20:
660:
621:
792:
If several known chemicals are dissolved in a single solution, the concentrations of each can be calculated using a light absorption analysis. First, the mass attenuation coefficients of each individual solute or solvent, ideally across a broad spectrum of wavelengths, must be measured or looked up.
431:
472:. In that case, the mass attenuation coefficient is defined by the same equation, except that the "density" is the density of only that one chemical species, and the "attenuation" is the attenuation due to only that one chemical species. The
897:
583:
39:
normalized by the density of the material; that is, the attenuation per unit mass (rather than per unit of distance). Thus, it characterizes how easily a mass of material can be penetrated by a beam of
255:
144:
297:
360:
592:
must also be included). This is a convenient concept because the mass attenuation coefficient of a species is approximately independent of its concentration (as long as
321:
799:
485:
1056:
84:). Other common units include cm/g (the most common unit for X-ray mass attenuation coefficients) and Lā
gā
cm (sometimes used in solution chemistry).
1156:
1125:
1094:
770:
652:
729:
337:
189:
670:
Z smaller than 100 collected for photons with energies from 1 keV to 20 MeV. The discontinuities in the values are due to
588:
where each term in the sum is the mass attenuation coefficient and density of a different component of the solution (the
769:
The actual values have been thoroughly examined and are available to the general public through three databases run by
1194:
112:
1014:
266:
73:
1184:
793:
Second, the attenuation coefficient of the actual solution must be measured. Finally, using the formula
426:{\displaystyle {\frac {\mu _{\mathrm {a} }}{\rho _{m}}},\quad {\frac {\mu _{\mathrm {s} }}{\rho _{m}}},}
61:
964:
92:
999:
725:
593:
476:
157:
36:
23:
Mass attenuation coefficients of selected elements for X-ray photons with energies up to 250 keV.
959:
947:
1090:
1152:
1148:
1019:
979:
756:
644:
636:
469:
306:
180:
1121:
19:
8:
1189:
744:
628:
1091:"Tables of X-Ray Mass Attenuation Coefficients and Mass Energy-Absorption Coefficients"
1004:
994:
969:
750:
659:
632:
600:
60:. In addition to visible light, mass attenuation coefficients can be defined for other
1029:
1066:
1070:
1061:
1024:
465:
333:
1117:
1086:
892:{\displaystyle \mu =(\mu /\rho )_{1}\rho _{1}+(\mu /\rho )_{2}\rho _{2}+\ldots ,}
765:, electron-positron production in the fields of the nucleus and atomic electrons.
762:
706:
671:
640:
578:{\displaystyle \mu =(\mu /\rho )_{1}\rho _{1}+(\mu /\rho )_{2}\rho _{2}+\ldots ,}
1009:
984:
718:
702:
620:
336:) beam passes through a volume, the beam will lose intensity to two processes:
1178:
1065:, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "
1034:
667:
1074:
989:
737:
686:
300:
172:
95:
where the effective area is defined per unit mass instead of per particle.
974:
698:
690:
733:
724:
The values of mass attenuation coefficients, based on proper values of
608:
341:
1115:
1147:
Chantler, C.T.; Olsen, K.; Dragoset, R.A.; Chang, J.; Kishore, A.R.;
714:
694:
1153:"X-Ray Form Factor, Attenuation and Scattering Tables (version 2.1)"
1146:
91:
The mass attenuation coefficient can be thought of as a variant of
77:
49:
1120:; S.M. Seltzer; J. Chang; J.S. Coursey; R. Sukumar; D.S. Zucker.
589:
464:
In chemistry, mass attenuation coefficients are often used for a
709:, and other branches of physics. The photons can be in form of
679:
648:
57:
53:
327:
710:
69:
65:
45:
41:
950:, although using more wavelengths gives more reliable data.
787:
740:
radiation caused by several different mechanisms such as
1085:
76:
of mass attenuation coefficient is the square metre per
323:
is the length, over which the attenuation takes place.
250:{\displaystyle I=I_{0}\,e^{-(\mu /\rho _{m})\lambda }}
802:
488:
363:
309:
269:
192:
115:
946:
measured wavelengths to create a solvable system of
891:
627:of iron with contributing sources of attenuation:
577:
425:
315:
291:
249:
138:
179:When using the mass attenuation coefficient, the
1176:
72:, or any other beam that can be attenuated. The
1157:National Institute of Standards and Technology
1126:National Institute of Standards and Technology
1095:National Institute of Standards and Technology
771:National Institute of Standards and Technology
939:solutes or solvents, this procedure requires
328:Mass absorption and scattering coefficients
98:
1052:
1050:
935:are functions of wavelength. If there are
139:{\displaystyle {\frac {\mu }{\rho _{m}}},}
788:Calculating the composition of a solution
209:
658:
619:
33:mass narrow beam attenuation coefficient
18:
1047:
292:{\displaystyle \lambda =\rho _{m}\ell }
1177:
1122:"XCOM: Photon Cross Sections Database"
693:(for medical and security purposes),
603:. They are quantitatively related by
1140:
1079:
916:, ā¦ as adjustable parameters, since
1109:
666:values shown for all elements with
13:
1062:Compendium of Chemical Terminology
607:(mass attenuation coefficient) Ć (
402:
372:
303:known also as mass thickness, and
183:is written in alternative form as
88:is an old term for this quantity.
14:
1206:
902:the spectrum can be fitted using
160:(linear attenuation coefficient);
459:
393:
861:
846:
824:
809:
547:
532:
510:
495:
455:is the scattering coefficient.
446:is the absorption coefficient;
239:
218:
1:
1040:
1015:Molar attenuation coefficient
683:mass attenuation coefficients
599:A closely related concept is
664:Mass attenuation coefficient
625:Mass attenuation coefficient
104:Mass attenuation coefficient
29:mass attenuation coefficient
7:
953:
352:mass scattering coefficient
348:Mass absorption coefficient
86:Mass extinction coefficient
10:
1211:
728:, are dependent upon the
615:
611:) = (molar absorptivity).
62:electromagnetic radiation
1195:Mass-specific quantities
965:Absorption cross section
757:photoelectric absorption
753:(incoherent scattering);
645:photoelectric absorption
637:photoelectric absorption
99:Mathematical definitions
93:absorption cross section
1075:10.1351/goldbook.A00516
1067:Attenuation coefficient
651:. Graph data came from
643:. The discontinuity of
477:attenuation coefficient
158:attenuation coefficient
37:attenuation coefficient
960:Absorption coefficient
948:simultaneous equations
893:
747:(coherent scattering);
675:
674:which were also shown.
656:
579:
427:
317:
293:
251:
140:
24:
894:
662:
633:incoherent scattering
623:
580:
428:
318:
316:{\displaystyle \ell }
294:
252:
141:
35:of a material is the
22:
16:Property of materials
1020:Propagation constant
800:
726:photon cross section
486:
361:
307:
267:
190:
113:
1185:Physical quantities
745:Rayleigh scattering
639:, and two types of
629:coherent scattering
594:certain assumptions
1005:High-energy X-rays
995:Compton scattering
970:Attenuation length
889:
751:Compton scattering
676:
657:
647:values are due to
601:molar absorptivity
575:
423:
313:
289:
247:
136:
25:
1149:Kotochigova, S.A.
1089:; Seltzer, S. M.
1030:Scattering theory
685:are essential in
655:'s XCOM database.
418:
388:
131:
1202:
1169:
1168:
1166:
1164:
1144:
1138:
1137:
1135:
1133:
1113:
1107:
1106:
1104:
1102:
1083:
1077:
1054:
1025:Radiation length
980:BeerāLambert law
934:
898:
896:
895:
890:
879:
878:
869:
868:
856:
842:
841:
832:
831:
819:
777:XAAMDI database;
672:absorption edges
596:are fulfilled).
584:
582:
581:
576:
565:
564:
555:
554:
542:
528:
527:
518:
517:
505:
466:chemical species
432:
430:
429:
424:
419:
417:
416:
407:
406:
405:
395:
389:
387:
386:
377:
376:
375:
365:
322:
320:
319:
314:
298:
296:
295:
290:
285:
284:
256:
254:
253:
248:
246:
245:
238:
237:
228:
208:
207:
181:BeerāLambert law
145:
143:
142:
137:
132:
130:
129:
117:
83:
1210:
1209:
1205:
1204:
1203:
1201:
1200:
1199:
1175:
1174:
1173:
1172:
1162:
1160:
1151:; Zucker, D.S.
1145:
1141:
1131:
1129:
1114:
1110:
1100:
1098:
1084:
1080:
1055:
1048:
1043:
956:
933:
921:
915:
908:
874:
870:
864:
860:
852:
837:
833:
827:
823:
815:
801:
798:
797:
790:
783:FFAST database.
763:pair production
707:crystallography
641:pair production
618:
560:
556:
550:
546:
538:
523:
519:
513:
509:
501:
487:
484:
483:
479:is computed by
468:dissolved in a
462:
454:
445:
412:
408:
401:
400:
396:
394:
382:
378:
371:
370:
366:
364:
362:
359:
358:
354:are defined as
332:When a narrow (
330:
308:
305:
304:
280:
276:
268:
265:
264:
233:
229:
224:
214:
210:
203:
199:
191:
188:
187:
170:
125:
121:
116:
114:
111:
110:
101:
81:
17:
12:
11:
5:
1208:
1198:
1197:
1192:
1187:
1171:
1170:
1139:
1108:
1087:Hubbell, J. H.
1078:
1045:
1044:
1042:
1039:
1038:
1037:
1032:
1027:
1022:
1017:
1012:
1010:Mean free path
1007:
1002:
997:
992:
987:
985:Cargo scanning
982:
977:
972:
967:
962:
955:
952:
929:
913:
906:
900:
899:
888:
885:
882:
877:
873:
867:
863:
859:
855:
851:
848:
845:
840:
836:
830:
826:
822:
818:
814:
811:
808:
805:
789:
786:
785:
784:
781:
780:XCOM database;
778:
767:
766:
760:
754:
748:
719:bremsstrahlung
703:interferometry
617:
614:
613:
612:
586:
585:
574:
571:
568:
563:
559:
553:
549:
545:
541:
537:
534:
531:
526:
522:
516:
512:
508:
504:
500:
497:
494:
491:
461:
458:
457:
456:
452:
447:
443:
434:
433:
422:
415:
411:
404:
399:
392:
385:
381:
374:
369:
329:
326:
325:
324:
312:
288:
283:
279:
275:
272:
258:
257:
244:
241:
236:
232:
227:
223:
220:
217:
213:
206:
202:
198:
195:
177:
176:
166:
161:
147:
146:
135:
128:
124:
120:
106:is defined as
100:
97:
15:
9:
6:
4:
3:
2:
1207:
1196:
1193:
1191:
1188:
1186:
1183:
1182:
1180:
1158:
1154:
1150:
1143:
1127:
1123:
1119:
1112:
1096:
1092:
1088:
1082:
1076:
1072:
1068:
1064:
1063:
1058:
1053:
1051:
1046:
1036:
1035:Transmittance
1033:
1031:
1028:
1026:
1023:
1021:
1018:
1016:
1013:
1011:
1008:
1006:
1003:
1001:
1000:Cross section
998:
996:
993:
991:
988:
986:
983:
981:
978:
976:
973:
971:
968:
966:
963:
961:
958:
957:
951:
949:
945:
942:
938:
932:
928:
924:
919:
912:
905:
886:
883:
880:
875:
871:
865:
857:
853:
849:
843:
838:
834:
828:
820:
816:
812:
806:
803:
796:
795:
794:
782:
779:
776:
775:
774:
772:
764:
761:
758:
755:
752:
749:
746:
743:
742:
741:
739:
735:
731:
727:
722:
720:
716:
712:
708:
704:
700:
696:
692:
688:
684:
681:
673:
669:
668:atomic number
665:
661:
654:
650:
646:
642:
638:
634:
630:
626:
622:
610:
606:
605:
604:
602:
597:
595:
591:
572:
569:
566:
561:
557:
551:
543:
539:
535:
529:
524:
520:
514:
506:
502:
498:
492:
489:
482:
481:
480:
478:
475:
471:
467:
451:
448:
442:
439:
438:
437:
420:
413:
409:
397:
390:
383:
379:
367:
357:
356:
355:
353:
349:
345:
343:
339:
335:
310:
302:
286:
281:
277:
273:
270:
263:
262:
261:
242:
234:
230:
225:
221:
215:
211:
204:
200:
196:
193:
186:
185:
184:
182:
174:
169:
165:
162:
159:
155:
152:
151:
150:
133:
126:
122:
118:
109:
108:
107:
105:
96:
94:
89:
87:
79:
75:
71:
67:
63:
59:
55:
51:
47:
43:
38:
34:
30:
21:
1161:. Retrieved
1142:
1130:. Retrieved
1118:J.H. Hubbell
1116:M.J.Berger;
1111:
1099:. Retrieved
1081:
1060:
990:Compton edge
943:
940:
936:
930:
926:
922:
917:
910:
903:
901:
791:
768:
723:
687:radiological
682:
677:
663:
624:
598:
587:
473:
463:
460:In solutions
449:
440:
435:
351:
347:
346:
331:
301:area density
259:
178:
173:mass density
167:
163:
153:
148:
103:
102:
90:
85:
32:
28:
26:
975:Attenuation
699:diffraction
691:radiography
52:, or other
1190:Radiometry
1179:Categories
1041:References
734:scattering
730:absorption
715:gamma rays
678:Tables of
609:molar mass
342:scattering
338:absorption
334:collimated
920:and each
884:…
872:ρ
858:ρ
850:μ
835:ρ
821:ρ
813:μ
804:μ
695:dosimetry
689:physics,
570:…
558:ρ
544:ρ
536:μ
521:ρ
507:ρ
499:μ
490:μ
410:ρ
398:μ
380:ρ
368:μ
311:ℓ
287:ℓ
278:ρ
271:λ
243:λ
231:ρ
222:μ
216:−
123:ρ
119:μ
64:(such as
50:particles
954:See also
941:at least
773:(NIST):
738:incident
470:solution
78:kilogram
736:of the
590:solvent
299:is the
171:is the
156:is the
74:SI unit
1159:(NIST)
1128:(NIST)
1097:(NIST)
717:, and
711:X-rays
680:photon
649:K-edge
616:X-rays
474:actual
436:where
350:, and
260:where
149:where
66:X-rays
58:matter
54:energy
1163:2 Nov
1132:2 Nov
1101:2 Nov
1057:IUPAC
70:sound
46:sound
42:light
31:, or
1165:2007
1134:2007
1103:2007
732:and
653:NIST
340:and
82:m/kg
27:The
1071:doi
1069:".
68:),
56:or
1181::
1155:.
1124:.
1093:.
1059:,
1049:^
909:,
721:.
713:,
705:,
701:,
697:,
635:,
631:,
344:.
48:,
44:,
1167:.
1136:.
1105:.
1073::
944:N
937:N
931:i
927:Ļ
925:/
923:Ī¼
918:Ī¼
914:2
911:Ļ
907:1
904:Ļ
887:,
881:+
876:2
866:2
862:)
854:/
847:(
844:+
839:1
829:1
825:)
817:/
810:(
807:=
759:;
573:,
567:+
562:2
552:2
548:)
540:/
533:(
530:+
525:1
515:1
511:)
503:/
496:(
493:=
453:s
450:Ī¼
444:a
441:Ī¼
421:,
414:m
403:s
391:,
384:m
373:a
282:m
274:=
240:)
235:m
226:/
219:(
212:e
205:0
201:I
197:=
194:I
175:.
168:m
164:Ļ
154:Ī¼
134:,
127:m
80:(
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