Solucionario Capitulo 39 - Paul E. Tippens
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Transcript of Solucionario Capitulo 39 - Paul E. Tippens
Chapter 39. Nuclear Physics and the Nucleus Physics, 6th Edition
Chapter 39. Nuclear Physics and the Nucleus
The Elements
39-1. How many neutrons are in the nucleus of 82208 Pb ? How many protons? What is the ratio
N/Z? (N is the number of neutrons and Z is the number of protons.)
A = N + Z; N = A – Z = 126 neutrons; Z = 82 protons; 1.54A
Z
39-2. The nucleus of a certain isotope contains 143 neutrons and 92 protons. Write the symbol
for this nucleus.
A = N + Z = 143 + 92 = 235; Z = 92: 23592 U
39-3. From a stability curve it is determined that the ratio of neutrons to protons for a cesium
nucleus is 1.49. What is the mass number for this isotope of cesium?
Z = 55; 1.49; 1.49(55) 81.95; ;N N A N Z
Z
A = 137
39-4. Most nuclei are nearly spherical in shape and have a radius that may be approximated by
1153
0 0 1.2 x 10 mr r A r
What is the approximate radius of the nucleus of a gold atom 19779 Au ?
15 -153(1.2 10 m) 197 6.98 x 10 mr x ; r = 6.98 x 10-15 m
538
Chapter 39. Nuclear Physics and the Nucleus Physics, 6th Edition
39-5. Study Table 39-4 for information on the several nuclides. Determine the ratio of N/Z for
the following nuclides: Beryllium-9, Copper-64, and Radium 224.
Beryllium: A = 9; Z = 4; N = 9 – 4 = 5; 1.25N
Z
39-5. (Cont.) Copper: A = 64; Z = 29; N = 64 – 29 = 35; 1.21N
Z
Radium: A = 224; Z = 88; N = 224 – 88 = 136; 1.55N
Z
The Atomic Mass Unit
39-6. Find the mass in grams of a gold particle containing two million atomic mass units?
-276 1.66 x 10 kg2 x 10 u ;
1.00 um
m = 3.32 x 10-21 kg
39-7. Find the mass of a 2-kg copper cylinder in atomic mass units? In Mev? In joules?
-27
1 u2 kg ;1.6606 x 10 kg
m
m = 1.20 x 1027 u
27 931 MeVm = 1.204 x 10 u ;1 u
m = 1.12 x 1030 MeV
539
Chapter 39. Nuclear Physics and the Nucleus Physics, 6th Edition
-1330 1.6 x 10 Jm = 1.12 x 10 MeV ;
1 MeV m = 1.79 x 1017 J
39-8. A certain nuclear reaction releases an energy of 5.5 MeV. How much mass (in atomic
mass units) is required to produce this energy?
1 u5.5 MeV ;931 MeV
m
m = 0.00591 u
39-9. The periodic table gives the average mass of a silver atom as 107.842 u. What is the
average mass of the silver nucleus? (Recall that me = 0.00055 u )
For silver, Z = 47. Thus, the nuclear mass is reduced by the mass of 47 electrons.
m = 107.842 u – 47(0.00055 u); m = 107.816 u
*39-10. Consider the mass spectrometer as illustrated by Fig. 39-3. A uniform magnetic field of
0.6 T is placed across both upper and lower sections of the spectrometer., and the electric
field in the velocity selector is 120 V/m. A singly charged neon atom (+1.6 x 10-19 C) of
mass 19.992 u passes through the velocity selector and into the spectrometer. What is the
velocity of the neon atom as it emerges from the velocity selector?
120,000 V/m ;0.6 T
EvB
v = 2 x 105 m/s
*39-11. What is the radius of the circular path followed by the
neon atom of Problem 19-10?
540
B = 0.6 T into paper
R
Chapter 39. Nuclear Physics and the Nucleus Physics, 6th Edition
-27261.66 x 10 kg19.992 u 3.32 10 kg
1 um x
2
; mv mvqvB RR qB
;
-27 5
-19
(3.32 x 10 kg)(2 x 10 m/s) ;(1.6 x 10 C)(0.600 T)
R R = 6.92 cm
Mass Defects and Binding Energy (Refer to Table 39-4 for Nuclidic Masses.)
*39-12. Calculate the mass defect and binding energy for the neon-20 atom 2010 Ne .
[( )] 10(1.007825 u) 10(1.008665 u) 19.99244 uD H nm Zm Nm M
mD = 20.016490 u –19.99244 u ; mD = 0.17246 u
2 931 MeV(0.17246 u) 160.6 MeV1 uDE m c
; E = 161 MeV
*39-13. Calculate the binding energy and the binding energy per nucleon for tritium 31 H . How
much energy in joules is required to tear the nucleus apart into its constituent nucleons?
[( )] 1(1.007825 u) 2(1.008665 u) 3.016049 uD H nm Zm Nm M
39-13. (Cont.) mD = 0.009106 u;
2 931 MeV(0.009106 u) 8.48 MeV1 uDE m c
541
Chapter 39. Nuclear Physics and the Nucleus Physics, 6th Edition
E = 8.48 MeV;
8.48 MeV3
BEA
;
2.83 MeV/nucleonBEA
Energy to tear apart: EB = 8.48 MeV(1.6 x 10-13 J/MeV) = 1.36 x 10-12 J
*39-14. Calculate the mass defect of 37 Li . What is the binding energy per nucleon?
[( )] 3(1.007825 u) 4(1.008665 u) 7.016930 uD H nm Zm Nm M
mD = 7.058135 u –7.016930 u ; mD = 0.041205 u
2 931 MeV(0.041205 u) 38.4 MeV1 uDE m c
; E = 38.4 MeV
38.4 MeV ;7
BEA
5.48 MeV/nucleonBEA
*39-15. Determine the binding energy per nucleon for carbon-12 ( 126 C ).
6(1.007825 u) 6(1.008665 u) 12.0000 u 0.09894 uDm
2 931 MeV(0.09894 u) ;1 uDE m c
92.1 MeV12
BEA
= 7.68 MeV/nucleon
*39-16. What is the mass defect and the binding energy for a gold atom 19779 Au ?
542
Chapter 39. Nuclear Physics and the Nucleus Physics, 6th Edition
79(1.007825 u) 118(1.008665 u) 196.966541 u 1.674104 uDm
2 931 MeV(1.674104 u) 1.56 GeV;1 uDE m c
1.56 GeV197
BEA
= 7.91 MeV/nucleon
*39-17. Determine the binding energy per nucleon for tin-120 ( 12050 Sn ).
50(1.007825 u) 70(1.008665 u) 119.902108 u 1.09569 uDm
(1.09569 u)(931 MeV/u ;120
BEA
BEA
8.50 MeV/nucleon
Radioactivity and Nuclear Decay
39-18. The activity of a certain sample is rated as 2.8 Ci. How many nuclei will have
disintegrated in a time of one minute?
10 -13.7 x 10 s2.8 Ci (60 s);1 Ci
Nuclei
nuclei = 6.22 x 1012 nuclei
543
Chapter 39. Nuclear Physics and the Nucleus Physics, 6th Edition
39-19. The cobalt nucleus 6027 Co emits gamma rays of approximately 1.2 MeV. How much mass
is lost by the nucleus when it emits a gamma ray of this energy?
1 u1.2 MeV ;931 MeV
E m = 0.00129 u
39-20. The half-life of the radioactive isotope indium-109 is 4.30 h. If the activity of a sample is
1 mCi at the start, how much activity remains after 4.30, 8.60, and 12.9 h?
½/ 1
0½
1 4.3 h 1; 1; (1 mCi) ;2 4.3 h 2
t T tR R RT
R = 0.5 mCi
½/ 2
0½
1 8.6 h 1; 2; (1 mCi) ;2 4.3 h 2
t T tR R RT
R = 0.25 mCi
½/ 3
0½
1 12.9 h 1; 3; (1 mCi) ;2 4.3 h 2
t T tR R RT
R = 0.125 mCi
39-21. The initial activity of a sample containing 7.7 x 1011 bismuth-212 nuclei is 4.0 mCi. The
half-life of this isotope is 60 min. How many bismuth-212 nuclei remain after 30 min?
What is the activity at the end of that time?
½/ ½11
0½
1 30 min 1; 0.5; (7.7 x 10 )2 60 min 2
t T tN N NT
= 5.44 x 1011 nucl.
544
Chapter 39. Nuclear Physics and the Nucleus Physics, 6th Edition
½/ ½
01 1; (4 mCi) ;2 2
t T
R R R R = 2.83 mCi
*39-22. Strontium-90 is produced in appreciable quantities in the atmosphere during a nuclear
explosion. If this isotope has a half-life of 28 years, how long will it take for the initial
activity to drop to one-fourth of its original activity?
00
1 1 1; ; 22 2 4
n nRR R nR
½
2; 2(28 yr); 28 yr
t tn tT
t = 56 yr
*39-23. Consider a pure, 4.0-g sample of radioactive Gallium-67. If the half-life is 78 h, how
much time is required for 2.8 g of this sample to decay?
When 2.8 g decay, that leaves 4 g – 2.8 g or 1.20 g remaining.
00
1 1.2 g 1; 0.300; 0.3002 4 g 2
n nmm mm
The solution is accomplished by taking the common log of both sides:
0.523log(0.5) log(0.300); 0.301 0.523; 1.740.301
n n n
545
Chapter 39. Nuclear Physics and the Nucleus Physics, 6th Edition
½
1.74;78 h
t tnT
t = 1.74 (78 h) t = 135 h
*39-24. If one-fifth of a pure radioactive sample remains after 10 h, what is the half-life?
1 1 ; 0.200 = (0.5) ; log(0.5) log(0.2); 0.301 0.6995 2
nn n n
½½ ½
10 h 10 h2.32; ;2.32
tn TT T
T½ = 4.31 h
Nuclear Reactions
*39-25. Determine the minimum energy released in the nuclear reaction
19 1 4 169 1 2 8F H He + O + energy
The atomic mass of 919 F is 18.998403 u,
4 12 1He 4.002603 u, H = 1.007824 u.
19 1 4 169 1 2 8 F + H - He - O ;E (Energy comes from mass defect)
E = 18.998403 u + 1.007825 u – 4.002603 – 15.994915 u = 0.0087 u
931 MeV(0.00871 u) ;1 u
E E = 8.11 MeV
546
Chapter 39. Nuclear Physics and the Nucleus Physics, 6th Edition
*39-26. Determine the approximate kinetic energy imparted to the alpha particle when Radium-
226 decays to form Radon-222. Neglect the energy imparted to the radon nucleus.
226 222 4 22688 86 2 88Ra Rn + He + Energy; Ra = 226.02536
931 MeV226.02536 u - 222.017531 u - 4.002603 u = 0.00523 u1 u
E = 4.87 MeV
*39-27. Find the energy involved in the production of two alpha particles in the reaction
7 1 4 43 1 2 2Li H He He + energy
931 MeV7.016003 u + 1.007825 u - 2(4.002603 u) = 0.018622 u1 u
E = 17.3 MeV
*39-28. Compute the kinetic energy released in the beta minus decay of thorium-233.
233 233 0 233 23390 91 +1 90 91Th Pa + + energy; Th = 233.041469 u; Pa = 233.040130
233.041469 u - 233.040130 u - 0.00055 u = 0.000789 uE
931 MeV0.000789 u ;1 u
E E = 0.735 MeV
*39-29. What must be the energy of an alpha particle as it bombards a Nitrogen-14 nucleus
producing 17 1 178 1 8O and H? ( O = 16.999130 u) .
547
Chapter 39. Nuclear Physics and the Nucleus Physics, 6th Edition
4 14 17 12 7 8 1He + N + Energy O + H
931 MeV16.999130 u + 1.007825 u - 14.003074 - 4.002603 u = 0.001278 u1 u
E
E = 1.19 MeV This is the Threshold Energy for the reaction
Challenge Problems
*39-30. What is the average mass in kilograms of the nucleus of a boron-11 atom?
-271.66 x 10 kg11.009305 u ;1.00 u
m
m = 1.83 x 10-26 kg
*39-31. What are the mass defect and the binding energy per nucleon for boron-11?
[( )] 5(1.007825 u) 6(1.008665 u) 11.009305 uD H nm Zm Nm M
mD = 11.09112 u –11.009305 u ; mD = 0.08181 u
2 931 MeV(0.08181 u) 76.2 MeV1 uDE m c
; E = 76.2 MeV
76.2 MeV ;11
BEA
6.92 MeV/nucleonBEA
*39-32. Find the binding energy per nucleon for Thallium-206.
548
Chapter 39. Nuclear Physics and the Nucleus Physics, 6th Edition
81(1.007825 u) 125(1.008665 u) 205.976104 u 1.740846 uDm
2 931 MeV(1.740846 u) ;1 uDE m c
1621 MeV206
BEA
= 7.87 MeV/nucleon
*39-33. Calculate the energy required to separate the nucleons in mercury-204.
80(1.007825 u) 124(1.008665 u) 203.973865 u 1.7266 uDm
2 931 MeV(1.7266 u) ;1 uDE m c
EB = 1610 MeV
*39-34. The half-life of a radioactive sample is 6.8 h. How much time passes before the activity
drops to one-fifth of its initial value?
0
1 1 ; 0.200 = (0.5) ; log(0.5) log(0.2); 0.301 0.6995 2
nnR n n
R
½½ ½
0.699 6.8 h 6.8 h2.32; 2.32; ;0.301 2.32
tn n TT T
T½ = 2.93 h
*39-35. How much energy is required to tear apart a deuterium atom? 21( H 2.014102 u)
549
Chapter 39. Nuclear Physics and the Nucleus Physics, 6th Edition
1(1.007825 u) 1(1.008665 u) 2.014102 u 0.002388 uDm
2 931 MeV(0.002388 u) ;1 uDE m c
EB = 2.22 MeV
*39-36. Plutonium-232 decays by alpha emission with a half-life of 30 min. How much of this
substance remains after 4 h if the original sample had a mass of 4.0 g? Write the equation
for the decay?
½/ 8
0½
1 4 h 1; 8.00; (4 g) ;2 0.5 h 2
t T tm m mT
m = 15.6 mg
232 228 494 92 2Pu U + He + energy
*39-37. If 32 x 109 atoms of a radioactive isotope are reduced to only 2 x 109 atoms in a time of
48 h, what is the half-life of this material?
9
90
2 x 10 1 ; 0.0625 = (0.5) ; log(0.5) log(0.0625); 0.301 1.20432 x 10 2
nnN n n
N
550
Chapter 39. Nuclear Physics and the Nucleus Physics, 6th Edition
½½ ½
1.204 48 h 48 h4.00; 4.00; ;0.301 4.00
tn n TT T
T½ = 12.0 h
*39-38. A certain radioactive isotope retains only 10 percent of its original activity after a time of
4 h. What is the half-life?
0
1 1 ; 0.100 = (0.5) ; log(0.5) log(0.100); 0.301 1.0010 2
nnN n n
N
½½ ½
1.00 4 h 4 h3.32; 3.32; ;0.301 3.32
tn n TT T
T½ = 72.3 min
*39-39. When a 36 Li nucleus is struck by a proton, an alpha particle and a produce nucleus are
released. Write the equation for this reaction. What is the net energy transfer in this case?
6 1 4 33 1 2 2Li H He He + energy
931 MeV6.015126 u + 1.007825 u - 4.002603 u - 3.016030 = 0.00432 u1 u
E = 4.02 MeV
*39-40. Uranium-238 undergoes alpha decay. Write the equation for the reaction and calculate
the disintegration energy.
238 224 492 90 2U Th + He + energy
551
Chapter 39. Nuclear Physics and the Nucleus Physics, 6th Edition
238.05079 u - 234.04363 u - 4.002603 u = 0.00456 uE
931 MeV0.00456 u ;1 u
E E = 4.24 MeV
*39-41. A 9-g sample of radioactive material has an initial activity of 5.0 Ci. Forty minutes later,
the activity is only 3.0 Ci. What is the half-life? How much of the pure sample remains?
0
3 Ci 1 ; 0.600 = (0.5) ; log(0.5) log(0.6); 0.301 0.2225 Ci 2
nnR n n
R
½½ ½
0.222 40 min 40 min0.737; 0.737; ;0.301 0.737
tn n TT T
T½ = 54.3 min
0.737
01 1(9 g)2 2
n
m m m = 5.40 g
Critical Thinking Problems
*39-42. Nuclear fusion is a process that can produce enormous energy without the harmful
byproducts of nuclear fission. Calculate the energy released in the following nuclear
fusion reaction:
3 3 4 1 12 2 2 1 1H He He H+ H energy
552
Chapter 39. Nuclear Physics and the Nucleus Physics, 6th Edition
931 MeV2(3.016030 u) - 4.002603 u - 2(1.007825 u) = 0.013807 u1 u
E
E = 12.9 MeV
*39-43. Carbon-14 decays very slowly with a half-life of 5740 years. Carbon dating can be
accomplished by seeing what fraction of carbon-14 remains, assuming the decay process
began with the death of a living organism. What would be the age of a chunk of charcoal
if it was determined that the radioactive C-14 remaining was only 40 percent of what
would be expected in a living organism?
0
10.40 ; 0.400 = (0.5) ; log(0.5) log(0.4); 0.301 0.3992
nnR n n
R
½
0.399 0.737; 1.32; t 1.32(5740 yr);0.301 5740 yr
t tn nT
t = 7590 yr
*39-44. The velocity selector in a mass spectrometer has a magnetic field of 0.2 T perpendicular
to an electric field of 50 kV/m. The same magnetic field is across the lower region. What
is the velocity of singly charged Lithium-7 atoms as they leave the selector? If the radius
of the path in the spectrometer is 9.10 cm, find the atomic mass of the lithium atom?
50,000 V/m ;0.2 T
EvB
v = 2.5 x 105 m/s
553B = 0.2 T into paper
R
Chapter 39. Nuclear Physics and the Nucleus Physics, 6th Edition
2
; mv qBRqvB mR v
;
-19
5
(1.6 x 10 C)(0.2 T)(0.091 m) ;(2.5 x 10 m/s)
m
-26-27
1 um = 1.165 x 10 kg ;1.66 x 10 kg
m = 7.014 u
*39-45. A nuclear reactor operates at a power level of 2.0 MW. Assuming that approximately
200 MeV of energy is released for a single fission of U-235, how many fission processes
are occurring each second in the reactor?
6 1919
-19
2 x 10 J/s 1.25 x 10 MeV/s1.25 x 10 MeV/s; 1.6 x 10 J/MeV 200 MeV/fission
P 6.25 x 10216 fissions/s
*39-46. Consider an experiment which bombards 714 N with an alpha particle. One of the two
product nuclides is 11H . The reaction is
2 He N X H4714
11 Z
A
What is the product nuclide indicated by the symbol X? How much kinetic energy must
the alpha particle have in order to produce the reaction?
Conservation of nucleons means: 4 14 17 12 7 8 1He N + O Henery
16.99913 u + 1.007825 u - 4.002603 u - 14.003074 u = 0.001282 uE
554
Chapter 39. Nuclear Physics and the Nucleus Physics, 6th Edition
931 MeV0.001282 u ;1 u
E E = 1.19 MeV
*39-47. When passing a stream of ionized lithium atoms through a mass spectrometer, the radius
of the path followed by 37 Li (7.0169 u) is 14.00 cm. A lighter line is formed by the 3
6 Li
(6.0151 u). What is the radius of the path followed by the 36 Li isotopes?
2
; ;mv mvqvB RR qB
(See Problems 39-10 and 39-11)
1 1 2 12
2 2 1
(6.0151 u)(14 cm); ;7.0169 u
m R m RRm R m
R2 = 6.92 cm
555