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Question 15.5: Calculate the Q-value of the decay of the 238 92 U into 234 ...

Calculate the Q-value of the decay of the 92238U^{238}_{ 92} U  into 90234Th^{234}_{ 90} T h.

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Using the masses of the 92238U,90234Th^{238}_{ 92}U,^{234}_{ 90} T h, and 24He^{4}_{ 2}H e nuclei given in Appendix B, we find that the mass loss in the α-decay is 0.004585 u. The Q-value of the α-decay is found by multiplying the mass loss by 931.5 MeV/u giving 4.27  MeV.

Appendix B
Atomic masses
Relative Atomic Mass and Isotopic Compositions. Only the most common and most stable of the heavy elements are given.(From the NIST web pages.)
Isotope Mass Percent Isotope Mass Percent
1 H 1 1.007825 99.99 10 Ne 20 19.992440 90.48
D 2 2.014102 0.01 21 20.993847 0.27
T 3 3.016049 22 21.991386 9.25
2 He 3 3.016029 0.00 11 Na 23 22.989770 100
4 4.002603 100.0
12 Mg 24 23.985042 78.99
3 Li 6 6.015122 7.59 25 24.985837 10.00
7 7.016004 92.41 26 25.982593 11.01
4 Be 9 9.012182 100 13 Al 27 26.981538 100
5 B 10 10.012937 19.9 14 Si 28 27.976927 92.23
11 11.009306 80.1 29 28.976495 4.68
30 29.973770 3.09
6 C 12 12.000000 98.93
13 13.003355 1.07 15 P 31 30.973762 100
14 14.003241
16 S 32 31.972071 94.93
7 N 14 14.003074 99.63 33 32.971459 0.76
15 15.000109 0.37 34 33.967867 4.29
36 35.967081 0.02
8 O 16 15.994915 99.75
17 16.999132 0.038 17 Cl 35 34.968853 75.78
18 17.999160 0.205 37 36.965903 24.22
9 F 19 18.998403 100 18 Ar 36 35.967546 0.34
38 37.962732 0.06
49 39.962383 99.60
19 K 39 38.963707 93.26 26 Fe 54 53.939615 5.85
40 39.963999 0.01 56 55.934942 91.75
41 40.961826 6.73 57 56.935399 2.12
58 57.933281 0.28
20 Ca 40 39.962591 96.94
42 41.958618 0.65 27 Co 59 58.933200 100
43 42.958766 0.14
44 43.955481 2.09 28 Ni 58 57.935348 68.08
46 45.953693 0.00 60 59.930791 26.22
48 47.952534 0.19 61 60.931060 1.14
62 61.928349 3.63
21 Sc 45 45.952630 100 64 63.927970 0.93
22 Ti 46 45.952630 8.25 29 Cu 63 62.929601 69.17
47 46.951764 7.44 65 64.927794 30.83
48 47.947947 73.72
49 48.947871 5.41 30 Zn 64 63.929147 48.63
50 49.944792 5.18 66 65.926037 27.90
67 66.927131 4.10
23 V 50 49.947163 0.25 68 67.924848 18.75
51 50.943964 99.75 70 69.925325 0.62
24 Cr 50 49.946050 4.35 31 Ga 69 68.925581 60.11
52 51.940512 83.79 71 70.924705 39.89
53 52.940654 9.50
54 53.938885 2.37 32 Ge 70 69.924250 20.84
72 71.922076 27.54
25 Mn 55 54.938050 100 73 72.923459 7.73
74 73.921178 36.28
76 75.921403 7.61
33 As 75 4.921596 100 40 Zr 90 89.904704 51.45
91 90.905645 11.22
34 Se 74 73.922477 0.89 92 91.905040 17.15
76 75.919214 9.37 94 93.906316 17.38
77 76.919915 7.63 96 95.908276 2.80
78 77.917310 23.77
80 79.916522 49.61 41 Nb 93 92.906378 100
82 81.916700 8.73
42 Mo 92 91.906810 14.84
35 Br 79 78.918338 50.69 94 93.905088 9.25
81 80.916291 49.31 95 94.905842 15.92
96 95.904679 16.68
36 Kr 78 77.920386 0.35 97 96.906021 9.55
80 79.916378 2.28 98 97.905408 24.13
82 81.913485 11.58 100 99.907477 9.63
83 82.914136 11.49
84 83.911507 57.00 43 Tc 97 96.906365
86 85.910610 17.30 98 97.907216
99 98.906255
37 Rb 85 84.911 789 72.17
87 86.909184 27.83 44 Ru 96 95.907598 5.54
98 97.905287 1.87
38 Sr 84 83.913425 0.56 99 98.905939 12.76
86 85.909262 9.86 100 99.904220 12.60
87 86.908879 7.00 101 100.905582 17.06
88 87.905614 82.58 102 101.904350 31.55
104 103.905430 18.62
39 Y 89 88.905848 100
45 Rh 103 102.905504 100
46 Pd 102 101.905608 1.02 51 Sb 121 120.903818 57.21
104 103.904035 11.14 123 122.904216 42.79
105 104.905084 22.33
106 105.903483 27.33 52 Te 120 119.904020 0.09
108 107.903894 26.46 122 121.903047 2.25
110 109.905152 11.72 123 122.904273 0.89
124 123.902820 4.74
47 Ag 107 106.905093 51.91 125 124.904425 7.07
109 108.904756 48.16 126 125.903306 18.84
128 127.904461 31.74
48 Cd 106 105.906458 1.25 130 129.906223 34.08
108 107.904183 0.89
110 109.903006 12.49 53 I 127 126.904468 100
111 110.904182 12.80
112 111.902757 24.13 54 Xe 124 123.905896 0.09
113 112.904401 12.22 126 125.904269 0.09
114 113.903358 28.73 128 127.903530 1.92
116 115.904755 7.49 129 128.904780 26.44
130 129.903508 4.08
49 In 113 112.904061 4.29 131 130.905082 21.18
115 114.903878 95.71 132 131.904155 26.89
134 133.905395 10.44
50 Sn 112 111.904821 0.97 136 135.907220 8.87
114 113.902782 0.66
115 114.903346 0.34 55 Cs 133 132.905447 100
116 115.901744 14.54
117 116.902954 7.68 56 Ba 130 129.906310 100
118 117.901606 24.22 132 131.905056
119 118.903309 8.59 134 133.904503 100
120 119.902197 32.58 135 134.905683
122 121.903440 4.63 136 135.904570 100
124 123.905275 5.79 137 136.905821
138 137.905241
57 La 138 137.907107 0.09 64 Gd 152 151.919788 0.20
139 138.906348 99.91 154 153.920862 2.18
155 154.922619 14.80
58 Ce 136 135.907140 0.19 156 155.922120 20.47
138 137.905986 0.25 157 156.923957 15.65
140 139.905434 88.45 158 157.924101 24.84
142 141.909240 11.11 160 159.927051 21.86
59 Pr 141 140.907648 100 65 Tb 159 158.925343 100
60 Nd 142 141.907719 27.2 66 Dy 156 155.924278 0.06
143 142.909810 12.2 158 157.924405 0.10
144 143.910083 23.8 160 159.925194 2.34
145 144.912569 8.3 161 160.926930 18.91
146 145.913112 17.2 162 161.926795 25.51
148 147.916889 5.7 163 162.928728 24.9
150 149.920887 5.6 164 163.929171 28.18
61 Pm 145 115.904755 67 Ho 165 164.930319 100
147 114.903346
68 Er 162 161.928775 0.14
62 Sm 144 143.911995 3.07 164 163.929197 1.61
147 146.914893 14.99 166 165.930290 33.61
148 147.914818 11.24 167 166.932045 22.93
149 148.917180 13.82 168 167.932368 26.78
150 149.917271 7.38 170 169.935460 14.93
152 151.919728 26.75
154 153.922205 22.75 69 Tm 169 168.934211 100
63 Eu 151 150.919846 47.81 70 Yb 168 167.933894 0.13
153 152.921226 52.19 170 169.934759 3.04
171 170.936322 14.28
172 171.936378 21.83
70 Yb 173 172.938207 16.13 78 Pt 190 189.959930 0.01
174 173.938858 31.83 192 191.961035 0.78
176 175.942568 12.76 194 193.962664 32.97
195 194.964774 33.83
71 Lu 175 174.940768 97.41 196 195.964935 25.24
176 175.942682 2.59 198 197.967876 7.16
72 Hf 174 173.940040 0.16 79 Au 197 196.966552 100
176 175.941402 5.26
177 176.943220 18.60 80 Hg 196 195.965815 0.15
178 177.943698 27.28 198 197.966752 9.97
179 178.945815 13.62 199 198.968262 16.87
180 179.946549 35.08 200 199.968309 23.10
201 200.970285 13.18
73 Ta 180 179.947466 0.01 202 201.970626 29.86
181 180.947996 99.99 204 203.973476 6.87
74 W 180 179.946706 0.12 81 Ti 203 202.972329 29.52
182 181.948206 26.50 205 204.974412 70.48
183 182.950225 14.31
184 183.950933 30.64 82 Pb 204 203.973029 0.4
186 185.954362 28.43 206 205.974449 24.1
207 206.975881 22.1
75 Re 185 184.952956 37.40 208 207.976636 52.4
187 186.955751 62.60
83 Bi 209 208.980383 100
76 Os 184 183.952491 0.02
186 185.953838 1.59
187 186.955748 1.96 90 Th 232 232.038050 100
188 187.955836 13.24
189 188.958145 16.15 91 Pa 231 231.035879 100
190 189.958445 26.26
192 191.961479 40.78 92 U 235 235.043923 0.72
238 238.050782 99.27
77 Ir 191 190.960591 37.3
193 192.962924 62.7 Pu 240 240.053807
242 242.058737

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