 8{3} } "MW"} {}$

(b) $8.03×1019fission/s8.03×1019fission/s size 12{8 "." "04" times "10" rSup { size 8{"19"} } "fission/s"} {}$

(c) 991 kg

51.

0.56 g

53.

4.781 MeV

55.

(a) Blast yields $2.1×1012J2.1×1012J size 12{2 "." "10" times "10" rSup { size 8{"12"} } J} {}$ to $8.4×1011J8.4×1011J size 12{8 "." 4 times "10" rSup { size 8{"11"} } J} {}$, or 2.5 to 1, conventional to radiation enhanced.

(b) Prompt radiation yields $6.3×1011J6.3×1011J size 12{6 "." 3 times "10" rSup { size 8{"11"} } J} {}$ to $2.1×1011J2.1×1011J size 12{2 "." "10" times "10" rSup { size 8{"11"} } J} {}$, or 3 to 1, radiation enhanced to conventional.

57.

(a) $1 . 1 × 10 25 fissions 1 . 1 × 10 25 fissions$ , 4.4 kg

(b) $3.2 × 10 26 fusions 3.2 × 10 26 fusions size 12{3 "." 2 times "10" rSup { size 8{"26"} } "fusions"} {}$ , 2.7 kg

(c) The nuclear fuel totals only 6 kg, so it is quite reasonable that some missiles carry 10 overheads. The mass of the fuel would only be 60 kg and therefore the mass of the 10 warheads, weighing about 10 times the nuclear fuel, would be only 1500 lbs. If the fuel for the missiles weighs 5 times the total weight of the warheads, the missile would weigh about 9000 lbs or 4.5 tons. This is not an unreasonable weight for a missile.

59.

$7 × 10 4 g 7 × 10 4 g size 12{7 times "10" rSup { size 8{4} } g} {}$

61.

(a) $4.86×109W4.86×109W size 12{4 "." "86" times "10" rSup { size 8{9} } `W} {}$

(b) 11.0 y

1.

(b)

3.

(c)

5.

(d)

7.

(d)

9.

(b)

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