Semi-Empirical Mass Formula
electron =
0.511
MeV
neutron =
939.57
MeV
proton =
938.27
MeV
a1
a2
a3
a4
a5
amu =
931.45
MeV
0.0157
0.0178
0.00071
0.0236
0.036
M0
M1
M2
M3
M4
M5
Binding
Volume
Surface
Coulomb
Symmetry
Odd/Even
Volume
Surface
Coulomb
Symmetry
Odd-Even
Experimental
*Tab. Of Nuclides
Nucleons
Energy/Nucleon
Protons
Neutrons
Protons
Neutrons
Electrons
Energy
Tension
Energy
Energy
Effect
Curve
Curve
Curve
Energy
Energy
Curve
Experimental
A
(MeV)
Z
N
Mass (MeV)
Mass (MeV)
Mass (MeV)
Energy (MeV)
(MeV)
(MeV)
(MeV)
(MeV)
M1
M1-M2
M1-M2-M3
M1-M2-M3-M4
M1-M2-M3-M4-M5
MeV/A
KeV
1
-23.94
1
0
938
0
0.51
14.6
16.6
0.0
22.0
0.00000
14.62
-1.96
-1.96
-1.96
-23.94
0.00
0
2
1.46
1
1
938
940
0.51
29.2
26.3
0.0
0.0
19.93837
14.62
1.46
1.46
-8.51
-8.51
1.11
2,225
4
3.97
2
2
1,877
1,879
1.02
58.5
41.8
0.8
0.0
-11.85542
14.62
4.18
3.97
6.93
6.93
7.07
28,296
7
5.21
3
4
2,815
3,758
1.53
102.4
60.7
2.1
3.1
0.00000
14.62
5.96
5.66
5.66
5.21
5.61
39,245
9
5.96
4
5
3,753
4,698
2.04
131.6
71.7
3.8
2.4
0.00000
14.62
6.65
6.23
6.23
5.96
6.46
58,165
11
6.45
5
6
4,691
5,637
2.56
160.9
82.0
5.9
2.0
0.00000
14.62
7.17
6.63
6.63
6.45
6.93
76,205
12
6.66
6
6
5,630
5,637
3.07
175.5
86.9
8.7
0.0
-5.20087
14.62
7.38
6.66
7.09
7.09
7.68
92,162
14
6.92
7
7
6,568
6,577
3.58
204.7
96.3
11.5
0.0
0.00497
14.62
7.74
6.92
6.92
6.92
7.48
104,659
16
7.12
8
8
7,506
7,517
4.09
234.0
105.3
14.7
0.0
-4.19153
14.62
8.04
7.12
7.39
7.39
7.98
127,619
19
7.41
9
10
8,444
9,396
4.60
277.9
118.1
17.8
1.2
0.00000
14.62
8.41
7.47
7.47
7.41
7.78
147,801
20
7.42
10
10
9,383
9,396
5.11
292.5
122.2
21.9
0.0
-3.54560
14.62
8.52
7.42
7.60
7.60
8.03
160,645
23
7.64
11
12
10,321
11,275
5.62
336.3
134.1
25.6
1.0
0.00000
14.62
8.79
7.68
7.68
7.64
8.11
186,564
24
7.61
12
12
11,259
11,275
6.13
351.0
138.0
30.3
0.0
-3.09246
14.62
8.88
7.61
7.74
7.74
8.26
198,257
27
7.79
13
14
12,198
13,154
6.64
394.8
149.2
34.4
0.8
0.00000
14.62
9.10
7.82
7.82
7.79
8.33
224,952
28
7.75
14
14
13,136
13,154
7.15
409.5
152.9
39.6
0.0
-2.75482
14.62
9.16
7.75
7.85
7.85
8.45
236,537
31
7.90
15
16
14,074
15,033
7.67
453.3
163.6
44.2
0.7
0.00000
14.62
9.35
7.92
7.92
7.90
8.48
262,917
32
7.84
16
16
15,012
15,033
8.18
468.0
167.1
50.0
0.0
-2.49230
14.62
9.40
7.84
7.92
7.92
8.49
271,781
35
7.97
17
18
15,951
16,912
8.69
511.8
177.4
55.0
0.6
0.00000
14.62
9.55
7.98
7.98
7.97
8.52
298,210
40
8.08
18
22
16,889
20,671
9.20
585.0
193.9
59.2
8.8
-2.10823
14.62
9.78
8.30
8.35
8.13
8.60
343,810
39
8.01
19
20
17,827
18,791
9.71
570.3
190.7
66.7
0.6
0.00000
14.62
9.73
8.02
8.02
8.01
8.56
333,724
40
7.94
20
20
18,765
18,791
10.22
585.0
193.9
73.5
0.0
-2.10823
14.62
9.78
7.94
7.99
7.99
8.55
342,052
45
8.13
21
24
19,704
22,550
10.73
658.1
209.8
78.1
4.4
0.00000
14.62
9.96
8.23
8.23
8.13
8.62
387,849
48
8.16
22
26
20,642
24,429
11.24
701.9
219.0
84.1
7.3
-1.83879
14.62
10.06
8.31
8.35
8.20
8.72
418,699
51
8.17
23
28
21,580
26,308
11.75
745.8
228.0
90.2
10.8
0.00000
14.62
10.15
8.38
8.38
8.17
8.74
445,841
52
8.17
24
28
22,518
26,308
12.26
760.4
231.0
97.8
6.8
-1.73165
14.62
10.18
8.30
8.33
8.20
8.78
456,345
55
8.18
25
30
23,457
28,187
12.78
804.3
239.8
104.4
10.0
0.00000
14.62
10.26
8.37
8.37
8.18
8.76
482,070
56
8.17
26
30
24,395
28,187
13.29
818.9
242.7
112.4
6.3
-1.63803
14.62
10.29
8.28
8.31
8.20
8.79
492,254
59
8.18
27
32
25,333
30,066
13.80
862.8
251.3
119.3
9.3
0.00000
14.62
10.36
8.34
8.34
8.18
8.77
517,308
59
8.13
28
31
26,272
29,127
14.31
862.8
251.3
128.4
3.4
-1.57515
14.62
10.36
8.19
8.21
8.16
8.74
515,453
64
8.19
29
35
27,210
32,885
14.82
935.9
265.3
134.3
12.4
1.48193
14.62
10.48
8.38
8.36
8.16
8.74
559,297
65
8.17
30
35
28,148
32,885
15.33
950.5
268.1
143.1
8.5
0.00000
14.62
10.50
8.30
8.30
8.17
8.72
567,073
70
8.18
31
39
29,086
36,643
15.84
1,023.7
281.6
149.3
20.1
1.38560
14.62
10.60
8.47
8.45
8.16
8.71
609,644
73
8.17
32
41
30,025
38,522
16.35
1,067.5
289.6
157.0
24.4
0.00000
14.62
10.66
8.51
8.51
8.17
8.71
635,468
75
8.17
33
42
30,963
39,462
16.86
1,096.8
294.9
165.6
23.7
0.00000
14.62
10.69
8.48
8.48
8.17
8.70
652,564
79
8.14
34
45
31,901
42,281
17.37
1,155.3
305.3
173.0
33.7
0.00000
14.62
10.76
8.57
8.57
8.14
8.70
686,951
80
8.15
35
45
32,839
42,281
17.89
1,169.9
307.9
182.7
27.5
1.25356
14.62
10.78
8.49
8.48
8.13
8.68
694,212
84
8.12
36
48
33,778
45,099
18.40
1,228.4
318.1
190.3
37.7
-1.20852
14.62
10.84
8.57
8.59
8.14
8.72
732,257
85
8.13
37
48
34,716
45,099
18.91
1,243.0
320.6
200.4
31.3
0.00000
14.62
10.85
8.49
8.49
8.13
8.70
739,283
87
8.12
38
49
35,654
46,039
19.42
1,272.3
325.6
209.9
30.6
0.00000
14.62
10.88
8.47
8.47
8.12
8.71
757,354
89
8.11
39
50
36,593
46,979
19.93
1,301.5
330.6
219.6
29.9
0.00000
14.62
10.91
8.44
8.44
8.11
8.71
775,538
91
8.10
40
51
37,531
47,918
20.44
1,330.8
335.5
229.4
29.2
0.00000
14.62
10.94
8.42
8.42
8.10
8.69
791,087
93
8.08
41
52
38,469
48,858
20.95
1,360.0
340.4
239.4
28.6
0.00000
14.62
10.96
8.39
8.39
8.08
8.66
805,765
96
8.07
42
54
39,407
50,737
21.46
1,403.9
347.7
248.7
33.0
-1.09335
14.62
11.00
8.41
8.42
8.08
8.65
830,779
98
8.05
43
55
40,346
51,676
21.97
1,433.1
352.5
259.1
32.3
1.07657
14.62
11.03
8.38
8.37
8.04
8.61
843,776
101
8.04
44
57
41,284
53,555
22.48
1,477.0
359.6
268.7
36.8
0.00000
14.62
11.06
8.40
8.40
8.04
8.60
868,730
103
8.02
45
58
42,222
54,495
23.00
1,506.2
364.4
279.4
36.1
0.00000
14.62
11.09
8.37
8.37
8.02
8.58
884,163
106
8.01
46
60
43,160
56,374
23.51
1,550.1
371.4
289.3
40.6
-1.01504
14.62
11.12
8.39
8.40
8.02
8.58
909,477
108
7.99
47
61
44,099
57,314
24.02
1,579.4
376.1
300.3
39.9
0.00107
14.62
11.14
8.36
8.36
7.99
8.54
922,536
112
7.97
48
64
45,037
60,132
24.53
1,637.9
385.3
309.6
50.2
-0.97398
14.62
11.18
8.42
8.43
7.98
8.54
957,016
115
7.95
49
66
45,975
62,012
25.04
1,681.7
392.1
319.9
55.2
0.00000
14.62
11.21
8.43
8.43
7.95
8.52
979,404
119
7.92
50
69
46,914
64,830
25.55
1,740.2
401.2
329.5
66.7
0.00000
14.62
11.25
8.48
8.48
7.92
8.50
1,011,437
122
7.90
51
71
47,852
66,709
26.06
1,784.1
407.9
340.1
72.1
0.91347
14.62
11.28
8.49
8.49
7.89
8.47
1,033,130
128
7.84
52
76
48,790
71,407
26.57
1,871.8
421.2
348.1
98.9
-0.88116
14.62
11.33
8.61
8.62
7.85
8.45
1,081,441
127
7.87
53
74
49,728
69,528
27.08
1,857.2
419.0
362.7
76.3
0.00000
14.62
11.32
8.47
8.47
7.87
8.45
1,072,580
131
7.84
54
77
50,667
72,347
27.59
1,915.7
427.7
372.7
88.8
0.00000
14.62
11.36
8.51
8.51
7.84
8.42
1,103,512
133
7.82
55
78
51,605
73,286
28.11
1,945.0
432.1
384.9
87.4
0.00000
14.62
11.38
8.48
8.48
7.82
8.41
1,118,532
137
7.79
56
81
52,543
76,105
28.62
2,003.5
440.7
395.2
100.3
0.00000
14.62
11.41
8.52
8.52
7.79
8.39
1,149,686
140
7.77
57
83
53,481
77,984
29.13
2,047.3
447.1
406.6
106.1
0.00088
14.62
11.43
8.53
8.53
7.77
8.36
1,169,717
140
7.78
58
82
54,420
77,045
29.64
2,047.3
447.1
421.1
90.4
-0.82388
14.62
11.43
8.42
8.43
7.78
8.38
1,172,696
141
7.77
59
82
55,358
77,045
30.15
2,062.0
449.2
434.9
82.5
0.00000
14.62
11.44
8.35
8.35
7.77
8.35
1,177,923
144
7.75
60
84
56,296
78,924
30.66
2,105.8
455.6
446.7
87.9
-0.80666
14.62
11.46
8.36
8.36
7.75
8.33
1,199,087
145
7.74
61
84
57,234
78,924
31.17
2,120.4
457.7
460.8
80.2
0.00000
14.62
11.47
8.29
8.29
7.74
8.30
1,203,897
150
7.70
62
88
58,173
82,682
31.68
2,193.6
468.1
470.8
99.1
-0.78234
14.62
11.50
8.36
8.37
7.71
8.26
1,239,254
152
7.69
63
89
59,111
83,622
32.19
2,222.8
472.3
484.1
97.8
0.01273
14.62
11.52
8.33
8.33
7.69
8.23
1,250,451
157
7.65
64
93
60,049
87,380
32.70
2,295.9
482.6
494.4
117.8
0.00000
14.62
11.55
8.40
8.40
7.65
8.20
1,287,961
159
7.64
65
94
60,988
88,320
33.22
2,325.2
486.7
507.9
116.3
0.00000
14.62
11.56
8.37
8.37
7.64
8.19
1,302,030
162
7.61
66
96
61,926
90,199
33.73
2,369.0
492.8
520.5
122.1
-0.73846
14.62
11.58
8.37
8.37
7.62
8.17
1,324,109
165
7.59
67
98
62,864
92,078
34.24
2,412.9
498.9
533.3
128.0
0.00000
14.62
11.60
8.37
8.37
7.59
8.15
1,344,258
167
7.58
68
99
63,802
93,017
34.75
2,442.2
502.9
547.2
126.5
0.00000
14.62
11.61
8.34
8.34
7.58
8.13
1,358,010
169
7.56
69
100
64,741
93,957
35.26
2,471.4
506.9
561.3
125.0
0.00000
14.62
11.62
8.30
8.30
7.56
8.11
1,371,353
173
7.53
70
103
65,679
96,776
35.77
2,529.9
514.9
573.4
138.4
0.00000
14.62
11.65
8.33
8.33
7.53
8.09
1,399,134
175
7.52
71
104
66,617
97,715
36.28
2,559.2
518.8
587.7
136.8
0.00000
14.62
11.66
8.30
8.30
7.52
8.07
1,412,109
178
7.50
72
106
67,555
99,594
36.79
2,603.0
524.7
601.1
142.8
-0.68809
14.62
11.68
8.30
8.30
7.50
8.05
1,432,811
181
7.47
73
108
68,494
101,474
37.30
2,646.9
530.6
614.6
148.8
0.00000
14.62
11.69
8.30
8.30
7.47
8.02
1,452,239
184
7.45
74
110
69,432
103,353
37.81
2,690.8
536.5
628.2
154.8
-0.67119
14.62
11.71
8.29
8.30
7.46
8.01
1,472,935
186
7.44
75
111
70,370
104,292
38.33
2,720.0
540.3
643.1
153.2
0.66577
14.62
11.72
8.26
8.26
7.43
7.98
1,484,519
190
7.41
76
114
71,309
107,111
38.84
2,778.5
548.1
655.8
167.1
-0.65523
14.62
11.74
8.29
8.29
7.41
7.96
1,512,801
192
7.39
77
115
72,247
108,051
39.35
2,807.8
551.9
671.0
165.3
0.00070
14.62
11.75
8.25
8.25
7.39
7.94
1,524,289
195
7.37
78
117
73,185
109,930
39.86
2,851.6
557.6
685.1
171.5
0.00000
14.62
11.76
8.25
8.25
7.37
7.93
1,545,697
197
7.36
79
118
74,123
110,869
40.37
2,880.9
561.4
700.5
169.7
0.00000
14.62
11.77
8.22
8.22
7.36
7.92
1,559,402
200
7.33
80
120
75,062
112,748
40.88
2,924.8
567.1
714.8
175.9
-0.63051
14.62
11.79
8.21
8.22
7.34
7.91
1,581,197
204
7.31
81
123
76,000
115,567
41.39
2,983.2
574.7
728.1
190.1
0.62121
14.62
11.81
8.24
8.23
7.30
7.88
1,607,539
207
7.28
82
125
76,938
117,446
41.90
3,027.1
580.3
742.7
196.4
0.00000
14.62
11.82
8.23
8.23
7.28
7.87
1,629,078
209
7.27
83
126
77,876
118,386
42.41
3,056.4
584.0
758.6
194.5
0.00000
14.62
11.83
8.20
8.20
7.27
7.85
1,640,244
209
7.27
84
125
78,815
117,446
42.92
3,056.4
584.0
777.1
176.8
0.00000
14.62
11.83
8.11
8.11
7.27
7.84
1,637,568
210
7.25
85
125
79,753
117,446
43.44
3,071.0
585.9
794.5
167.5
0.60785
14.62
11.83
8.05
8.05
7.25
7.81
1,640,465
222
7.17
86
136
80,691
127,782
43.95
3,246.5
608.0
798.5
247.5
-0.58304
14.62
11.89
8.29
8.29
7.18
7.69
1,708,184
223
7.17
87
136
81,629
127,782
44.46
3,261.1
609.8
816.1
236.7
0.00000
14.62
11.89
8.23
8.23
7.17
7.68
1,713,461
226
7.15
88
138
82,568
129,661
44.97
3,305.0
615.3
831.4
243.2
-0.57528
14.62
11.90
8.22
8.23
7.15
7.66
1,731,610
227
7.14
89
138
83,506
129,661
45.48
3,319.6
617.1
849.2
232.5
0.00000
14.62
11.91
8.16
8.16
7.14
7.65
1,736,715
232
7.10
90
142
84,444
133,419
45.99
3,392.7
626.1
862.3
256.2
-0.56409
14.62
11.93
8.21
8.21
7.11
7.62
1,766,691
231
7.11
91
140
85,383
131,540
46.50
3,378.1
624.3
882.9
228.5
0.00000
14.62
11.92
8.10
8.10
7.11
7.62
1,759,860
238
7.06
92
146
86,321
137,177
47.01
3,480.5
636.9
893.6
269.3
-0.55339
14.62
11.95
8.19
8.20
7.06
7.57
1,801,695
