491:
700:
47:
466:. However, they soon realized that the definition of the metre at the time, based on a material artifact, was not accurate enough for their work. So, around 1907 they defined their own unit of length, which they called "Ångström", based on the wavelength of a specific spectral line. It was only in 1960, when the metre was redefined in the same way, that the angstrom became again equal to
993:. Spellings "Ångström" (capitalized) and "angstrom" (lowercase); symbols "Å", "Å.U.", "A.U." Quote: "The International Ångström (I.Å.) was defined in 1907 in terms of the wavelength of cadmium which in standard conditions is 6438·4696 I.Å. When the metre was defined in terms of the wavelength of krypton in 1960 the Ångström became exactly equal to 10 cm."
1279:, volume 11, pages 1–85. Quote from p. 85, back-translated: "... the final conclusion of this work is that the fundamental unit of the metric system is represented by the following numbers of wavelengths of three emissions of cadmium, in air at 15 °C and at a pressure of 760 mm: Red emission … 1 m =
1377:
Curtis, I.; Morgan, I.; Hart, M.; Milne, A.D. (August 1971). "A New
Determination of Avogadro's Number". In Langenberg, D. N.; Taylor, B.N. (eds.). Proceedings of the International Congress on Precision Measurement and Fundamental Constants (Report). Vol. 343. National Bureau of Standards.
627:
After the redefinition of the meter in spectroscopic terms, the
Angstrom was formally redefined to be 0.1 nanometers. However, there was briefly thought to be a need for a separate unit of comparable size defined directly in terms of spectroscopy. In 1965, J.A. Bearden defined the
554:
in Paris in a carefully controlled environment. Reliance on that material standard had led to an early error of about one part in 6000 in the tabulated wavelengths. Ångström took the precaution of having the standard bar he used checked against a standard in Paris, but the
687:(NIST). However, it is not mentioned in the 9th edition of the official SI standard, the "BIPM Brochure" (2019) or in the NIST version of the same, and BIPM officially discourages its use. The angstrom is also not included in the
666:
of the version derived from the new meter. Within ten years, the unit had been deemed both insufficiently accurate (with accuracies closer to 15 parts per million) and obsolete due to higher precision measuring equipment.
611:(CGPM) in 1927, but the material definition of the metre was retained until 1960. From 1927 to 1960, the angstrom remained a secondary unit of length for use in spectroscopy, defined separately from the metre.
1390:"Council Directive 80/181/EEC of 20 December 1979 on the approximation of the laws of the Member States relating to Unit of measurement and on the repeal of Directive 71/354/EEC"
1474:
1132:
660:
542: metres, that definition was not accurate enough for spectroscopy work. Until 1960 the metre was defined as the distance between two scratches on a bar of
1487:
1334:(1907): "Nouvelle Détermination du mètre en longueurs d'ondes lumineuses" (= "A new determination of the metre in terms of the wavelength of light").
1051:
600:) defined the international angstrom as precisely 1/6438.4696 of the wavelength of that line (in dry air at 15 °C (hydrogen scale) and 760
619:
In 1960, the metre itself was redefined in spectroscopic terms, which allowed the angstrom to be redefined as being exactly 0.1 nanometres.
1275:" (= "Experimental determination of the value of the meter in terms of the lengths of light waves"); translated to French by Jean-René Benoît.
684:
1029:
1006:
680:
551:
1352:
1297:... It follows that the wavelengths of these emissions, always at 15 °C and at 760 mm, are (averages of three determinations):
1147:
608:
578:, working at the BIPM with specially developed equipment, determined that the length of the international metre standard was equal to
1128:
862:
688:
1441:
1415:
1389:
823:
1246:
1256:
1023:
965:
945:
256:
597:
1084:
1460:, Beijing, China. Quote: "... recommends ... 5. that the unique symbol 'au' be used for the astronomical unit."
990:
791:
562:
reported it to be so incorrect that Ångström's corrected results were more in error than the uncorrected ones.
70:
676:
1510:
1405:
503:
302:
101:
523:
408:
31:
17:
635:
1515:
1351:(= "Proceedings of the 7 meeting of the General Conference of Weights and Measures"), pages 85–88.
511:
368:, no matter how the unit is spelled. However, "A" or "A.U." may be used in less formal contexts or
1486:
American
Astronomical Society (2016): "Manuscript Preparation: AJ & ApJ Author Instructions".
1010:
675:
Although still widely used in physics and chemistry, the angstrom is not officially a part of the
596:
vapor. In 1907, the
International Union for Cooperation in Solar Research (which later became the
522:
community, which adopted the unit and named it after him. It subsequently spread to the fields of
455:
1104:
898:
1348:
601:
1202:
1453:
1226:
575:
518:.) Ångström's chart and table of wavelengths in the solar spectrum became widely used in the
1214:
8:
1433:
829:
747:
571:
527:
51:
The width of a hydrogen atom is about 1.1 angstroms; the width of a proton (in black) is
1477:
Quote: "The units of length/distance are Å, nm, μm, mm, cm, m, km, au, light-year, pc."
663:
412:
878:
1437:
1411:
1364:
1252:
1116:
1019:
961:
941:
803:
787:
589:
490:
459:
1272:
1061:
1185:
1164:
1112:
1065:
1056:
783:
746:. However, version 5 of the standard already deprecates that code point and has it
463:
365:
350:
320:
306:
226:
1428:
1273:
Détermination expérimentale de la valeur du mètre en longueurs d'ondes lumineuses
1180:
J. A. Bearden (1965): "Selection of the W Kα₁ as the X-Ray
Wavelength Standard".
416:
400:
376:
349:). The latter spelling is still listed in some dictionaries, but is now rare in
1331:
1490:. Quote: "Use standard abbreviations for ... natural units (e.g., au, pc, cm)."
1349:"Comptes rendus de la 7 réunion de la Conférence générale des poids et mesures"
1232:
786:'s 1921 classical paper on the structure of ice, which gives the c- and a-axis
499:
296:
265:
173:
1458:
Proceedings of the XXVIII General
Assembly of International Astronomical Union
1504:
1327:
1189:
1060:, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "
519:
451:
450:
of a metre as a convenient unit to express the wavelengths of characteristic
436:
396:
1165:
Special
Publication 330: The International System of Units (SI) 2019 Edition
1069:
1005:
510:, in which he expressed the wavelengths of electromagnetic radiation in the
795:
559:
193:
699:
1091:, National Institutes of Standards and Technology. Accessed on 2019-03-02
799:
790:
as 4.52 A.U. and 7.34 A.U., respectively. Ambiguously, the abbreviation "
782:
was unavailable, the unit was sometimes written as "A.U.". An example is
732:
556:
440:
420:
404:
392:
380:
369:
284:
1454:
Resolution B2: On the re-definition of the astronomical unit of length
474:
system of units, and has been increasingly replaced by the nanometre (
902:
530:, and then to other sciences that deal with atomic-scale structures.
299:
292:
288:
155:
922:
Webster's
Encyclopedic Unabridged Dictionary of the English Language
1363:
NIST CODATA - Committee on Data for
Science and Technology (2024):
1336:
Comptes rendus hebdomadaires des séances de l'Académie des sciences
1213:
The 1869 edition (printed by
Ferdinand Dümmler in Berlin) contains
1131:" Lecture slides for MatSci162_172, Geometry; Stanford University.
908:. Accessed on 2024-07-26. Spelling "angstrom" , ; symbols "Å", "A".
543:
507:
432:
428:
388:
133:
662:
line. This auxiliary unit was intended to be accurate to within 5
711:
703:
679:(SI). Up to 2019, it was listed as a compatible unit by both the
593:
547:
276:
1277:
Travaux et Mémoires du Bureau International des Poids et Mesures
46:
834:
424:
83:
985:
Oxford University Press (1986) Entry "Ångström (unit)" in the
632:(symbol: Å*) as 0.202901 times the wavelength of the tungsten
1248:
Lines of Light: Sources of Dispersive Spectroscopy, 1800-1930
779:
341:
280:
272:
247:
728:
384:
353:
texts. Some popular US dictionaries list only the spelling
329:
235:
361:
326:
706:
codification. The third option shall not be used anymore.
232:
471:
638:
514:
in multiples of one ten-millionth of a millimetre (or
1376:
614:
332:
257:
238:
1469:
Oxford Journals (2012): "Instructions for Authors".
881:
in the . Accessed 2024-01-30. Spelling "angstrom" ,
338:
335:
244:
241:
1347:Bureau international des poids et measures (1927):
1146:Bureau international des poids et measures (2019):
857:Oxford University Press (2019) Entry "angstrom" by
323:
229:
865:. Spellings "angstrom" and "ångström"; symbol "Å"
824:Orders of magnitude (length) § 100 picometres
654:
446:In the late 19th century, spectroscopists adopted
1471:Monthly Notices of the Royal Astronomical Society
1228:A Brief (Incomplete) History of Light and Spectra
1502:
727:for the angstrom symbol, which is accessible in
533:
1410:; Chapter 22.2 "Letterlike Symbols", page 839.
1211:] (in French). Uppsala, Sweden: W. Schultz.
470:metre. Yet the angstrom was never part of the
689:European Union's catalogue of units of measure
685:National Institute of Standards and Technology
1109:Proceedings of the Physical Society of London
1083:Ambler Thompson and Barry N. Taylor (2009): "
691:that may be used within its internal market.
305:(1814–1874). It was originally spelled with
1400:
1398:
1388:Council of the European Communities (1979):
1007:International Bureau of Weights and Measures
681:International Bureau of Weights and Measures
588:times the wavelength of the red line of the
1176:
1174:
1158:
1156:
1099:
1097:
1085:B.8 Factors for Units Listed Alphabetically
1079:
1077:
1452:International Astronomical Union (2012): "
981:
979:
977:
975:
973:
932:
930:
916:
914:
873:
871:
853:
851:
849:
609:General Conference on Weights and Measures
565:
45:
1463:
1395:
1184:, volume 137, issue 2B, pages 455B–B461.
893:
891:
889:
887:
1420:
1370:
1357:
1341:
1320:
1265:
1238:
1219:
1200:
1194:
1171:
1153:
1142:
1140:
1121:
1094:
1074:
958:Cambridge English Pronouncing Dictionary
698:
607:This definition was endorsed at the 7th
489:
443:in the range of 4000–7000 Å.
1480:
1446:
1382:
1367:. Symbol: "Å*". Accessed on 2024-07-26.
1001:
999:
970:
950:
927:
911:
868:
846:
14:
1503:
1012:The International System of Units (SI)
884:
802:—about 0.53 Å—or the much larger
761:LATIN CAPITAL LETTER A WITH RING ABOVE
1244:
1137:
750:into the code for the Swedish letter
604:under a gravity of 9.8067 m/s).
1209:Investigations of the solar spectrum
1045:
996:
431:are about 1 angstrom, while that of
778:In older publications, where the Å
538:Although intended to correspond to
506:created a chart of the spectrum of
24:
1407:The Unicode Standard, Version 14.0
1057:Compendium of Chemical Terminology
615:Redefinition in terms of the metre
375:The angstrom is often used in the
25:
1527:
1496:
1429:The Unicode Standard, Version 5.0
1204:Recherches sur le spectre solaire
1150:, complete brochure, 9th edition.
1148:Le système international d'unités
775:), which should be used instead.
670:
1235:website. Accessed on 2024-07-26.
938:Longman Pronunciation Dictionary
622:
598:International Astronomical Union
401:arrangement of atoms in crystals
319:
225:
1426:The Unicode Consortium (2008):
1404:The Unicode Consortium (2021):
1215:sketches of the solar spectrum.
1035:from the original on 2021-06-04
655:{\textstyle \kappa _{\alpha 1}}
1338:, volume 144, pages 1082-1086.
1111:, volume 34, issue 1, page 98
1105:"The Crystal Structure of Ice"
295:. The unit is named after the
13:
1:
1271:Albert A. Michelson (1895): "
1018:(8th ed.), p. 127,
840:
677:International System of Units
534:Early connection to the metre
7:
1475:Archived on 22 October 2012
1127:Arturas Vailionis (2015): "
826:(for objects on this scale)
817:
710:For compatibility reasons,
494:Portrait of Anders Ångström
395:structures, and lengths of
283:, a hundred-millionth of a
10:
1532:
1245:Brand, John C. D. (1995).
1182:Physical Review 2nd series
1117:10.1088/1478-7814/34/1/322
904:Collins English Dictionary
859:Oxford Living Dictionaries
485:
29:
1392:. Accessed on 2011-09-23.
1251:. CRC Press. p. 47.
1103:William H. Bragg (1921):
987:Oxford English Dictionary
694:
524:astronomical spectroscopy
409:electromagnetic radiation
189:
169:
151:
129:
125:
107:
97:
89:
79:
69:
64:
44:
39:
32:Angstrom (disambiguation)
1190:10.1103/PhysRev.137.B455
920:Merriam-Webster (1989):
877:Merriam-Webster (2024):
794:" may also refer to the
592:of electrically excited
512:electromagnetic spectrum
435:is about 0.5 angstroms.
1201:Ångström, A.J. (1868).
1070:10.1351/goldbook.N00350
566:Cadmium line definition
417:atomic (covalent) radii
1488:Archived on 2016-02-21
1353:Archived on 2018-11-18
1133:Archived on 2015-03-19
991:Archived on 2021-11-22
989:, 2nd edition (1986);
936:John C. Wells (2008):
924:. Portland House, 1989
897:HarperCollins (2024):
863:Archived on 2019-03-06
707:
656:
495:
393:microscopic biological
714:assigns a code point
702:
657:
504:Anders Jonas Ångström
493:
360:The unit's symbol is
303:Anders Jonas Ångström
102:Anders Jonas Ångström
1129:Geometry of Crystals
1089:NIST Guide to the SI
956:Peter Roach (2011):
636:
411:, and dimensions of
383:to express sizes of
30:For other uses, see
1511:Non-SI metric units
830:Conversion of units
572:Albert A. Michelson
550:alloy, kept at the
528:atomic spectroscopy
275:; that is, one ten-
120:... is equal to ...
65:General information
1326:Jean-René Benoît,
708:
683:(BIPM) and the US
652:
496:
458:components of the
413:integrated circuit
364:, a letter of the
199:
191:
179:
171:
161:
153:
139:
131:
75:Non-SI metric unit
1442:978-0-321-48091-0
1416:978-1-936213-29-0
804:astronomical unit
788:lattice constants
664:parts per million
590:emission spectrum
478:m) or picometre (
464:chemical elements
460:emission spectrum
217:
216:
108:Conversions
16:(Redirected from
1523:
1491:
1484:
1478:
1467:
1461:
1450:
1444:
1424:
1418:
1402:
1393:
1386:
1380:
1379:
1374:
1368:
1361:
1355:
1345:
1339:
1324:
1318:
1316:
1315:
1312:
1309:
1296:
1295:
1287:
1284:
1269:
1263:
1262:
1242:
1236:
1223:
1217:
1212:
1198:
1192:
1178:
1169:
1160:
1151:
1144:
1135:
1125:
1119:
1101:
1092:
1081:
1072:
1049:
1043:
1042:
1041:
1040:
1034:
1017:
1003:
994:
983:
968:
960:, 18th edition.
954:
948:
934:
925:
918:
909:
899:Entry "angstrom"
895:
882:
879:Entry "angstrom"
875:
866:
855:
813:
811:
774:
770:
766:
762:
759:
756:
754:
745:
741:
737:
726:
723:
720:
718:
661:
659:
658:
653:
651:
650:
587:
586:
583:
576:Jean-René Benoît
541:
517:
481:
477:
469:
449:
377:natural sciences
366:Swedish alphabet
348:
347:
344:
343:
340:
337:
334:
331:
328:
325:
271:
260:
254:
253:
250:
249:
246:
243:
240:
237:
234:
231:
213:
205:
200:
192:
184:
180:
172:
165:
162:
154:
147:
143:
140:
132:
58:
56:
49:
37:
36:
21:
1531:
1530:
1526:
1525:
1524:
1522:
1521:
1520:
1516:Units of length
1501:
1500:
1499:
1494:
1485:
1481:
1468:
1464:
1451:
1447:
1432:; Chapter 15, "
1425:
1421:
1403:
1396:
1387:
1383:
1375:
1371:
1365:"Angstrom star"
1362:
1358:
1346:
1342:
1325:
1321:
1313:
1310:
1307:
1305:
1303:
1294:
1288:
1285:
1282:
1280:
1270:
1266:
1259:
1243:
1239:
1225:ChemTeam (2024)
1224:
1220:
1199:
1195:
1179:
1172:
1161:
1154:
1145:
1138:
1126:
1122:
1102:
1095:
1082:
1075:
1050:
1046:
1038:
1036:
1032:
1026:
1015:
1004:
997:
984:
971:
955:
951:
940:, 3rd edition.
935:
928:
919:
912:
896:
885:
876:
869:
856:
847:
843:
820:
809:
807:
798:of length, the
772:
768:
764:
760:
757:
752:
751:
743:
739:
735:
724:
721:
716:
715:
697:
673:
643:
639:
637:
634:
633:
625:
617:
584:
581:
579:
568:
539:
536:
515:
488:
479:
475:
467:
447:
372:limited media.
370:typographically
322:
318:
307:Swedish letters
269:
258:
228:
224:
212:
203:
201:
198:
190:
182:
178:
170:
163:
160:
152:
145:
141:
138:
130:
60:
54:
52:
35:
28:
23:
22:
15:
12:
11:
5:
1529:
1519:
1518:
1513:
1498:
1497:External links
1495:
1493:
1492:
1479:
1462:
1445:
1419:
1394:
1381:
1369:
1356:
1340:
1319:
1301:
1292:
1264:
1257:
1237:
1218:
1193:
1170:
1152:
1136:
1120:
1093:
1073:
1044:
1024:
995:
969:
949:
926:
910:
883:
867:
844:
842:
839:
838:
837:
832:
827:
819:
816:
696:
693:
672:
671:Current status
669:
649:
646:
642:
624:
621:
616:
613:
570:In 1892–1895,
567:
564:
535:
532:
487:
484:
452:spectral lines
397:chemical bonds
266:unit of length
215:
214:
210:
196:
187:
186:
176:
174:Imperial units
167:
166:
158:
149:
148:
136:
127:
126:
123:
122:
117:
110:
109:
105:
104:
99:
95:
94:
91:
87:
86:
81:
77:
76:
73:
67:
66:
62:
61:
50:
42:
41:
27:Unit of length
26:
9:
6:
4:
3:
2:
1528:
1517:
1514:
1512:
1509:
1508:
1506:
1489:
1483:
1476:
1472:
1466:
1459:
1455:
1449:
1443:
1439:
1436:", page 493.
1435:
1431:
1430:
1423:
1417:
1413:
1409:
1408:
1401:
1399:
1391:
1385:
1373:
1366:
1360:
1354:
1350:
1344:
1337:
1333:
1329:
1328:Charles Fabry
1323:
1300:
1291:
1278:
1274:
1268:
1260:
1258:9782884491631
1254:
1250:
1249:
1241:
1234:
1230:
1229:
1222:
1216:
1210:
1206:
1205:
1197:
1191:
1187:
1183:
1177:
1175:
1167:
1166:
1162:NIST (2019):
1159:
1157:
1149:
1143:
1141:
1134:
1130:
1124:
1118:
1114:
1110:
1106:
1100:
1098:
1090:
1086:
1080:
1078:
1071:
1067:
1063:
1059:
1058:
1053:
1048:
1031:
1027:
1025:92-822-2213-6
1021:
1014:
1013:
1008:
1002:
1000:
992:
988:
982:
980:
978:
976:
974:
967:
966:9780521152532
963:
959:
953:
947:
946:9781405881180
943:
939:
933:
931:
923:
917:
915:
907:
905:
900:
894:
892:
890:
888:
880:
874:
872:
864:
860:
854:
852:
850:
845:
836:
833:
831:
828:
825:
822:
821:
815:
805:
801:
797:
793:
789:
785:
781:
776:
763:(HTML entity
749:
740:Å
734:
730:
725:ANGSTROM SIGN
713:
705:
701:
692:
690:
686:
682:
678:
668:
665:
647:
644:
640:
631:
630:Angstrom Star
623:Angstrom star
620:
612:
610:
605:
603:
599:
595:
591:
577:
573:
563:
561:
558:
553:
549:
545:
531:
529:
525:
521:
520:solar physics
513:
509:
505:
501:
492:
483:
473:
465:
461:
457:
456:monochromatic
453:
444:
442:
438:
437:Visible light
434:
430:
426:
422:
418:
414:
410:
406:
402:
398:
394:
390:
386:
382:
378:
373:
371:
367:
363:
358:
356:
352:
346:
316:
313:and later as
312:
308:
304:
301:
298:
294:
290:
286:
282:
278:
274:
267:
263:
262:
252:
222:
209:
197:
195:
188:
177:
175:
168:
159:
157:
150:
137:
135:
128:
124:
121:
118:
116:
112:
111:
106:
103:
100:
96:
92:
88:
85:
82:
78:
74:
72:
68:
63:
48:
43:
38:
33:
19:
1482:
1470:
1465:
1457:
1448:
1427:
1422:
1406:
1384:
1378:p. 285.
1372:
1359:
1343:
1335:
1332:Alfred Pérot
1322:
1298:
1289:
1276:
1267:
1247:
1240:
1227:
1221:
1208:
1203:
1196:
1181:
1163:
1123:
1108:
1088:
1055:
1047:
1037:, retrieved
1011:
986:
957:
952:
937:
921:
903:
858:
777:
709:
674:
629:
626:
618:
606:
569:
560:Henri Tresca
537:
497:
445:
374:
359:
354:
314:
310:
220:
218:
207:
194:Planck units
119:
114:
80:Unit of
1231:, from the
796:atomic unit
765:Å
744:Å
736:Å
557:metrologist
441:wavelengths
415:parts. The
405:wavelengths
146:0.1 nm
98:Named after
71:Unit system
1505:Categories
1317:" (where "
1039:2021-12-16
841:References
773:Å
769:Å
748:normalized
516:10 mm
502:physicist
421:phosphorus
381:technology
293:picometres
285:centimetre
185:10 in
164:10 cm
59:angstroms.
812:10 m
645:α
641:κ
498:In 1868,
389:molecules
300:physicist
291:, or 100
289:nanometre
277:billionth
268:equal to
156:CGS Units
142:10 m
113:1 Å
18:Angstroms
1233:ChemTeam
1062:Ångström
1030:archived
1009:(2006),
861:online;
818:See also
722:Å
544:platinum
508:sunlight
433:hydrogen
429:chlorine
355:angstrom
315:ångström
311:Ångström
221:angstrom
206:10
181:3.937008
134:SI Units
40:angstrom
1434:Symbols
901:in the
806:(about
731:as the
712:Unicode
704:Unicode
594:cadmium
548:iridium
500:Swedish
486:History
351:English
297:Swedish
264:) is a
1440:
1414:
1330:, and
1255:
1022:
964:
944:
906:online
835:X unit
758:Å
755:
753:U+00C5
733:entity
719:
717:U+212B
695:Symbol
427:, and
425:sulfur
287:, 0.1
261:-strəm
115:in ...
90:Symbol
84:Length
1306:0,643
1286:163,5
1207:[
1052:IUPAC
1033:(PDF)
1016:(PDF)
784:Bragg
780:glyph
771:, or
742:, or
585:163.5
462:) of
385:atoms
309:, as
281:metre
279:of a
202:6.187
1438:ISBN
1412:ISBN
1253:ISBN
1020:ISBN
962:ISBN
942:ISBN
800:bohr
792:a.u.
729:HTML
602:mmHg
574:and
552:BIPM
482:m).
439:has
379:and
219:The
1456:".
1308:847
1283:553
1186:doi
1113:doi
1087:".
1066:doi
1064:".
814:).
808:1.5
582:553
419:of
407:of
259:ANG
53:1.7
1507::
1473:.
1397:^
1311:22
1304:=
1173:^
1155:^
1139:^
1107:.
1096:^
1076:^
1054:,
1028:,
998:^
972:^
929:^
913:^
886:^
870:^
848:^
767:,
738:,
540:10
526:,
480:10
476:10
472:SI
468:10
448:10
423:,
403:,
399:,
391:,
387:,
357:.
342:əm
270:10
255:;
248:əm
144:=
57:10
1314:μ
1302:R
1299:λ
1293:R
1290:λ
1281:1
1261:.
1188::
1168:.
1115::
1068::
810:×
648:1
580:1
546:-
454:(
362:Å
345:/
339:r
336:t
333:s
330:ŋ
327:ɒ
324:ˈ
321:/
317:(
273:m
251:/
245:r
242:t
239:s
236:ŋ
233:æ
230:ˈ
227:/
223:(
211:P
208:l
204:×
183:×
93:Å
55:×
34:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.