Read in the Radioactivity Data (from a Cloud directory)

data1= Import["/Users/darrelsmith/Library/Mobile Documents/com~apple~CloudDocs/Documents/ERAU/Web Stuff/Darrel Home Page folder/Darrel Home Page/Courses/CoursesS2017/PS315/NonLinearFit/radio.csv","csv"];

Read in the Radioactivity Data (from a website)

data1= Import["http://physicsx.pr.erau.edu/Courses/CoursesS2017/PS315/NonLinearFit/radio.csv","csv"];

List the Data

data1

Length[data1]

data1[[17,3]]

Make a new data structure by peeling off the "header" information removing the "zero" data in the tail.

data2=Table[{data1[[i,2]],data1[[i,3]]},{i,17,876}]

Plot the # of radioactive decays as a function of time.  Dwell time = 1.00 sec.

g1=ListPlot[data2]

sol=FindFit[data2,a (E^(- ((t Log[2])/t12)))+c,{a,c,t12},t]

How well does the fitting function align with the data?    t12 = half-life          Be careful !!  This is not the best fit
because no uncertainty information (i.e., error bars) were included in the FindFit results.

Plot[a (E^(- ((t Log[2])/t12)))+c/.sol,{t,0,860},AxesOrigin->{0,0},PlotRange->{Automatic},Epilog->Prepend[Point/@data2,PointSize[0.002]]]

chiSquare=(∑_(i=1)^860)(((((data2[[i,2]]-(a (E^(- ((data2[[i,1]] Log[2])/t12)))+c)/.sol)/(Sqrt[data2[[i,2]]]))))^2)

We just calculated the (χ^2) assuming the correct error bars, but the fitted parameters are not the
result of a “best fit” (i.e., FindFit) because no error bars were included in the FindFit calculation.
While the reduced chi-square looks good (919/857) appears good, it still does not represent the
best chi-square for this data analysis.

In this particular data set, there are 860 - 3 = 857 degrees of freedom.  
Let’s create a  (χ^2)  function as a function of half-life and plot it.

chiSq[thalf_]:=(∑_(i=1)^860)(((((data2[[i,2]]-(a (E^(- ((data2[[i,1]] Log[2])/thalf)))+c)/.sol)/(Sqrt[data2[[i,2]]]))))^2)

Be careful.  This is a hybrid (χ^2) plot using parameters from FindFit (no error bars) and a (χ^2) function
that does include error bars.  Do not expect this plot to match the above (χ^2) and thalf values.

Plot[chiSq[t12],{t12,149.,150.4}]

Let’s create the correct (χ^2) function and minimize that.  Note:  this (χ^2) function includes the correct values for the errors.

chiSquare3[a_,c_,t_]:=(∑_(i=1)^860)(((((data2[[i,2]]-(a (E^(- ((data2[[i,1]] Log[2])/t)))+c))/(Sqrt[data2[[i,2]]]))))^2)

Simultaneously fit all 3 parameters:  a,  c,  and  t = half-life
Notice that the “newly obtained” (χ^2)  is 907.83, the best minimum value of (χ^2)  that can be obtained.  Compare this
to the above value of (χ^2) .  By correctly including the errors, this gives the lowest possible value of (χ^2).

sol3=FindMinimum[chiSquare3[a,c,t],{{a,1531.},{c,55.},{t,180}}]

ccc=sol3[[2,2,2]] ;
aaa=sol3[[2,1,2]];
Plot[chiSquare3[aaa,ccc,tau],{tau,150.9,151.8},AxesOrigin->{151.295,907.83}]

Δt=FindRoot[chiSquare3[aaa,ccc,Δt12]==908.83,{Δt12,150.}];
sol3[[2,3,2]];
Print["Halflife = ",sol3[[2,3,2]], " ± ",Abs[Δt[[1,2]]-sol3[[2,3,2]]] ]

Calculate the relative uncertainty of this measurement.

relUnc = ((Abs[Δt[[1,2]]-sol3[[2,3,2]]])/(sol3[[2,3,2]])) 100 "%"

(χ^2) plot as a function of a and t

Plot3D[chiSquare3[a,52.3,t],{a,1520.,1540.},{t,150.3,152.1}]

g2=Plot[220*PDF[ChiSquareDistribution[857],x],{x,700,1000}]

Spectrum Name:,,
Description:,,
Student ID:,,
Detector Used:,,
Comments:,,
Acquisition Mode:,MCS,
MCS Dwell Time:,1.000 Seconds,
High Voltage:,600,
Conversion Gain:,1024,
Coarse Gain:,8,
Fine Gain:,2,
ULD:,106%,
LLD:,2%,

Channel Data:,,
Chan,Dwell(Sec.),Counts
0,1,1652
1,2,1592
2,3,1557
3,4,1539
4,5,1550
5,6,1590
6,7,1499
7,8,1479
8,9,1537
9,10,1542
10,11,1544
11,12,1435
12,13,1493
13,14,1474
14,15,1439
15,16,1441
16,17,1440
17,18,1512
18,19,1486
19,20,1419
20,21,1480
21,22,1478
22,23,1403
23,24,1425
24,25,1406
25,26,1394
26,27,1418
27,28,1418
28,29,1393
29,30,1426
30,31,1372
31,32,1388
32,33,1395
33,34,1393
34,35,1309
35,36,1384
36,37,1413
37,38,1394
38,39,1366
39,40,1331
40,41,1323
41,42,1245
42,43,1284
43,44,1329
44,45,1237
45,46,1271
46,47,1296
47,48,1209
48,49,1220
49,50,1293
50,51,1333
51,52,1269
52,53,1341
53,54,1328
54,55,1271
55,56,1215
56,57,1291
57,58,1322
58,59,1219
59,60,1268
60,61,1232
61,62,1191
62,63,1208
63,64,1148
64,65,1202
65,66,1248
66,67,1149
67,68,1145
68,69,1196
69,70,1150
70,71,1227
71,72,1092
72,73,1219
73,74,1112
74,75,1148
75,76,1146
76,77,1108
77,78,1129
78,79,1117
79,80,1124
80,81,1127
81,82,1093
82,83,1103
83,84,1096
84,85,1135
85,86,1100
86,87,1086
87,88,1047
88,89,1022
89,90,1056
90,91,1048
91,92,1026
92,93,1037
93,94,1055
94,95,1049
95,96,1020
96,97,1005
97,98,1009
98,99,1016
99,100,1052
100,101,976
101,102,992
102,103,949
103,104,950
104,105,957
105,106,982
106,107,1020
107,108,947
108,109,954
109,110,959
110,111,925
111,112,983
112,113,955
113,114,961
114,115,892
115,116,985
116,117,929
117,118,932
118,119,992
119,120,940
120,121,939
121,122,902
122,123,922
123,124,960
124,125,878
125,126,861
126,127,898
127,128,968
128,129,865
129,130,948
130,131,916
131,132,878
132,133,868
133,134,841
134,135,864
135,136,882
136,137,890
137,138,822
138,139,868
139,140,828
140,141,881
141,142,842
142,143,831
143,144,800
144,145,826
145,146,795
146,147,797
147,148,811
148,149,875
149,150,846
150,151,831
151,152,791
152,153,820
153,154,775
154,155,786
155,156,813
156,157,778
157,158,850
158,159,753
159,160,801
160,161,774
161,162,771
162,163,779
163,164,777
164,165,757
165,166,735
166,167,758
167,168,774
168,169,783
169,170,725
170,171,758
171,172,728
172,173,701
173,174,759
174,175,742
175,176,694
176,177,768
177,178,723
178,179,723
179,180,759
180,181,716
181,182,684
182,183,700
183,184,704
184,185,677
185,186,739
186,187,636
187,188,673
188,189,689
189,190,659
190,191,652
191,192,671
192,193,689
193,194,673
194,195,640
195,196,700
196,197,689
197,198,699
198,199,630
199,200,657
200,201,703
201,202,641
202,203,686
203,204,652
204,205,640
205,206,649
206,207,599
207,208,688
208,209,617
209,210,642
210,211,621
211,212,615
212,213,631
213,214,597
214,215,614
215,216,618
216,217,611
217,218,636
218,219,587
219,220,638
220,221,582
221,222,596
222,223,605
223,224,610
224,225,557
225,226,599
226,227,599
227,228,577
228,229,594
229,230,609
230,231,578
231,232,545
232,233,602
233,234,569
234,235,621
235,236,590
236,237,632
237,238,557
238,239,575
239,240,598
240,241,537
241,242,595
242,243,554
243,244,567
244,245,563
245,246,540
246,247,527
247,248,533
248,249,579
249,250,538
250,251,535
251,252,517
252,253,556
253,254,566
254,255,561
255,256,564
256,257,572
257,258,524
258,259,508
259,260,490
260,261,508
261,262,527
262,263,515
263,264,502
264,265,513
265,266,512
266,267,513
267,268,472
268,269,489
269,270,522
270,271,469
271,272,491
272,273,519
273,274,495
274,275,455
275,276,501
276,277,482
277,278,437
278,279,485
279,280,479
280,281,480
281,282,463
282,283,469
283,284,484
284,285,436
285,286,471
286,287,411
287,288,454
288,289,460
289,290,501
290,291,480
291,292,418
292,293,455
293,294,444
294,295,427
295,296,472
296,297,428
297,298,453
298,299,458
299,300,463
300,301,439
301,302,460
302,303,454
303,304,470
304,305,437
305,306,426
306,307,441
307,308,440
308,309,425
309,310,373
310,311,431
311,312,394
312,313,413
313,314,443
314,315,426
315,316,449
316,317,416
317,318,464
318,319,378
319,320,422
320,321,407
321,322,423
322,323,390
323,324,397
324,325,405
325,326,392
326,327,377
327,328,382
328,329,375
329,330,401
330,331,374
331,332,394
332,333,432
333,334,383
334,335,412
335,336,431
336,337,353
337,338,406
338,339,350
339,340,352
340,341,376
341,342,362
342,343,396
343,344,358
344,345,337
345,346,344
346,347,361
347,348,388
348,349,356
349,350,367
350,351,336
351,352,375
352,353,347
353,354,337
354,355,383
355,356,354
356,357,371
357,358,317
358,359,350
359,360,337
360,361,359
361,362,348
362,363,349
363,364,353
364,365,322
365,366,345
366,367,365
367,368,364
368,369,355
369,370,329
370,371,369
371,372,353
372,373,328
373,374,339
374,375,368
375,376,334
376,377,341
377,378,320
378,379,321
379,380,350
380,381,290
381,382,307
382,383,308
383,384,362
384,385,317
385,386,325
386,387,290
387,388,324
388,389,313
389,390,299
390,391,295
391,392,297
392,393,267
393,394,304
394,395,307
395,396,322
396,397,306
397,398,279
398,399,306
399,400,284
400,401,281
401,402,299
402,403,287
403,404,341
404,405,287
405,406,293
406,407,304
407,408,272
408,409,297
409,410,283
410,411,275
411,412,262
412,413,280
413,414,288
414,415,298
415,416,305
416,417,284
417,418,275
418,419,255
419,420,276
420,421,268
421,422,258
422,423,305
423,424,291
424,425,231
425,426,250
426,427,262
427,428,266
428,429,246
429,430,259
430,431,255
431,432,252
432,433,277
433,434,244
434,435,261
435,436,230
436,437,258
437,438,252
438,439,236
439,440,239
440,441,262
441,442,244
442,443,243
443,444,254
444,445,250
445,446,250
446,447,227
447,448,232
448,449,251
449,450,242
450,451,230
451,452,235
452,453,258
453,454,242
454,455,241
455,456,236
456,457,225
457,458,276
458,459,253
459,460,211
460,461,236
461,462,257
462,463,247
463,464,238
464,465,237
465,466,194
466,467,228
467,468,240
468,469,225
469,470,234
470,471,238
471,472,218
472,473,214
473,474,211
474,475,226
475,476,251
476,477,221
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480,481,242
481,482,235
482,483,219
483,484,218
484,485,236
485,486,227
486,487,225
487,488,210
488,489,230
489,490,238
490,491,255
491,492,204
492,493,246
493,494,221
494,495,225
495,496,227
496,497,216
497,498,206
498,499,215
499,500,215
500,501,210
501,502,206
502,503,208
503,504,211
504,505,202
505,506,215
506,507,211
507,508,212
508,509,210
509,510,191
510,511,191
511,512,222
512,513,202
513,514,195
514,515,181
515,516,187
516,517,194
517,518,176
518,519,209
519,520,197
520,521,208
521,522,177
522,523,189
523,524,184
524,525,182
525,526,212
526,527,193
527,528,181
528,529,165
529,530,204
530,531,193
531,532,164
532,533,158
533,534,180
534,535,166
535,536,204
536,537,201
537,538,182
538,539,162
539,540,192
540,541,186
541,542,184
542,543,169
543,544,197
544,545,190
545,546,184
546,547,158
547,548,219
548,549,178
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550,551,186
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552,553,191
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555,556,173
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558,559,163
559,560,172
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563,564,209
564,565,177
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568,569,180
569,570,156
570,571,137
571,572,174
572,573,163
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579,580,173
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586,587,172
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589,590,159
590,591,150
591,592,181
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593,594,140
594,595,142
595,596,168
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597,598,131
598,599,136
599,600,149
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601,602,143
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603,604,159
604,605,143
605,606,145
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610,611,160
611,612,122
612,613,147
613,614,129
614,615,121
615,616,146
616,617,147
617,618,133
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619,620,126
620,621,167
621,622,136
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623,624,152
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663,664,126
664,665,147
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695,696,122
696,697,136
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698,699,110
699,700,120
700,701,118
701,702,118
702,703,116
703,704,122
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707,708,99
708,709,109
709,710,125
710,711,113
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712,713,100
713,714,111
714,715,119
715,716,110
716,717,113
717,718,104
718,719,121
719,720,107
720,721,125
721,722,113
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723,724,106
724,725,110
725,726,139
726,727,111
727,728,110
728,729,126
729,730,100
730,731,113
731,732,109
732,733,113
733,734,129
734,735,92
735,736,100
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739,740,124
740,741,92
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745,746,104
746,747,103
747,748,104
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755,756,90
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761,762,99
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763,764,113
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765,766,98
766,767,93
767,768,80
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800,801,96
801,802,84
802,803,90
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804,805,85
805,806,90
806,807,107
807,808,78
808,809,72
809,810,101
810,811,84
811,812,79
812,813,93
813,814,84
814,815,102
815,816,78
816,817,92
817,818,77
818,819,86
819,820,97
820,821,87
821,822,104
822,823,90
823,824,75
824,825,90
825,826,95
826,827,82
827,828,74
828,829,80
829,830,90
830,831,90
831,832,84
832,833,80
833,834,95
834,835,79
835,836,90
836,837,81
837,838,99
838,839,102
839,840,71
840,841,90
841,842,91
842,843,85
843,844,85
844,845,87
845,846,86
846,847,76
847,848,68
848,849,91
849,850,81
850,851,77
851,852,86
852,853,81
853,854,63
854,855,72
855,856,80
856,857,84
857,858,87
858,859,84
859,860,79
860,861,14
861,862,0
862,863,0
863,864,0
864,865,0
865,866,0
866,867,0
867,868,0
868,869,0
869,870,0
870,871,0
871,872,0
872,873,0
873,874,0
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892,893,0
893,894,0
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896,897,0
897,898,0
898,899,0
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902,903,0
903,904,0
904,905,0
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906,907,0
907,908,0
908,909,0
909,910,0
910,911,0
911,912,0
912,913,0
913,914,0
914,915,0
915,916,0
916,917,0
917,918,0
918,919,0
919,920,0
920,921,0
921,922,0
922,923,0
923,924,0
924,925,0
925,926,0
926,927,0
927,928,0
928,929,0
929,930,0
930,931,0
931,932,0
932,933,0
933,934,0
934,935,0
935,936,0
936,937,0
937,938,0
938,939,0
939,940,0
940,941,0
941,942,0
942,943,0
943,944,0
944,945,0
945,946,0
946,947,0
947,948,0
948,949,0
949,950,0
950,951,0
951,952,0
952,953,0
953,954,0
954,955,0
955,956,0
956,957,0
957,958,0
958,959,0
959,960,0
960,961,0
961,962,0
962,963,0
963,964,0
964,965,0
965,966,0
966,967,0
967,968,0
968,969,0
969,970,0
970,971,0
971,972,0
972,973,0
973,974,0
974,975,0
975,976,0
976,977,0
977,978,0
978,979,0
979,980,0
980,981,0
981,982,0
982,983,0
983,984,0
984,985,0
985,986,0
986,987,0
987,988,0
988,989,0
989,990,0
990,991,0
991,992,0
992,993,0
993,994,0
994,995,0
995,996,0
996,997,0
997,998,0
998,999,0
999,1000,0
1000,1001,0
1001,1002,0
1002,1003,0
1003,1004,0
1004,1005,0
1005,1006,0
1006,1007,0
1007,1008,0
1008,1009,0
1009,1010,0
1010,1011,0
1011,1012,0
1012,1013,0
1013,1014,0
1014,1015,0
1015,1016,0
1016,1017,0
1017,1018,0
1018,1019,0
1019,1020,0
1020,1021,0
1021,1022,0
1022,1023,0
1023,1024,0

Spectrum Name:,,
Description:,,
Student ID:,,
Detector Used:,,
Comments:,,
Acquisition Mode:,MCS,
MCS Dwell Time:,1.000 Seconds,
High Voltage:,600,
Conversion Gain:,1024,
Coarse Gain:,8,
Fine Gain:,2,
ULD:,106%,
LLD:,2%,

Channel Data:,,
Chan,Dwell(Sec.),Counts
0,1,1652
1,2,1592
2,3,1557
3,4,1539
4,5,1550
5,6,1590
6,7,1499
7,8,1479
8,9,1537
9,10,1542
10,11,1544
11,12,1435
12,13,1493
13,14,1474
14,15,1439
15,16,1441
16,17,1440
17,18,1512
18,19,1486
19,20,1419
20,21,1480
21,22,1478
22,23,1403
23,24,1425
24,25,1406
25,26,1394
26,27,1418
27,28,1418
28,29,1393
29,30,1426
30,31,1372
31,32,1388
32,33,1395
33,34,1393
34,35,1309
35,36,1384
36,37,1413
37,38,1394
38,39,1366
39,40,1331
40,41,1323
41,42,1245
42,43,1284
43,44,1329
44,45,1237
45,46,1271
46,47,1296
47,48,1209
48,49,1220
49,50,1293
50,51,1333
51,52,1269
52,53,1341
53,54,1328
54,55,1271
55,56,1215
56,57,1291
57,58,1322
58,59,1219
59,60,1268
60,61,1232
61,62,1191
62,63,1208
63,64,1148
64,65,1202
65,66,1248
66,67,1149
67,68,1145
68,69,1196
69,70,1150
70,71,1227
71,72,1092
72,73,1219
73,74,1112
74,75,1148
75,76,1146
76,77,1108
77,78,1129
78,79,1117
79,80,1124
80,81,1127
81,82,1093
82,83,1103
83,84,1096
84,85,1135
85,86,1100
86,87,1086
87,88,1047
88,89,1022
89,90,1056
90,91,1048
91,92,1026
92,93,1037
93,94,1055
94,95,1049
95,96,1020
96,97,1005
97,98,1009
98,99,1016
99,100,1052
100,101,976
101,102,992
102,103,949
103,104,950
104,105,957
105,106,982
106,107,1020
107,108,947
108,109,954
109,110,959
110,111,925
111,112,983
112,113,955
113,114,961
114,115,892
115,116,985
116,117,929
117,118,932
118,119,992
119,120,940
120,121,939
121,122,902
122,123,922
123,124,960
124,125,878
125,126,861
126,127,898
127,128,968
128,129,865
129,130,948
130,131,916
131,132,878
132,133,868
133,134,841
134,135,864
135,136,882
136,137,890
137,138,822
138,139,868
139,140,828
140,141,881
141,142,842
142,143,831
143,144,800
144,145,826
145,146,795
146,147,797
147,148,811
148,149,875
149,150,846
150,151,831
151,152,791
152,153,820
153,154,775
154,155,786
155,156,813
156,157,778
157,158,850
158,159,753
159,160,801
160,161,774
161,162,771
162,163,779
163,164,777
164,165,757
165,166,735
166,167,758
167,168,774
168,169,783
169,170,725
170,171,758
171,172,728
172,173,701
173,174,759
174,175,742
175,176,694
176,177,768
177,178,723
178,179,723
179,180,759
180,181,716
181,182,684
182,183,700
183,184,704
184,185,677
185,186,739
186,187,636
187,188,673
188,189,689
189,190,659
190,191,652
191,192,671
192,193,689
193,194,673
194,195,640
195,196,700
196,197,689
197,198,699
198,199,630
199,200,657
200,201,703
201,202,641
202,203,686
203,204,652
204,205,640
205,206,649
206,207,599
207,208,688
208,209,617
209,210,642
210,211,621
211,212,615
212,213,631
213,214,597
214,215,614
215,216,618
216,217,611
217,218,636
218,219,587
219,220,638
220,221,582
221,222,596
222,223,605
223,224,610
224,225,557
225,226,599
226,227,599
227,228,577
228,229,594
229,230,609
230,231,578
231,232,545
232,233,602
233,234,569
234,235,621
235,236,590
236,237,632
237,238,557
238,239,575
239,240,598
240,241,537
241,242,595
242,243,554
243,244,567
244,245,563
245,246,540
246,247,527
247,248,533
248,249,579
249,250,538
250,251,535
251,252,517
252,253,556
253,254,566
254,255,561
255,256,564
256,257,572
257,258,524
258,259,508
259,260,490
260,261,508
261,262,527
262,263,515
263,264,502
264,265,513
265,266,512
266,267,513
267,268,472
268,269,489
269,270,522
270,271,469
271,272,491
272,273,519
273,274,495
274,275,455
275,276,501
276,277,482
277,278,437
278,279,485
279,280,479
280,281,480
281,282,463
282,283,469
283,284,484
284,285,436
285,286,471
286,287,411
287,288,454
288,289,460
289,290,501
290,291,480
291,292,418
292,293,455
293,294,444
294,295,427
295,296,472
296,297,428
297,298,453
298,299,458
299,300,463
300,301,439
301,302,460
302,303,454
303,304,470
304,305,437
305,306,426
306,307,441
307,308,440
308,309,425
309,310,373
310,311,431
311,312,394
312,313,413
313,314,443
314,315,426
315,316,449
316,317,416
317,318,464
318,319,378
319,320,422
320,321,407
321,322,423
322,323,390
323,324,397
324,325,405
325,326,392
326,327,377
327,328,382
328,329,375
329,330,401
330,331,374
331,332,394
332,333,432
333,334,383
334,335,412
335,336,431
336,337,353
337,338,406
338,339,350
339,340,352
340,341,376
341,342,362
342,343,396
343,344,358
344,345,337
345,346,344
346,347,361
347,348,388
348,349,356
349,350,367
350,351,336
351,352,375
352,353,347
353,354,337
354,355,383
355,356,354
356,357,371
357,358,317
358,359,350
359,360,337
360,361,359
361,362,348
362,363,349
363,364,353
364,365,322
365,366,345
366,367,365
367,368,364
368,369,355
369,370,329
370,371,369
371,372,353
372,373,328
373,374,339
374,375,368
375,376,334
376,377,341
377,378,320
378,379,321
379,380,350
380,381,290
381,382,307
382,383,308
383,384,362
384,385,317
385,386,325
386,387,290
387,388,324
388,389,313
389,390,299
390,391,295
391,392,297
392,393,267
393,394,304
394,395,307
395,396,322
396,397,306
397,398,279
398,399,306
399,400,284
400,401,281
401,402,299
402,403,287
403,404,341
404,405,287
405,406,293
406,407,304
407,408,272
408,409,297
409,410,283
410,411,275
411,412,262
412,413,280
413,414,288
414,415,298
415,416,305
416,417,284
417,418,275
418,419,255
419,420,276
420,421,268
421,422,258
422,423,305
423,424,291
424,425,231
425,426,250
426,427,262
427,428,266
428,429,246
429,430,259
430,431,255
431,432,252
432,433,277
433,434,244
434,435,261
435,436,230
436,437,258
437,438,252
438,439,236
439,440,239
440,441,262
441,442,244
442,443,243
443,444,254
444,445,250
445,446,250
446,447,227
447,448,232
448,449,251
449,450,242
450,451,230
451,452,235
452,453,258
453,454,242
454,455,241
455,456,236
456,457,225
457,458,276
458,459,253
459,460,211
460,461,236
461,462,257
462,463,247
463,464,238
464,465,237
465,466,194
466,467,228
467,468,240
468,469,225
469,470,234
470,471,238
471,472,218
472,473,214
473,474,211
474,475,226
475,476,251
476,477,221
477,478,241
478,479,234
479,480,203
480,481,242
481,482,235
482,483,219
483,484,218
484,485,236
485,486,227
486,487,225
487,488,210
488,489,230
489,490,238
490,491,255
491,492,204
492,493,246
493,494,221
494,495,225
495,496,227
496,497,216
497,498,206
498,499,215
499,500,215
500,501,210
501,502,206
502,503,208
503,504,211
504,505,202
505,506,215
506,507,211
507,508,212
508,509,210
509,510,191
510,511,191
511,512,222
512,513,202
513,514,195
514,515,181
515,516,187
516,517,194
517,518,176
518,519,209
519,520,197
520,521,208
521,522,177
522,523,189
523,524,184
524,525,182
525,526,212
526,527,193
527,528,181
528,529,165
529,530,204
530,531,193
531,532,164
532,533,158
533,534,180
534,535,166
535,536,204
536,537,201
537,538,182
538,539,162
539,540,192
540,541,186
541,542,184
542,543,169
543,544,197
544,545,190
545,546,184
546,547,158
547,548,219
548,549,178
549,550,143
550,551,186
551,552,184
552,553,191
553,554,167
554,555,171
555,556,173
556,557,162
557,558,174
558,559,163
559,560,172
560,561,169
561,562,176
562,563,175
563,564,209
564,565,177
565,566,159
566,567,162
567,568,141
568,569,180
569,570,156
570,571,137
571,572,174
572,573,163
573,574,164
574,575,148
575,576,154
576,577,140
577,578,181
578,579,183
579,580,173
580,581,151
581,582,175
582,583,131
583,584,148
584,585,162
585,586,157
586,587,172
587,588,130
588,589,149
589,590,159
590,591,150
591,592,181
592,593,143
593,594,140
594,595,142
595,596,168
596,597,141
597,598,131
598,599,136
599,600,149
600,601,137
601,602,143
602,603,158
603,604,159
604,605,143
605,606,145
606,607,141
607,608,159
608,609,162
609,610,146
610,611,160
611,612,122
612,613,147
613,614,129
614,615,121
615,616,146
616,617,147
617,618,133
618,619,125
619,620,126
620,621,167
621,622,136
622,623,129
623,624,152
624,625,149
625,626,148
626,627,154
627,628,171
628,629,126
629,630,132
630,631,158
631,632,129
632,633,147
633,634,139
634,635,155
635,636,141
636,637,121
637,638,151
638,639,140
639,640,134
640,641,141
641,642,122
642,643,140
643,644,150
644,645,131
645,646,129
646,647,132
647,648,159
648,649,146
649,650,135
650,651,137
651,652,118
652,653,139
653,654,142
654,655,113
655,656,138
656,657,139
657,658,131
658,659,116
659,660,129
660,661,137
661,662,119
662,663,118
663,664,126
664,665,147
665,666,118
666,667,145
667,668,124
668,669,131
669,670,134
670,671,114
671,672,115
672,673,130
673,674,118
674,675,135
675,676,127
676,677,125
677,678,118
678,679,126
679,680,117
680,681,140
681,682,120
682,683,120
683,684,133
684,685,125
685,686,125
686,687,101
687,688,129
688,689,121
689,690,120
690,691,119
691,692,124
692,693,115
693,694,111
694,695,129
695,696,122
696,697,136
697,698,111
698,699,110
699,700,120
700,701,118
701,702,118
702,703,116
703,704,122
704,705,112
705,706,105
706,707,113
707,708,99
708,709,109
709,710,125
710,711,113
711,712,109
712,713,100
713,714,111
714,715,119
715,716,110
716,717,113
717,718,104
718,719,121
719,720,107
720,721,125
721,722,113
722,723,103
723,724,106
724,725,110
725,726,139
726,727,111
727,728,110
728,729,126
729,730,100
730,731,113
731,732,109
732,733,113
733,734,129
734,735,92
735,736,100
736,737,114
737,738,109
738,739,101
739,740,124
740,741,92
741,742,103
742,743,94
743,744,116
744,745,103
745,746,104
746,747,103
747,748,104
748,749,93
749,750,118
750,751,106
751,752,84
752,753,105
753,754,99
754,755,116
755,756,90
756,757,89
757,758,91
758,759,102
759,760,89
760,761,77
761,762,99
762,763,108
763,764,113
764,765,88
765,766,98
766,767,93
767,768,80
768,769,89
769,770,99
770,771,94
771,772,94
772,773,118
773,774,102
774,775,90
775,776,104
776,777,87
777,778,88
778,779,99
779,780,116
780,781,96
781,782,83
782,783,106
783,784,91
784,785,97
785,786,90
786,787,91
787,788,100
788,789,89
789,790,71
790,791,92
791,792,84
792,793,96
793,794,87
794,795,90
795,796,92
796,797,86
797,798,112
798,799,112
799,800,102
800,801,96
801,802,84
802,803,90
803,804,95
804,805,85
805,806,90
806,807,107
807,808,78
808,809,72
809,810,101
810,811,84
811,812,79
812,813,93
813,814,84
814,815,102
815,816,78
816,817,92
817,818,77
818,819,86
819,820,97
820,821,87
821,822,104
822,823,90
823,824,75
824,825,90
825,826,95
826,827,82
827,828,74
828,829,80
829,830,90
830,831,90
831,832,84
832,833,80
833,834,95
834,835,79
835,836,90
836,837,81
837,838,99
838,839,102
839,840,71
840,841,90
841,842,91
842,843,85
843,844,85
844,845,87
845,846,86
846,847,76
847,848,68
848,849,91
849,850,81
850,851,77
851,852,86
852,853,81
853,854,63
854,855,72
855,856,80
856,857,84
857,858,87
858,859,84
859,860,79
860,861,14
861,862,0
862,863,0
863,864,0
864,865,0
865,866,0
866,867,0
867,868,0
868,869,0
869,870,0
870,871,0
871,872,0
872,873,0
873,874,0
874,875,0
875,876,0
876,877,0
877,878,0
878,879,0
879,880,0
880,881,0
881,882,0
882,883,0
883,884,0
884,885,0
885,886,0
886,887,0
887,888,0
888,889,0
889,890,0
890,891,0
891,892,0
892,893,0
893,894,0
894,895,0
895,896,0
896,897,0
897,898,0
898,899,0
899,900,0
900,901,0
901,902,0
902,903,0
903,904,0
904,905,0
905,906,0
906,907,0
907,908,0
908,909,0
909,910,0
910,911,0
911,912,0
912,913,0
913,914,0
914,915,0
915,916,0
916,917,0
917,918,0
918,919,0
919,920,0
920,921,0
921,922,0
922,923,0
923,924,0
924,925,0
925,926,0
926,927,0
927,928,0
928,929,0
929,930,0
930,931,0
931,932,0
932,933,0
933,934,0
934,935,0
935,936,0
936,937,0
937,938,0
938,939,0
939,940,0
940,941,0
941,942,0
942,943,0
943,944,0
944,945,0
945,946,0
946,947,0
947,948,0
948,949,0
949,950,0
950,951,0
951,952,0
952,953,0
953,954,0
954,955,0
955,956,0
956,957,0
957,958,0
958,959,0
959,960,0
960,961,0
961,962,0
962,963,0
963,964,0
964,965,0
965,966,0
966,967,0
967,968,0
968,969,0
969,970,0
970,971,0
971,972,0
972,973,0
973,974,0
974,975,0
975,976,0
976,977,0
977,978,0
978,979,0
979,980,0
980,981,0
981,982,0
982,983,0
983,984,0
984,985,0
985,986,0
986,987,0
987,988,0
988,989,0
989,990,0
990,991,0
991,992,0
992,993,0
993,994,0
994,995,0
995,996,0
996,997,0
997,998,0
998,999,0
999,1000,0
1000,1001,0
1001,1002,0
1002,1003,0
1003,1004,0
1004,1005,0
1005,1006,0
1006,1007,0
1007,1008,0
1008,1009,0
1009,1010,0
1010,1011,0
1011,1012,0
1012,1013,0
1013,1014,0
1014,1015,0
1015,1016,0
1016,1017,0
1017,1018,0
1018,1019,0
1019,1020,0
1020,1021,0
1021,1022,0
1022,1023,0
1023,1024,0

Spectrum Name:,,
Description:,,
Student ID:,,
Detector Used:,,
Comments:,,
Acquisition Mode:,MCS,
MCS Dwell Time:,1.000 Seconds,
High Voltage:,600,
Conversion Gain:,1024,
Coarse Gain:,8,
Fine Gain:,2,
ULD:,106%,
LLD:,2%,

Channel Data:,,
Chan,Dwell(Sec.),Counts
0,1,1652
1,2,1592
2,3,1557
3,4,1539
4,5,1550
5,6,1590
6,7,1499
7,8,1479
8,9,1537
9,10,1542
10,11,1544
11,12,1435
12,13,1493
13,14,1474
14,15,1439
15,16,1441
16,17,1440
17,18,1512
18,19,1486
19,20,1419
20,21,1480
21,22,1478
22,23,1403
23,24,1425
24,25,1406
25,26,1394
26,27,1418
27,28,1418
28,29,1393
29,30,1426
30,31,1372
31,32,1388
32,33,1395
33,34,1393
34,35,1309
35,36,1384
36,37,1413
37,38,1394
38,39,1366
39,40,1331
40,41,1323
41,42,1245
42,43,1284
43,44,1329
44,45,1237
45,46,1271
46,47,1296
47,48,1209
48,49,1220
49,50,1293
50,51,1333
51,52,1269
52,53,1341
53,54,1328
54,55,1271
55,56,1215
56,57,1291
57,58,1322
58,59,1219
59,60,1268
60,61,1232
61,62,1191
62,63,1208
63,64,1148
64,65,1202
65,66,1248
66,67,1149
67,68,1145
68,69,1196
69,70,1150
70,71,1227
71,72,1092
72,73,1219
73,74,1112
74,75,1148
75,76,1146
76,77,1108
77,78,1129
78,79,1117
79,80,1124
80,81,1127
81,82,1093
82,83,1103
83,84,1096
84,85,1135
85,86,1100
86,87,1086
87,88,1047
88,89,1022
89,90,1056
90,91,1048
91,92,1026
92,93,1037
93,94,1055
94,95,1049
95,96,1020
96,97,1005
97,98,1009
98,99,1016
99,100,1052
100,101,976
101,102,992
102,103,949
103,104,950
104,105,957
105,106,982
106,107,1020
107,108,947
108,109,954
109,110,959
110,111,925
111,112,983
112,113,955
113,114,961
114,115,892
115,116,985
116,117,929
117,118,932
118,119,992
119,120,940
120,121,939
121,122,902
122,123,922
123,124,960
124,125,878
125,126,861
126,127,898
127,128,968
128,129,865
129,130,948
130,131,916
131,132,878
132,133,868
133,134,841
134,135,864
135,136,882
136,137,890
137,138,822
138,139,868
139,140,828
140,141,881
141,142,842
142,143,831
143,144,800
144,145,826
145,146,795
146,147,797
147,148,811
148,149,875
149,150,846
150,151,831
151,152,791
152,153,820
153,154,775
154,155,786
155,156,813
156,157,778
157,158,850
158,159,753
159,160,801
160,161,774
161,162,771
162,163,779
163,164,777
164,165,757
165,166,735
166,167,758
167,168,774
168,169,783
169,170,725
170,171,758
171,172,728
172,173,701
173,174,759
174,175,742
175,176,694
176,177,768
177,178,723
178,179,723
179,180,759
180,181,716
181,182,684
182,183,700
183,184,704
184,185,677
185,186,739
186,187,636
187,188,673
188,189,689
189,190,659
190,191,652
191,192,671
192,193,689
193,194,673
194,195,640
195,196,700
196,197,689
197,198,699
198,199,630
199,200,657
200,201,703
201,202,641
202,203,686
203,204,652
204,205,640
205,206,649
206,207,599
207,208,688
208,209,617
209,210,642
210,211,621
211,212,615
212,213,631
213,214,597
214,215,614
215,216,618
216,217,611
217,218,636
218,219,587
219,220,638
220,221,582
221,222,596
222,223,605
223,224,610
224,225,557
225,226,599
226,227,599
227,228,577
228,229,594
229,230,609
230,231,578
231,232,545
232,233,602
233,234,569
234,235,621
235,236,590
236,237,632
237,238,557
238,239,575
239,240,598
240,241,537
241,242,595
242,243,554
243,244,567
244,245,563
245,246,540
246,247,527
247,248,533
248,249,579
249,250,538
250,251,535
251,252,517
252,253,556
253,254,566
254,255,561
255,256,564
256,257,572
257,258,524
258,259,508
259,260,490
260,261,508
261,262,527
262,263,515
263,264,502
264,265,513
265,266,512
266,267,513
267,268,472
268,269,489
269,270,522
270,271,469
271,272,491
272,273,519
273,274,495
274,275,455
275,276,501
276,277,482
277,278,437
278,279,485
279,280,479
280,281,480
281,282,463
282,283,469
283,284,484
284,285,436
285,286,471
286,287,411
287,288,454
288,289,460
289,290,501
290,291,480
291,292,418
292,293,455
293,294,444
294,295,427
295,296,472
296,297,428
297,298,453
298,299,458
299,300,463
300,301,439
301,302,460
302,303,454
303,304,470
304,305,437
305,306,426
306,307,441
307,308,440
308,309,425
309,310,373
310,311,431
311,312,394
312,313,413
313,314,443
314,315,426
315,316,449
316,317,416
317,318,464
318,319,378
319,320,422
320,321,407
321,322,423
322,323,390
323,324,397
324,325,405
325,326,392
326,327,377
327,328,382
328,329,375
329,330,401
330,331,374
331,332,394
332,333,432
333,334,383
334,335,412
335,336,431
336,337,353
337,338,406
338,339,350
339,340,352
340,341,376
341,342,362
342,343,396
343,344,358
344,345,337
345,346,344
346,347,361
347,348,388
348,349,356
349,350,367
350,351,336
351,352,375
352,353,347
353,354,337
354,355,383
355,356,354
356,357,371
357,358,317
358,359,350
359,360,337
360,361,359
361,362,348
362,363,349
363,364,353
364,365,322
365,366,345
366,367,365
367,368,364
368,369,355
369,370,329
370,371,369
371,372,353
372,373,328
373,374,339
374,375,368
375,376,334
376,377,341
377,378,320
378,379,321
379,380,350
380,381,290
381,382,307
382,383,308
383,384,362
384,385,317
385,386,325
386,387,290
387,388,324
388,389,313
389,390,299
390,391,295
391,392,297
392,393,267
393,394,304
394,395,307
395,396,322
396,397,306
397,398,279
398,399,306
399,400,284
400,401,281
401,402,299
402,403,287
403,404,341
404,405,287
405,406,293
406,407,304
407,408,272
408,409,297
409,410,283
410,411,275
411,412,262
412,413,280
413,414,288
414,415,298
415,416,305
416,417,284
417,418,275
418,419,255
419,420,276
420,421,268
421,422,258
422,423,305
423,424,291
424,425,231
425,426,250
426,427,262
427,428,266
428,429,246
429,430,259
430,431,255
431,432,252
432,433,277
433,434,244
434,435,261
435,436,230
436,437,258
437,438,252
438,439,236
439,440,239
440,441,262
441,442,244
442,443,243
443,444,254
444,445,250
445,446,250
446,447,227
447,448,232
448,449,251
449,450,242
450,451,230
451,452,235
452,453,258
453,454,242
454,455,241
455,456,236
456,457,225
457,458,276
458,459,253
459,460,211
460,461,236
461,462,257
462,463,247
463,464,238
464,465,237
465,466,194
466,467,228
467,468,240
468,469,225
469,470,234
470,471,238
471,472,218
472,473,214
473,474,211
474,475,226
475,476,251
476,477,221
477,478,241
478,479,234
479,480,203
480,481,242
481,482,235
482,483,219
483,484,218
484,485,236
485,486,227
486,487,225
487,488,210
488,489,230
489,490,238
490,491,255
491,492,204
492,493,246
493,494,221
494,495,225
495,496,227
496,497,216
497,498,206
498,499,215
499,500,215
500,501,210
501,502,206
502,503,208
503,504,211
504,505,202
505,506,215
506,507,211
507,508,212
508,509,210
509,510,191
510,511,191
511,512,222
512,513,202
513,514,195
514,515,181
515,516,187
516,517,194
517,518,176
518,519,209
519,520,197
520,521,208
521,522,177
522,523,189
523,524,184
524,525,182
525,526,212
526,527,193
527,528,181
528,529,165
529,530,204
530,531,193
531,532,164
532,533,158
533,534,180
534,535,166
535,536,204
536,537,201
537,538,182
538,539,162
539,540,192
540,541,186
541,542,184
542,543,169
543,544,197
544,545,190
545,546,184
546,547,158
547,548,219
548,549,178
549,550,143
550,551,186
551,552,184
552,553,191
553,554,167
554,555,171
555,556,173
556,557,162
557,558,174
558,559,163
559,560,172
560,561,169
561,562,176
562,563,175
563,564,209
564,565,177
565,566,159
566,567,162
567,568,141
568,569,180
569,570,156
570,571,137
571,572,174
572,573,163
573,574,164
574,575,148
575,576,154
576,577,140
577,578,181
578,579,183
579,580,173
580,581,151
581,582,175
582,583,131
583,584,148
584,585,162
585,586,157
586,587,172
587,588,130
588,589,149
589,590,159
590,591,150
591,592,181
592,593,143
593,594,140
594,595,142
595,596,168
596,597,141
597,598,131
598,599,136
599,600,149
600,601,137
601,602,143
602,603,158
603,604,159
604,605,143
605,606,145
606,607,141
607,608,159
608,609,162
609,610,146
610,611,160
611,612,122
612,613,147
613,614,129
614,615,121
615,616,146
616,617,147
617,618,133
618,619,125
619,620,126
620,621,167
621,622,136
622,623,129
623,624,152
624,625,149
625,626,148
626,627,154
627,628,171
628,629,126
629,630,132
630,631,158
631,632,129
632,633,147
633,634,139
634,635,155
635,636,141
636,637,121
637,638,151
638,639,140
639,640,134
640,641,141
641,642,122
642,643,140
643,644,150
644,645,131
645,646,129
646,647,132
647,648,159
648,649,146
649,650,135
650,651,137
651,652,118
652,653,139
653,654,142
654,655,113
655,656,138
656,657,139
657,658,131
658,659,116
659,660,129
660,661,137
661,662,119
662,663,118
663,664,126
664,665,147
665,666,118
666,667,145
667,668,124
668,669,131
669,670,134
670,671,114
671,672,115
672,673,130
673,674,118
674,675,135
675,676,127
676,677,125
677,678,118
678,679,126
679,680,117
680,681,140
681,682,120
682,683,120
683,684,133
684,685,125
685,686,125
686,687,101
687,688,129
688,689,121
689,690,120
690,691,119
691,692,124
692,693,115
693,694,111
694,695,129
695,696,122
696,697,136
697,698,111
698,699,110
699,700,120
700,701,118
701,702,118
702,703,116
703,704,122
704,705,112
705,706,105
706,707,113
707,708,99
708,709,109
709,710,125
710,711,113
711,712,109
712,713,100
713,714,111
714,715,119
715,716,110
716,717,113
717,718,104
718,719,121
719,720,107
720,721,125
721,722,113
722,723,103
723,724,106
724,725,110
725,726,139
726,727,111
727,728,110
728,729,126
729,730,100
730,731,113
731,732,109
732,733,113
733,734,129
734,735,92
735,736,100
736,737,114
737,738,109
738,739,101
739,740,124
740,741,92
741,742,103
742,743,94
743,744,116
744,745,103
745,746,104
746,747,103
747,748,104
748,749,93
749,750,118
750,751,106
751,752,84
752,753,105
753,754,99
754,755,116
755,756,90
756,757,89
757,758,91
758,759,102
759,760,89
760,761,77
761,762,99
762,763,108
763,764,113
764,765,88
765,766,98
766,767,93
767,768,80
768,769,89
769,770,99
770,771,94
771,772,94
772,773,118
773,774,102
774,775,90
775,776,104
776,777,87
777,778,88
778,779,99
779,780,116
780,781,96
781,782,83
782,783,106
783,784,91
784,785,97
785,786,90
786,787,91
787,788,100
788,789,89
789,790,71
790,791,92
791,792,84
792,793,96
793,794,87
794,795,90
795,796,92
796,797,86
797,798,112
798,799,112
799,800,102
800,801,96
801,802,84
802,803,90
803,804,95
804,805,85
805,806,90
806,807,107
807,808,78
808,809,72
809,810,101
810,811,84
811,812,79
812,813,93
813,814,84
814,815,102
815,816,78
816,817,92
817,818,77
818,819,86
819,820,97
820,821,87
821,822,104
822,823,90
823,824,75
824,825,90
825,826,95
826,827,82
827,828,74
828,829,80
829,830,90
830,831,90
831,832,84
832,833,80
833,834,95
834,835,79
835,836,90
836,837,81
837,838,99
838,839,102
839,840,71
840,841,90
841,842,91
842,843,85
843,844,85
844,845,87
845,846,86
846,847,76
847,848,68
848,849,91
849,850,81
850,851,77
851,852,86
852,853,81
853,854,63
854,855,72
855,856,80
856,857,84
857,858,87
858,859,84
859,860,79
860,861,14
861,862,0
862,863,0
863,864,0
864,865,0
865,866,0
866,867,0
867,868,0
868,869,0
869,870,0
870,871,0
871,872,0
872,873,0
873,874,0
874,875,0
875,876,0
876,877,0
877,878,0
878,879,0
879,880,0
880,881,0
881,882,0
882,883,0
883,884,0
884,885,0
885,886,0
886,887,0
887,888,0
888,889,0
889,890,0
890,891,0
891,892,0
892,893,0
893,894,0
894,895,0
895,896,0
896,897,0
897,898,0
898,899,0
899,900,0
900,901,0
901,902,0
902,903,0
903,904,0
904,905,0
905,906,0
906,907,0
907,908,0
908,909,0
909,910,0
910,911,0
911,912,0
912,913,0
913,914,0
914,915,0
915,916,0
916,917,0
917,918,0
918,919,0
919,920,0
920,921,0
921,922,0
922,923,0
923,924,0
924,925,0
925,926,0
926,927,0
927,928,0
928,929,0
929,930,0
930,931,0
931,932,0
932,933,0
933,934,0
934,935,0
935,936,0
936,937,0
937,938,0
938,939,0
939,940,0
940,941,0
941,942,0
942,943,0
943,944,0
944,945,0
945,946,0
946,947,0
947,948,0
948,949,0
949,950,0
950,951,0
951,952,0
952,953,0
953,954,0
954,955,0
955,956,0
956,957,0
957,958,0
958,959,0
959,960,0
960,961,0
961,962,0
962,963,0
963,964,0
964,965,0
965,966,0
966,967,0
967,968,0
968,969,0
969,970,0
970,971,0
971,972,0
972,973,0
973,974,0
974,975,0
975,976,0
976,977,0
977,978,0
978,979,0
979,980,0
980,981,0
981,982,0
982,983,0
983,984,0
984,985,0
985,986,0
986,987,0
987,988,0
988,989,0
989,990,0
990,991,0
991,992,0
992,993,0
993,994,0
994,995,0
995,996,0
996,997,0
997,998,0
998,999,0
999,1000,0
1000,1001,0
1001,1002,0
1002,1003,0
1003,1004,0
1004,1005,0
1005,1006,0
1006,1007,0
1007,1008,0
1008,1009,0
1009,1010,0
1010,1011,0
1011,1012,0
1012,1013,0
1013,1014,0
1014,1015,0
1015,1016,0
1016,1017,0
1017,1018,0
1018,1019,0
1019,1020,0
1020,1021,0
1021,1022,0
1022,1023,0
1023,1024,0

Spectrum Name:,,
Description:,,
Student ID:,,
Detector Used:,,
Comments:,,
Acquisition Mode:,MCS,
MCS Dwell Time:,1.000 Seconds,
High Voltage:,600,
Conversion Gain:,1024,
Coarse Gain:,8,
Fine Gain:,2,
ULD:,106%,
LLD:,2%,

Channel Data:,,
Chan,Dwell(Sec.),Counts
0,1,1652
1,2,1592
2,3,1557
3,4,1539
4,5,1550
5,6,1590
6,7,1499
7,8,1479
8,9,1537
9,10,1542
10,11,1544
11,12,1435
12,13,1493
13,14,1474
14,15,1439
15,16,1441
16,17,1440
17,18,1512
18,19,1486
19,20,1419
20,21,1480
21,22,1478
22,23,1403
23,24,1425
24,25,1406
25,26,1394
26,27,1418
27,28,1418
28,29,1393
29,30,1426
30,31,1372
31,32,1388
32,33,1395
33,34,1393
34,35,1309
35,36,1384
36,37,1413
37,38,1394
38,39,1366
39,40,1331
40,41,1323
41,42,1245
42,43,1284
43,44,1329
44,45,1237
45,46,1271
46,47,1296
47,48,1209
48,49,1220
49,50,1293
50,51,1333
51,52,1269
52,53,1341
53,54,1328
54,55,1271
55,56,1215
56,57,1291
57,58,1322
58,59,1219
59,60,1268
60,61,1232
61,62,1191
62,63,1208
63,64,1148
64,65,1202
65,66,1248
66,67,1149
67,68,1145
68,69,1196
69,70,1150
70,71,1227
71,72,1092
72,73,1219
73,74,1112
74,75,1148
75,76,1146
76,77,1108
77,78,1129
78,79,1117
79,80,1124
80,81,1127
81,82,1093
82,83,1103
83,84,1096
84,85,1135
85,86,1100
86,87,1086
87,88,1047
88,89,1022
89,90,1056
90,91,1048
91,92,1026
92,93,1037
93,94,1055
94,95,1049
95,96,1020
96,97,1005
97,98,1009
98,99,1016
99,100,1052
100,101,976
101,102,992
102,103,949
103,104,950
104,105,957
105,106,982
106,107,1020
107,108,947
108,109,954
109,110,959
110,111,925
111,112,983
112,113,955
113,114,961
114,115,892
115,116,985
116,117,929
117,118,932
118,119,992
119,120,940
120,121,939
121,122,902
122,123,922
123,124,960
124,125,878
125,126,861
126,127,898
127,128,968
128,129,865
129,130,948
130,131,916
131,132,878
132,133,868
133,134,841
134,135,864
135,136,882
136,137,890
137,138,822
138,139,868
139,140,828
140,141,881
141,142,842
142,143,831
143,144,800
144,145,826
145,146,795
146,147,797
147,148,811
148,149,875
149,150,846
150,151,831
151,152,791
152,153,820
153,154,775
154,155,786
155,156,813
156,157,778
157,158,850
158,159,753
159,160,801
160,161,774
161,162,771
162,163,779
163,164,777
164,165,757
165,166,735
166,167,758
167,168,774
168,169,783
169,170,725
170,171,758
171,172,728
172,173,701
173,174,759
174,175,742
175,176,694
176,177,768
177,178,723
178,179,723
179,180,759
180,181,716
181,182,684
182,183,700
183,184,704
184,185,677
185,186,739
186,187,636
187,188,673
188,189,689
189,190,659
190,191,652
191,192,671
192,193,689
193,194,673
194,195,640
195,196,700
196,197,689
197,198,699
198,199,630
199,200,657
200,201,703
201,202,641
202,203,686
203,204,652
204,205,640
205,206,649
206,207,599
207,208,688
208,209,617
209,210,642
210,211,621
211,212,615
212,213,631
213,214,597
214,215,614
215,216,618
216,217,611
217,218,636
218,219,587
219,220,638
220,221,582
221,222,596
222,223,605
223,224,610
224,225,557
225,226,599
226,227,599
227,228,577
228,229,594
229,230,609
230,231,578
231,232,545
232,233,602
233,234,569
234,235,621
235,236,590
236,237,632
237,238,557
238,239,575
239,240,598
240,241,537
241,242,595
242,243,554
243,244,567
244,245,563
245,246,540
246,247,527
247,248,533
248,249,579
249,250,538
250,251,535
251,252,517
252,253,556
253,254,566
254,255,561
255,256,564
256,257,572
257,258,524
258,259,508
259,260,490
260,261,508
261,262,527
262,263,515
263,264,502
264,265,513
265,266,512
266,267,513
267,268,472
268,269,489
269,270,522
270,271,469
271,272,491
272,273,519
273,274,495
274,275,455
275,276,501
276,277,482
277,278,437
278,279,485
279,280,479
280,281,480
281,282,463
282,283,469
283,284,484
284,285,436
285,286,471
286,287,411
287,288,454
288,289,460
289,290,501
290,291,480
291,292,418
292,293,455
293,294,444
294,295,427
295,296,472
296,297,428
297,298,453
298,299,458
299,300,463
300,301,439
301,302,460
302,303,454
303,304,470
304,305,437
305,306,426
306,307,441
307,308,440
308,309,425
309,310,373
310,311,431
311,312,394
312,313,413
313,314,443
314,315,426
315,316,449
316,317,416
317,318,464
318,319,378
319,320,422
320,321,407
321,322,423
322,323,390
323,324,397
324,325,405
325,326,392
326,327,377
327,328,382
328,329,375
329,330,401
330,331,374
331,332,394
332,333,432
333,334,383
334,335,412
335,336,431
336,337,353
337,338,406
338,339,350
339,340,352
340,341,376
341,342,362
342,343,396
343,344,358
344,345,337
345,346,344
346,347,361
347,348,388
348,349,356
349,350,367
350,351,336
351,352,375
352,353,347
353,354,337
354,355,383
355,356,354
356,357,371
357,358,317
358,359,350
359,360,337
360,361,359
361,362,348
362,363,349
363,364,353
364,365,322
365,366,345
366,367,365
367,368,364
368,369,355
369,370,329
370,371,369
371,372,353
372,373,328
373,374,339
374,375,368
375,376,334
376,377,341
377,378,320
378,379,321
379,380,350
380,381,290
381,382,307
382,383,308
383,384,362
384,385,317
385,386,325
386,387,290
387,388,324
388,389,313
389,390,299
390,391,295
391,392,297
392,393,267
393,394,304
394,395,307
395,396,322
396,397,306
397,398,279
398,399,306
399,400,284
400,401,281
401,402,299
402,403,287
403,404,341
404,405,287
405,406,293
406,407,304
407,408,272
408,409,297
409,410,283
410,411,275
411,412,262
412,413,280
413,414,288
414,415,298
415,416,305
416,417,284
417,418,275
418,419,255
419,420,276
420,421,268
421,422,258
422,423,305
423,424,291
424,425,231
425,426,250
426,427,262
427,428,266
428,429,246
429,430,259
430,431,255
431,432,252
432,433,277
433,434,244
434,435,261
435,436,230
436,437,258
437,438,252
438,439,236
439,440,239
440,441,262
441,442,244
442,443,243
443,444,254
444,445,250
445,446,250
446,447,227
447,448,232
448,449,251
449,450,242
450,451,230
451,452,235
452,453,258
453,454,242
454,455,241
455,456,236
456,457,225
457,458,276
458,459,253
459,460,211
460,461,236
461,462,257
462,463,247
463,464,238
464,465,237
465,466,194
466,467,228
467,468,240
468,469,225
469,470,234
470,471,238
471,472,218
472,473,214
473,474,211
474,475,226
475,476,251
476,477,221
477,478,241
478,479,234
479,480,203
480,481,242
481,482,235
482,483,219
483,484,218
484,485,236
485,486,227
486,487,225
487,488,210
488,489,230
489,490,238
490,491,255
491,492,204
492,493,246
493,494,221
494,495,225
495,496,227
496,497,216
497,498,206
498,499,215
499,500,215
500,501,210
501,502,206
502,503,208
503,504,211
504,505,202
505,506,215
506,507,211
507,508,212
508,509,210
509,510,191
510,511,191
511,512,222
512,513,202
513,514,195
514,515,181
515,516,187
516,517,194
517,518,176
518,519,209
519,520,197
520,521,208
521,522,177
522,523,189
523,524,184
524,525,182
525,526,212
526,527,193
527,528,181
528,529,165
529,530,204
530,531,193
531,532,164
532,533,158
533,534,180
534,535,166
535,536,204
536,537,201
537,538,182
538,539,162
539,540,192
540,541,186
541,542,184
542,543,169
543,544,197
544,545,190
545,546,184
546,547,158
547,548,219
548,549,178
549,550,143
550,551,186
551,552,184
552,553,191
553,554,167
554,555,171
555,556,173
556,557,162
557,558,174
558,559,163
559,560,172
560,561,169
561,562,176
562,563,175
563,564,209
564,565,177
565,566,159
566,567,162
567,568,141
568,569,180
569,570,156
570,571,137
571,572,174
572,573,163
573,574,164
574,575,148
575,576,154
576,577,140
577,578,181
578,579,183
579,580,173
580,581,151
581,582,175
582,583,131
583,584,148
584,585,162
585,586,157
586,587,172
587,588,130
588,589,149
589,590,159
590,591,150
591,592,181
592,593,143
593,594,140
594,595,142
595,596,168
596,597,141
597,598,131
598,599,136
599,600,149
600,601,137
601,602,143
602,603,158
603,604,159
604,605,143
605,606,145
606,607,141
607,608,159
608,609,162
609,610,146
610,611,160
611,612,122
612,613,147
613,614,129
614,615,121
615,616,146
616,617,147
617,618,133
618,619,125
619,620,126
620,621,167
621,622,136
622,623,129
623,624,152
624,625,149
625,626,148
626,627,154
627,628,171
628,629,126
629,630,132
630,631,158
631,632,129
632,633,147
633,634,139
634,635,155
635,636,141
636,637,121
637,638,151
638,639,140
639,640,134
640,641,141
641,642,122
642,643,140
643,644,150
644,645,131
645,646,129
646,647,132
647,648,159
648,649,146
649,650,135
650,651,137
651,652,118
652,653,139
653,654,142
654,655,113
655,656,138
656,657,139
657,658,131
658,659,116
659,660,129
660,661,137
661,662,119
662,663,118
663,664,126
664,665,147
665,666,118
666,667,145
667,668,124
668,669,131
669,670,134
670,671,114
671,672,115
672,673,130
673,674,118
674,675,135
675,676,127
676,677,125
677,678,118
678,679,126
679,680,117
680,681,140
681,682,120
682,683,120
683,684,133
684,685,125
685,686,125
686,687,101
687,688,129
688,689,121
689,690,120
690,691,119
691,692,124
692,693,115
693,694,111
694,695,129
695,696,122
696,697,136
697,698,111
698,699,110
699,700,120
700,701,118
701,702,118
702,703,116
703,704,122
704,705,112
705,706,105
706,707,113
707,708,99
708,709,109
709,710,125
710,711,113
711,712,109
712,713,100
713,714,111
714,715,119
715,716,110
716,717,113
717,718,104
718,719,121
719,720,107
720,721,125
721,722,113
722,723,103
723,724,106
724,725,110
725,726,139
726,727,111
727,728,110
728,729,126
729,730,100
730,731,113
731,732,109
732,733,113
733,734,129
734,735,92
735,736,100
736,737,114
737,738,109
738,739,101
739,740,124
740,741,92
741,742,103
742,743,94
743,744,116
744,745,103
745,746,104
746,747,103
747,748,104
748,749,93
749,750,118
750,751,106
751,752,84
752,753,105
753,754,99
754,755,116
755,756,90
756,757,89
757,758,91
758,759,102
759,760,89
760,761,77
761,762,99
762,763,108
763,764,113
764,765,88
765,766,98
766,767,93
767,768,80
768,769,89
769,770,99
770,771,94
771,772,94
772,773,118
773,774,102
774,775,90
775,776,104
776,777,87
777,778,88
778,779,99
779,780,116
780,781,96
781,782,83
782,783,106
783,784,91
784,785,97
785,786,90
786,787,91
787,788,100
788,789,89
789,790,71
790,791,92
791,792,84
792,793,96
793,794,87
794,795,90
795,796,92
796,797,86
797,798,112
798,799,112
799,800,102
800,801,96
801,802,84
802,803,90
803,804,95
804,805,85
805,806,90
806,807,107
807,808,78
808,809,72
809,810,101
810,811,84
811,812,79
812,813,93
813,814,84
814,815,102
815,816,78
816,817,92
817,818,77
818,819,86
819,820,97
820,821,87
821,822,104
822,823,90
823,824,75
824,825,90
825,826,95
826,827,82
827,828,74
828,829,80
829,830,90
830,831,90
831,832,84
832,833,80
833,834,95
834,835,79
835,836,90
836,837,81
837,838,99
838,839,102
839,840,71
840,841,90
841,842,91
842,843,85
843,844,85
844,845,87
845,846,86
846,847,76
847,848,68
848,849,91
849,850,81
850,851,77
851,852,86
852,853,81
853,854,63
854,855,72
855,856,80
856,857,84
857,858,87
858,859,84
859,860,79
860,861,14
861,862,0
862,863,0
863,864,0
864,865,0
865,866,0
866,867,0
867,868,0
868,869,0
869,870,0
870,871,0
871,872,0
872,873,0
873,874,0
874,875,0
875,876,0
876,877,0
877,878,0
878,879,0
879,880,0
880,881,0
881,882,0
882,883,0
883,884,0
884,885,0
885,886,0
886,887,0
887,888,0
888,889,0
889,890,0
890,891,0
891,892,0
892,893,0
893,894,0
894,895,0
895,896,0
896,897,0
897,898,0
898,899,0
899,900,0
900,901,0
901,902,0
902,903,0
903,904,0
904,905,0
905,906,0
906,907,0
907,908,0
908,909,0
909,910,0
910,911,0
911,912,0
912,913,0
913,914,0
914,915,0
915,916,0
916,917,0
917,918,0
918,919,0
919,920,0
920,921,0
921,922,0
922,923,0
923,924,0
924,925,0
925,926,0
926,927,0
927,928,0
928,929,0
929,930,0
930,931,0
931,932,0
932,933,0
933,934,0
934,935,0
935,936,0
936,937,0
937,938,0
938,939,0
939,940,0
940,941,0
941,942,0
942,943,0
943,944,0
944,945,0
945,946,0
946,947,0
947,948,0
948,949,0
949,950,0
950,951,0
951,952,0
952,953,0
953,954,0
954,955,0
955,956,0
956,957,0
957,958,0
958,959,0
959,960,0
960,961,0
961,962,0
962,963,0
963,964,0
964,965,0
965,966,0
966,967,0
967,968,0
968,969,0
969,970,0
970,971,0
971,972,0
972,973,0
973,974,0
974,975,0
975,976,0
976,977,0
977,978,0
978,979,0
979,980,0
980,981,0
981,982,0
982,983,0
983,984,0
984,985,0
985,986,0
986,987,0
987,988,0
988,989,0
989,990,0
990,991,0
991,992,0
992,993,0
993,994,0
994,995,0
995,996,0
996,997,0
997,998,0
998,999,0
999,1000,0
1000,1001,0
1001,1002,0
1002,1003,0
1003,1004,0
1004,1005,0
1005,1006,0
1006,1007,0
1007,1008,0
1008,1009,0
1009,1010,0
1010,1011,0
1011,1012,0
1012,1013,0
1013,1014,0
1014,1015,0
1015,1016,0
1016,1017,0
1017,1018,0
1018,1019,0
1019,1020,0
1020,1021,0
1021,1022,0
1022,1023,0
1023,1024,0