2551:. Arnold Bondi also conducted a study of this type, published in 1964, although he also considered other methods of determining the van der Waals radius in coming to his final estimates. Some of Bondi's figures are given in the table at the top of this article, and they remain the most widely used "consensus" values for the van der Waals radii of the elements. Scott Rowland and Robin Taylor re-examined these 1964 figures in the light of more recent crystallographic data: on the whole, the agreement was very good, although they recommend a value of 1.09 Å for the van der Waals radius of
1566:
1303:
1445:
1145:
284:
1781:
363:, is the atomic property most directly related to the van der Waals radius. It is the volume "occupied" by an individual atom (or molecule). The van der Waals volume may be calculated if the van der Waals radii (and, for molecules, the inter-atomic distances, and angles) are known. For a single atom, it is the volume of a sphere whose radius is the van der Waals radius of the atom:
2071:
attractive and repulsive forces are considered. For example, the mutual repulsion between molecules has the effect of excluding neighbors from a certain amount of space around each molecule. Thus, a fraction of the total space becomes unavailable to each molecule as it executes random motion. In the equation of state, this volume of exclusion (
2542:
molecules can approach one another is given by the sum of their van der Waals radii. By examining a large number of structures of molecular crystals, it is possible to find a minimum radius for each type of atom such that other non-bonded atoms do not encroach any closer. This approach was first
1865:
of a number of different experimental values, and, for this reason, different tables will often have different values for the van der Waals radius of the same atom. Indeed, there is no reason to assume that the van der Waals radius is a fixed property of the atom in all circumstances: rather, it
2070:
The van der Waals equation also has a microscopic interpretation: molecules interact with one another. The interaction is strongly repulsive at a very short distance, becomes mildly attractive at the intermediate range, and vanishes at a long distance. The ideal gas law must be corrected when
3069:
When the atomic polarizability is quoted in units of volume such as Å, as is often the case, it is equal to the van der Waals volume. However, the term "atomic polarizability" is preferred as polarizability is a precisely defined (and measurable)
1996:
2512:
2672:
2928:
3042:
426:
2141:
2396:
2789:
1891:
434:. The van der Waals volume of a molecule is always smaller than the sum of the van der Waals volumes of the constituent atoms: the atoms can be said to "overlap" when they form
495:
of the volume of the gas, the rest is empty space. Hence the molar van der Waals volume, which only counts the volume occupied by the atoms or molecules, is usually about
2041:
3127:
Rowland RS, Taylor R (1996). "Intermolecular nonbonded contact distances in organic crystal structures: comparison with distances expected from van der Waals radii".
2412: = 2.11 Å (≈ 200 picometers). This method may be extended to diatomic gases by approximating the molecule as a rod with rounded ends where the diameter is
2429:
2603:
2864:
2574:) and so the distance between the nuclei can be considered to be equal to twice the van der Waals radius. The density of solid helium at 1.1 K and 66
2984:
1791:
3083:
3534:
214:
366:
3486:
3339:
305:
2311:
volume can be used to calculate the van der Waals volume of an atom or molecule with experimental data derived from measurements on gases.
2348:
3226:
2064:
3308:
1820:
500:
331:
1802:
2729:
483:
of the substance. In general, at normal laboratory temperatures and pressures, the atoms or molecules of gas only occupy about
1838:
441:
The van der Waals volume of an atom or molecule may also be determined by experimental measurements on gases, notably from the
3529:
309:
255:
2094:
3161:
2566:) is to consider the case of solid helium, where the atoms are held together only by van der Waals forces (rather than by
2556:
1795:
3524:
251:
2723:
207:
3329:
294:
313:
298:
1801:
Help add sources such as review articles, monographs, or textbooks. Please also establish the relevance for any
462:. In all three cases, measurements are made on macroscopic samples and it is normal to express the results as
466:
quantities. To find the van der Waals volume of a single atom or molecule, it is necessary to divide by the
3220:
Mantina, Manjeera; Chamberlin, Adam C.; Valero, Rosendo; Cramer, Christopher J.; Truhlar, Donald G. (2009).
3074:, whereas "van der Waals volume" can have any number of definitions depending on the method of measurement.
2852:
3539:
3093:
2305:
2285:
1875:
442:
267:
259:
200:
3103:
629:
431:
2559:, carried out by Santiago Alvareza, provided a new set of values for 93 naturally occurring elements.
1709:
The shade of the box ranges from red to yellow as the radius increases; Gray indicate a lack of data.
3418:
3235:
3098:
538:
526:
3088:
2563:
2531:
2144:
3281:
2017:
3502:
2709:
1850:
1743:
1737:
456:
3508:
3457:
3444:
1853:). These various methods give values for the van der Waals radius which are similar (1–2
3482:
3389:
3335:
3304:
3263:
3071:
2575:
2527:
2335:
1991:{\displaystyle \left(p+a\left({\frac {n}{\tilde {V}}}\right)^{2}\right)({\tilde {V}}-nb)=nRT,}
1751:
1722:
1222:
467:
3426:
3379:
3369:
3253:
3243:
3169:
3136:
2716:
1726:
1280:
1122:
969:
816:
742:
668:
640:
590:
585:
580:
263:
3409:
2515:
575:
570:
565:
560:
555:
550:
545:
182:
177:
3422:
3239:
3475:
3258:
3221:
2845:
2675:
2168:
1880:
The van der Waals equation of state is the simplest and best-known modification of the
1861:) but not identical. Tabulated values of van der Waals radii are obtained by taking a
1846:
518:
449:
1866:
tends to vary with the particular chemical environment of the atom in any given case.
3518:
3361:
3325:
2571:
2567:
2544:
2535:
2323:
1881:
1862:
1316:
510:
435:
167:
2931:
2583:
1587:
1466:
1364:
600:
533:
480:
172:
17:
1716:
1667:
1651:
1643:
1412:
1380:
1372:
595:
463:
283:
2930:
and the electric susceptibility may be calculated from tabulated values of the
2507:{\displaystyle V_{\rm {w}}={4 \over 3}\pi r_{\rm {w}}^{3}+\pi r_{\rm {w}}^{2}d}
2667:{\displaystyle V_{\rm {w}}={\frac {\pi V_{\rm {m}}}{N_{\rm {A}}{\sqrt {18}}}}}
1693:
1522:
1506:
1482:
1420:
1356:
1332:
1308:
1024:
1016:
782:
98:
2923:{\displaystyle \alpha ={\varepsilon _{0}k_{\rm {B}}T \over p}\chi _{\rm {e}}}
2802:
at 0 °C and 101.325 kPa, which corresponds to a molar refractivity
27:
Size of an atom's imaginary sphere representing how close other atoms can get
3430:
1858:
1834:
1635:
1619:
1611:
1603:
1554:
1474:
1450:
1428:
1404:
1396:
1096:
1048:
1032:
1000:
982:
927:
871:
821:
766:
755:
681:
620:
610:
605:
3393:
3267:
3407:
Henshaw, D.G. (1958). "Structure of Solid Helium by
Neutron Diffraction".
2981:. The polarizability is related the van der Waals volume by the relation
1805:
cited. Unsourced or poorly sourced material may be challenged and removed.
2969:
at 0 °C and 101.325 kPa, which corresponds to a polarizability
2552:
2257:
2219:
2200:
1885:
1854:
1841:, from measurements of atomic spacing between pairs of unbonded atoms in
1675:
1571:
1498:
1490:
1388:
1285:
1262:
1254:
1230:
1206:
1174:
1166:
1150:
1088:
974:
943:
863:
855:
847:
839:
798:
724:
708:
645:
118:
88:
68:
48:
40:
3173:
3140:
3374:
3356:
1842:
1659:
1595:
1579:
1546:
1530:
1514:
1348:
1340:
1324:
1246:
1198:
1182:
1158:
1127:
1064:
1040:
1008:
992:
959:
951:
935:
919:
829:
774:
673:
615:
266:
and to demonstrate the physical consequences of their size through the
3384:
3248:
3037:{\displaystyle V_{\rm {w}}={1 \over {4\pi \varepsilon _{0}}}\alpha ,}
2315:
2238:
2091:). The other term that is introduced in the van der Waals equation,
1627:
1538:
1458:
1293:
1190:
1135:
1104:
1072:
1056:
903:
895:
887:
790:
747:
716:
700:
658:
247:
243:
128:
108:
78:
58:
2143:, describes a weak attractive force among molecules (known as the
1270:
1112:
806:
692:
2555:
as opposed to Bondi's 1.20 Å. A more recent analysis of the
1238:
1214:
911:
879:
732:
239:
3473:
Huheey, James E.; Keiter, Ellen A.; Keiter, Richard L. (1997).
479:
The molar van der Waals volume should not be confused with the
1845:
or from measurements of electrical or optical properties (the
1774:
1080:
277:
262:, as he was the first to recognise that atoms were not simply
2693: = 23.0 Å, corresponding to a van der Waals radius
2059:
corrects for finite atomic or molecular sizes; the value of
3477:
Inorganic
Chemistry: Principles of Structure and Reactivity
2562:
A simple example of the use of crystallographic data (here
421:{\displaystyle V_{\rm {w}}={4 \over 3}\pi r_{\rm {w}}^{3}.}
3222:"Consistent van der Waals Radii for the Whole Main Group"
2538:. In principle, the closest that two atoms belonging to
2077:) should be subtracted from the volume of the container (
2157:
29:
3059: = 0.2073 Å by this method, corresponding to
2954: − 1. The electric susceptibility of helium
2155:
decreases and molecules become more crowded together.
2136:{\textstyle a\left({\frac {n}{\tilde {V}}}\right)^{2}}
2097:
2063:
equals the van der Waals volume per mole of the gas.
2047:
is the specific gas constant on a unit mole basis and
3159:
Bondi, A. (1964). "van der Waals
Volumes and Radii".
2987:
2867:
2732:
2606:
2432:
2426:. The algebra is more complicated, but the relation
2398:
Therefore, the van der Waals volume of a single atom
2351:
2020:
1894:
369:
1837:
properties of gases (the original method), from the
2391:{\displaystyle V_{\rm {w}}={b \over {N_{\rm {A}}}}}
3474:
3036:
2922:
2783:
2666:
2506:
2390:
2135:
2035:
2006:is the number of moles of the gas in question and
1990:
420:
499:times smaller than the molar volume for a gas at
430:For a molecule, it is the volume enclosed by the
3357:"A cartography of the van der Waals territories"
2284:in Å (or in 100 picometers) calculated from the
3122:
3120:
3118:
1833:Van der Waals radii may be determined from the
2055:is a correction for intermolecular forces and
1714:Unless indicated otherwise, the data is from
208:
8:
3303:(62nd ed.). Boca Raton, FL: CRC Press.
3154:
3152:
3150:
2814:. Dividing by the Avogadro constant gives
2784:{\displaystyle A={\frac {RT(n^{2}-1)}{3p}}}
2405: = 39.36 Å, which corresponds to
312:. Unsourced material may be challenged and
3215:
3213:
3211:
3209:
3207:
3205:
3203:
2674:where the factor of π/√18 arises from the
1692:Values for the van der Waals radii are in
215:
201:
155:
3481:(4th ed.). New York: Prentice Hall.
3383:
3373:
3257:
3247:
3201:
3199:
3197:
3195:
3193:
3191:
3189:
3187:
3185:
3183:
3019:
3008:
3003:
2993:
2992:
2986:
2913:
2912:
2892:
2891:
2881:
2874:
2866:
2755:
2739:
2731:
2654:
2647:
2646:
2633:
2632:
2622:
2612:
2611:
2605:
2495:
2489:
2488:
2472:
2466:
2465:
2448:
2438:
2437:
2431:
2378:
2377:
2372:
2367:
2357:
2356:
2350:
2127:
2111:
2106:
2096:
2022:
2021:
2019:
1950:
1949:
1935:
1919:
1914:
1893:
1821:Learn how and when to remove this message
409:
403:
402:
385:
375:
374:
368:
332:Learn how and when to remove this message
3334:. Ithaca, NY: Cornell University Press.
3084:Atomic radii of the elements (data page)
2829: = 0.8685 Å, corresponding to
2600:. The van der Waals volume is given by
2514:can be solved by the normal methods for
3114:
1760:shows natural occurrence of the element
1315:
158:
3282:"van der Waals Radius of the elements"
3044:so the van der Waals volume of helium
2322: = 23.7 cm/mol. Helium is a
1586:
1465:
1363:
3301:CRC Handbook of Chemistry and Physics
1666:
1650:
1642:
1411:
1379:
1371:
254:for another atom. It is named after
7:
3503:van der Waals Radius of the elements
1521:
1505:
1481:
1419:
1355:
1331:
1307:
1023:
1015:
781:
310:adding citations to reliable sources
3227:The Journal of Physical Chemistry A
2326:, and each mole of helium contains
1634:
1618:
1610:
1602:
1553:
1473:
1449:
1427:
1403:
1395:
1095:
1047:
1031:
999:
981:
926:
870:
820:
765:
754:
680:
3509:van der Waals Radius – Periodicity
3458:Dielectric Properties of Materials
2994:
2914:
2893:
2648:
2634:
2613:
2490:
2467:
2439:
2379:
2358:
2289:of some diatomic gases. Values of
1733:
1674:
1570:
1497:
1489:
1387:
1284:
1261:
1253:
1229:
1205:
1173:
1165:
1149:
1087:
973:
942:
862:
854:
846:
838:
797:
723:
707:
644:
404:
376:
25:
2422:and the internuclear distance is
1658:
1594:
1578:
1545:
1529:
1513:
1347:
1339:
1323:
1245:
1221:
1197:
1181:
1157:
1126:
1063:
1039:
1007:
991:
958:
950:
934:
918:
828:
773:
672:
501:standard temperature and pressure
1884:to account for the behaviour of
1779:
1626:
1564:
1537:
1457:
1443:
1301:
1292:
1189:
1143:
1134:
1103:
1071:
1055:
902:
894:
886:
789:
746:
715:
699:
657:
282:
3331:The Nature of the Chemical Bond
2791:The refractive index of helium
2549:The Nature of the Chemical Bond
1870:Van der Waals equation of state
1269:
1111:
805:
691:
268:van der Waals equation of state
3535:Johannes Diderik van der Waals
3299:Weast, Robert C., ed. (1981).
2767:
2748:
2116:
2027:
2014:depend on the particular gas,
1970:
1955:
1946:
1924:
1237:
1213:
910:
878:
731:
256:Johannes Diderik van der Waals
139:van der Waals radii taken from
1:
2557:Cambridge Structural Database
2522:Crystallographic measurements
1796:secondary or tertiary sources
1079:
143:Values from other sources may
2264:
2245:
2226:
2207:
2036:{\displaystyle {\tilde {V}}}
507:Table of van der Waals radii
252:distance of closest approach
3355:Alvareza, Santiago (2013).
2851:of a gas is related to its
2715:of a gas is related to its
141:Bondi's compilation (1964).
3556:
2051:the absolute temperature;
1873:
1732:
1713:
1708:
1691:
1684:
1437:
762:
688:
654:
634:
619:
614:
609:
604:
599:
594:
589:
584:
579:
574:
569:
564:
559:
554:
549:
544:
542:
537:
532:
524:
513:
3445:Refractive index of gases
2275:
1803:primary research articles
1563:
1442:
137:
3456:Kaye & Laby Tables,
3443:Kaye & Laby Tables,
2147:), which increases when
1788:This scientific article
1771:Methods of determination
3431:10.1103/PhysRev.109.328
2853:electric susceptibility
2724:Lorentz–Lorenz equation
2286:van der Waals constants
517:of the elements in the
3094:van der Waals molecule
3038:
2924:
2785:
2668:
2508:
2392:
2306:van der Waals constant
2137:
2067:vary from gas to gas.
2037:
1992:
1876:Van der Waals equation
1727:Wolfram Research, Inc.
443:van der Waals constant
422:
260:Nobel Prize in Physics
145:differ significantly (
3530:Intermolecular forces
3104:van der Waals surface
3066: = 0.37 Å.
3039:
2932:relative permittivity
2925:
2836: = 0.59 Å.
2786:
2700: = 1.76 Å.
2669:
2582:, corresponding to a
2530:are held together by
2509:
2393:
2138:
2038:
1993:
432:van der Waals surface
423:
258:, winner of the 1910
246:of an imaginary hard
3505:at PeriodicTable.com
3099:van der Waals strain
2985:
2865:
2730:
2604:
2547:in his seminal work
2532:van der Waals forces
2430:
2349:
2277:van der Waals radii
2095:
2018:
1892:
515:Van der Waals radius
367:
346:van der Waals volume
306:improve this section
274:van der Waals volume
229:van der Waals radius
188:Van der Waals radius
31:van der Waals radii
3525:Chemical properties
3423:1958PhRv..109..328H
3240:2009JPCA..113.5806M
3174:10.1021/j100785a001
3089:van der Waals force
2940:using the relation
2564:neutron diffraction
2526:The molecules in a
2500:
2477:
2145:van der Waals force
414:
32:
18:Van der Waals radii
3511:at WebElements.com
3375:10.1039/C3DT50599E
3034:
2920:
2781:
2710:molar refractivity
2704:Molar refractivity
2676:packing of spheres
2664:
2580:0.214(6) g/cm
2504:
2484:
2461:
2388:
2297:from Weast (1981).
2133:
2033:
1988:
1851:molar refractivity
457:molar refractivity
418:
398:
355:, also called the
30:
3488:978-0-06-042995-9
3341:978-0-8014-0333-0
3249:10.1021/jp8111556
3234:(19): 5806–5812.
3141:10.1021/jp953141+
3135:(18): 7384–7391.
3072:physical quantity
3026:
2906:
2779:
2662:
2659:
2528:molecular crystal
2456:
2386:
2336:Avogadro constant
2302:
2301:
2298:
2121:
2119:
2030:
1958:
1929:
1927:
1831:
1830:
1823:
1790:needs additional
1768:
1767:
632:
530:
468:Avogadro constant
393:
342:
341:
334:
250:representing the
225:
224:
154:
153:
150:
16:(Redirected from
3547:
3492:
3480:
3461:
3454:
3448:
3441:
3435:
3434:
3404:
3398:
3397:
3387:
3377:
3352:
3346:
3345:
3322:
3316:
3314:
3296:
3290:
3289:
3278:
3272:
3271:
3261:
3251:
3217:
3178:
3177:
3156:
3145:
3144:
3124:
3058:
3056:
3043:
3041:
3040:
3035:
3027:
3025:
3024:
3023:
3004:
2999:
2998:
2997:
2980:
2978:
2968:
2966:
2929:
2927:
2926:
2921:
2919:
2918:
2917:
2907:
2902:
2898:
2897:
2896:
2886:
2885:
2875:
2861:by the relation
2828:
2826:
2813:
2811:
2801:
2800:
2790:
2788:
2787:
2782:
2780:
2778:
2770:
2760:
2759:
2740:
2721:
2717:refractive index
2714:
2692:
2690:
2673:
2671:
2670:
2665:
2663:
2661:
2660:
2655:
2653:
2652:
2651:
2640:
2639:
2638:
2637:
2623:
2618:
2617:
2616:
2599:
2597:
2581:
2513:
2511:
2510:
2505:
2499:
2494:
2493:
2476:
2471:
2470:
2457:
2449:
2444:
2443:
2442:
2425:
2421:
2397:
2395:
2394:
2389:
2387:
2385:
2384:
2383:
2382:
2368:
2363:
2362:
2361:
2333:
2331:
2276:
2158:
2154:
2150:
2142:
2140:
2139:
2134:
2132:
2131:
2126:
2122:
2120:
2112:
2107:
2090:
2080:
2076:
2062:
2058:
2054:
2050:
2046:
2042:
2040:
2039:
2034:
2032:
2031:
2023:
2013:
2009:
2005:
2001:
1997:
1995:
1994:
1989:
1960:
1959:
1951:
1945:
1941:
1940:
1939:
1934:
1930:
1928:
1920:
1915:
1826:
1819:
1815:
1812:
1806:
1783:
1782:
1775:
1761:
1754:
1748:
1746:
1740:
1703:
1701:
1678:
1670:
1662:
1654:
1646:
1638:
1630:
1622:
1614:
1606:
1598:
1590:
1582:
1574:
1568:
1567:
1557:
1549:
1541:
1533:
1525:
1517:
1509:
1501:
1493:
1485:
1477:
1469:
1461:
1453:
1447:
1446:
1431:
1423:
1415:
1407:
1399:
1391:
1383:
1375:
1367:
1359:
1351:
1343:
1335:
1327:
1319:
1311:
1305:
1304:
1296:
1288:
1273:
1265:
1257:
1249:
1241:
1233:
1225:
1217:
1209:
1201:
1193:
1185:
1177:
1169:
1161:
1153:
1147:
1146:
1138:
1130:
1115:
1107:
1099:
1091:
1083:
1075:
1067:
1059:
1051:
1043:
1035:
1027:
1019:
1011:
1003:
995:
985:
977:
962:
954:
946:
938:
930:
922:
914:
906:
898:
890:
882:
874:
866:
858:
850:
842:
832:
824:
809:
801:
793:
785:
777:
769:
758:
750:
735:
727:
719:
711:
703:
695:
684:
676:
661:
648:
627:
525:
511:
498:
494:
493:
492:
487:
427:
425:
424:
419:
413:
408:
407:
394:
386:
381:
380:
379:
361:molecular volume
337:
330:
326:
323:
317:
286:
278:
217:
210:
203:
156:
138:
33:
21:
3555:
3554:
3550:
3549:
3548:
3546:
3545:
3544:
3515:
3514:
3499:
3489:
3472:
3469:
3467:Further reading
3464:
3455:
3451:
3442:
3438:
3410:Physical Review
3406:
3405:
3401:
3368:(24): 8617–36.
3354:
3353:
3349:
3342:
3324:
3323:
3319:
3311:
3298:
3297:
3293:
3280:
3279:
3275:
3219:
3218:
3181:
3158:
3157:
3148:
3126:
3125:
3116:
3112:
3080:
3065:
3054:
3052:
3050:
3015:
2988:
2983:
2982:
2976:
2974:
2964:
2962:
2960:
2953:
2946:
2939:
2908:
2887:
2877:
2876:
2863:
2862:
2860:
2842:
2835:
2824:
2822:
2820:
2809:
2807:
2798:
2796:
2771:
2751:
2741:
2728:
2727:
2719:
2712:
2706:
2699:
2688:
2686:
2684:
2642:
2641:
2628:
2624:
2607:
2602:
2601:
2595:
2593:
2591:
2579:
2524:
2516:cubic functions
2433:
2428:
2427:
2423:
2420:
2413:
2411:
2404:
2373:
2352:
2347:
2346:
2344:
2329:
2327:
2288:
2283:
2194:
2185:
2152:
2148:
2102:
2101:
2093:
2092:
2082:
2078:
2072:
2060:
2056:
2052:
2048:
2044:
2043:is the volume,
2016:
2015:
2011:
2007:
2003:
1999:
1910:
1909:
1899:
1895:
1890:
1889:
1878:
1872:
1857:, 100–200
1827:
1816:
1810:
1807:
1800:
1784:
1780:
1773:
1764:
1763:
1756:
1750:
1744:
1742:
1736:
1699:
1697:
1676:
1668:
1660:
1652:
1644:
1636:
1628:
1620:
1612:
1604:
1596:
1588:
1580:
1572:
1565:
1555:
1547:
1539:
1531:
1523:
1515:
1507:
1499:
1491:
1483:
1475:
1467:
1459:
1451:
1444:
1438:
1429:
1421:
1413:
1405:
1397:
1389:
1381:
1373:
1365:
1357:
1349:
1341:
1333:
1325:
1317:
1309:
1302:
1294:
1286:
1271:
1263:
1255:
1247:
1239:
1231:
1223:
1215:
1207:
1199:
1191:
1183:
1175:
1167:
1159:
1151:
1144:
1136:
1128:
1113:
1105:
1097:
1089:
1081:
1073:
1065:
1057:
1049:
1041:
1033:
1025:
1017:
1009:
1001:
993:
983:
975:
960:
952:
944:
936:
928:
920:
912:
904:
896:
888:
880:
872:
864:
856:
848:
840:
830:
822:
807:
799:
791:
783:
775:
767:
763:
756:
748:
733:
725:
717:
709:
701:
693:
689:
682:
674:
659:
655:
651:
646:
635:
509:
496:
490:
489:
485:
484:
475:
370:
365:
364:
353:
338:
327:
321:
318:
303:
287:
276:
237:
221:
192:
183:Metallic radius
178:Covalent radius
144:
142:
140:
28:
23:
22:
15:
12:
11:
5:
3553:
3551:
3543:
3542:
3537:
3532:
3527:
3517:
3516:
3513:
3512:
3506:
3498:
3497:External links
3495:
3494:
3493:
3487:
3468:
3465:
3463:
3462:
3449:
3436:
3417:(2): 328–330.
3399:
3347:
3340:
3326:Pauling, Linus
3317:
3309:
3291:
3273:
3179:
3168:(3): 441–451.
3162:J. Phys. Chem.
3146:
3113:
3111:
3108:
3107:
3106:
3101:
3096:
3091:
3086:
3079:
3076:
3063:
3048:
3033:
3030:
3022:
3018:
3014:
3011:
3007:
3002:
2996:
2991:
2958:
2951:
2944:
2937:
2916:
2911:
2905:
2901:
2895:
2890:
2884:
2880:
2873:
2870:
2858:
2846:polarizability
2841:
2840:Polarizability
2838:
2833:
2818:
2777:
2774:
2769:
2766:
2763:
2758:
2754:
2750:
2747:
2744:
2738:
2735:
2705:
2702:
2697:
2682:
2658:
2650:
2645:
2636:
2631:
2627:
2621:
2615:
2610:
2589:
2572:metallic bonds
2536:chemical bonds
2523:
2520:
2503:
2498:
2492:
2487:
2483:
2480:
2475:
2469:
2464:
2460:
2455:
2452:
2447:
2441:
2436:
2418:
2409:
2402:
2381:
2376:
2371:
2366:
2360:
2355:
2342:
2300:
2299:
2281:
2273:
2272:
2269:
2266:
2263:
2260:
2254:
2253:
2250:
2247:
2244:
2241:
2235:
2234:
2231:
2228:
2225:
2222:
2216:
2215:
2212:
2209:
2206:
2203:
2197:
2196:
2192:
2187:
2183:
2178:
2172:
2162:
2130:
2125:
2118:
2115:
2110:
2105:
2100:
2029:
2026:
1987:
1984:
1981:
1978:
1975:
1972:
1969:
1966:
1963:
1957:
1954:
1948:
1944:
1938:
1933:
1926:
1923:
1918:
1913:
1908:
1905:
1902:
1898:
1874:Main article:
1871:
1868:
1847:polarizability
1839:critical point
1829:
1828:
1787:
1785:
1778:
1772:
1769:
1766:
1765:
1734:
1730:
1729:
1725:function from
1711:
1710:
1706:
1705:
1689:
1688:
1682:
1681:
1673:
1665:
1657:
1649:
1641:
1633:
1625:
1617:
1609:
1601:
1593:
1585:
1577:
1569:
1561:
1560:
1552:
1544:
1536:
1528:
1520:
1512:
1504:
1496:
1488:
1480:
1472:
1464:
1456:
1448:
1440:
1439:
1435:
1434:
1426:
1418:
1410:
1402:
1394:
1386:
1378:
1370:
1362:
1354:
1346:
1338:
1330:
1322:
1314:
1306:
1299:
1291:
1283:
1277:
1276:
1268:
1260:
1252:
1244:
1236:
1228:
1220:
1212:
1204:
1196:
1188:
1180:
1172:
1164:
1156:
1148:
1141:
1133:
1125:
1119:
1118:
1110:
1102:
1094:
1086:
1078:
1070:
1062:
1054:
1046:
1038:
1030:
1022:
1014:
1006:
998:
990:
988:
980:
972:
966:
965:
957:
949:
941:
933:
925:
917:
909:
901:
893:
885:
877:
869:
861:
853:
845:
837:
835:
827:
819:
813:
812:
804:
796:
788:
780:
772:
764:
761:
753:
745:
739:
738:
730:
722:
714:
706:
698:
690:
687:
679:
671:
665:
664:
656:
653:
643:
637:
636:
633:
624:
623:
618:
613:
608:
603:
598:
593:
588:
583:
578:
573:
568:
563:
558:
553:
548:
543:
541:
536:
531:
522:
521:
519:periodic table
508:
505:
473:
450:polarizability
436:chemical bonds
417:
412:
406:
401:
397:
392:
389:
384:
378:
373:
351:
340:
339:
290:
288:
281:
275:
272:
235:
223:
222:
220:
219:
212:
205:
197:
194:
193:
191:
190:
185:
180:
175:
170:
164:
161:
160:
159:Types of radii
152:
151:
135:
134:
131:
125:
124:
121:
115:
114:
111:
105:
104:
101:
95:
94:
91:
85:
84:
81:
75:
74:
71:
65:
64:
61:
55:
54:
51:
45:
44:
37:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
3552:
3541:
3540:Atomic radius
3538:
3536:
3533:
3531:
3528:
3526:
3523:
3522:
3520:
3510:
3507:
3504:
3501:
3500:
3496:
3490:
3484:
3479:
3478:
3471:
3470:
3466:
3459:
3453:
3450:
3446:
3440:
3437:
3432:
3428:
3424:
3420:
3416:
3412:
3411:
3403:
3400:
3395:
3391:
3386:
3381:
3376:
3371:
3367:
3364:
3363:
3362:Dalton Trans.
3358:
3351:
3348:
3343:
3337:
3333:
3332:
3327:
3321:
3318:
3312:
3310:0-8493-0462-8
3306:
3302:
3295:
3292:
3287:
3283:
3277:
3274:
3269:
3265:
3260:
3255:
3250:
3245:
3241:
3237:
3233:
3229:
3228:
3223:
3216:
3214:
3212:
3210:
3208:
3206:
3204:
3202:
3200:
3198:
3196:
3194:
3192:
3190:
3188:
3186:
3184:
3180:
3175:
3171:
3167:
3164:
3163:
3155:
3153:
3151:
3147:
3142:
3138:
3134:
3130:
3129:J. Phys. Chem
3123:
3121:
3119:
3115:
3109:
3105:
3102:
3100:
3097:
3095:
3092:
3090:
3087:
3085:
3082:
3081:
3077:
3075:
3073:
3067:
3062:
3047:
3031:
3028:
3020:
3016:
3012:
3009:
3005:
3000:
2989:
2979:10 C⋅m/V
2972:
2957:
2950:
2943:
2936:
2933:
2909:
2903:
2899:
2888:
2882:
2878:
2871:
2868:
2857:
2854:
2850:
2847:
2839:
2837:
2832:
2817:
2812:10 m/mol
2805:
2794:
2775:
2772:
2764:
2761:
2756:
2752:
2745:
2742:
2736:
2733:
2725:
2718:
2711:
2703:
2701:
2696:
2681:
2677:
2656:
2643:
2629:
2625:
2619:
2608:
2598:10 m/mol
2588:
2585:
2577:
2573:
2569:
2565:
2560:
2558:
2554:
2550:
2546:
2545:Linus Pauling
2541:
2537:
2533:
2529:
2521:
2519:
2517:
2501:
2496:
2485:
2481:
2478:
2473:
2462:
2458:
2453:
2450:
2445:
2434:
2417:
2408:
2401:
2374:
2369:
2364:
2353:
2341:
2337:
2325:
2324:monatomic gas
2321:
2317:
2312:
2310:
2307:
2296:
2292:
2287:
2280:
2274:
2270:
2267:
2261:
2259:
2256:
2255:
2251:
2248:
2242:
2240:
2237:
2236:
2232:
2229:
2223:
2221:
2218:
2217:
2213:
2210:
2204:
2202:
2199:
2198:
2191:
2188:
2182:
2179:
2176:
2173:
2170:
2166:
2163:
2160:
2159:
2156:
2151:increases or
2146:
2128:
2123:
2113:
2108:
2103:
2098:
2089:
2085:
2075:
2068:
2066:
2024:
2002:is pressure,
1985:
1982:
1979:
1976:
1973:
1967:
1964:
1961:
1952:
1942:
1936:
1931:
1921:
1916:
1911:
1906:
1903:
1900:
1896:
1887:
1883:
1882:ideal gas law
1877:
1869:
1867:
1864:
1863:weighted mean
1860:
1856:
1852:
1848:
1844:
1840:
1836:
1825:
1822:
1814:
1804:
1798:
1797:
1793:
1786:
1777:
1776:
1770:
1762:
1759:
1753:
1747:
1739:
1731:
1728:
1724:
1720:
1718:
1712:
1707:
1695:
1690:
1687:
1683:
1679:
1671:
1663:
1655:
1647:
1639:
1631:
1623:
1615:
1607:
1599:
1591:
1583:
1575:
1562:
1558:
1550:
1542:
1534:
1526:
1518:
1510:
1502:
1494:
1486:
1478:
1470:
1462:
1454:
1441:
1436:
1432:
1424:
1416:
1408:
1400:
1392:
1384:
1376:
1368:
1360:
1352:
1344:
1336:
1328:
1320:
1312:
1300:
1297:
1289:
1282:
1279:
1278:
1274:
1266:
1258:
1250:
1242:
1234:
1226:
1218:
1210:
1202:
1194:
1186:
1178:
1170:
1162:
1154:
1142:
1139:
1131:
1124:
1121:
1120:
1116:
1108:
1100:
1092:
1084:
1076:
1068:
1060:
1052:
1044:
1036:
1028:
1020:
1012:
1004:
996:
989:
986:
978:
971:
968:
967:
963:
955:
947:
939:
931:
923:
915:
907:
899:
891:
883:
875:
867:
859:
851:
843:
836:
833:
825:
818:
815:
814:
810:
802:
794:
786:
778:
770:
759:
751:
744:
741:
740:
736:
728:
720:
712:
704:
696:
685:
677:
670:
667:
666:
662:
649:
642:
639:
638:
631:
626:
625:
622:
617:
612:
607:
602:
597:
592:
587:
582:
577:
572:
567:
562:
557:
552:
547:
540:
535:
528:
523:
520:
516:
512:
506:
504:
502:
482:
477:
472:
469:
465:
461:
458:
454:
451:
447:
444:
439:
437:
433:
428:
415:
410:
399:
395:
390:
387:
382:
371:
362:
358:
357:atomic volume
354:
347:
336:
333:
325:
315:
311:
307:
301:
300:
296:
291:This section
289:
285:
280:
279:
273:
271:
269:
265:
261:
257:
253:
249:
245:
241:
234:
230:
218:
213:
211:
206:
204:
199:
198:
196:
195:
189:
186:
184:
181:
179:
176:
174:
171:
169:
168:Atomic radius
166:
165:
163:
162:
157:
148:
136:
132:
130:
127:
126:
122:
120:
117:
116:
112:
110:
107:
106:
102:
100:
97:
96:
92:
90:
87:
86:
82:
80:
77:
76:
72:
70:
67:
66:
62:
60:
57:
56:
52:
50:
47:
46:
42:
38:
35:
34:
19:
3476:
3452:
3439:
3414:
3408:
3402:
3365:
3360:
3350:
3330:
3320:
3300:
3294:
3285:
3276:
3231:
3225:
3165:
3160:
3132:
3128:
3068:
3060:
3045:
2970:
2955:
2948:
2941:
2934:
2855:
2848:
2843:
2830:
2815:
2803:
2792:
2707:
2694:
2679:
2586:
2584:molar volume
2561:
2548:
2539:
2534:rather than
2525:
2415:
2406:
2399:
2339:
2319:
2313:
2308:
2303:
2294:
2290:
2278:
2189:
2180:
2174:
2164:
2087:
2083:
2073:
2069:
2065:Their values
1879:
1832:
1817:
1808:
1789:
1757:
1735:
1715:
1685:
514:
481:molar volume
478:
470:
459:
452:
445:
440:
429:
360:
356:
349:
345:
343:
328:
319:
304:Please help
292:
232:
228:
226:
187:
173:Ionic radius
146:
3315:, p. D-166.
2334:atoms (the
1723:ElementData
1717:Mathematica
53:1.2 (1.09)
3519:Categories
3385:2445/48823
3110:References
2081:), thus: (
1886:real gases
1835:mechanical
1745:From decay
1738:Primordial
1694:picometers
99:Phosphorus
3057:10 m
3029:α
3017:ε
3013:π
2910:χ
2879:ε
2869:α
2827:10 m
2762:−
2691:10 m
2626:π
2540:different
2482:π
2459:π
2117:~
2028:~
1962:−
1956:~
1925:~
1811:June 2015
1792:citations
1752:Synthetic
1702:10 m
455:, or the
396:π
322:June 2015
293:does not
3394:23632803
3328:(1945).
3268:19382751
3078:See also
3051: =
2973: =
2961: =
2947: =
2821: =
2806: =
2795: =
2685: =
2592: =
2568:covalent
2553:hydrogen
2543:used by
2258:Chlorine
2220:Nitrogen
2205:0.74611
2201:Hydrogen
2177:(cmmol)
1849:and the
1843:crystals
238:, of an
147:see text
119:Chlorine
89:Fluorine
69:Nitrogen
49:Hydrogen
39:radius (
3419:Bibcode
3286:Wolfram
3259:3658832
3236:Bibcode
2722:by the
2224:1.0975
1755:
1749:
1741:
1696:(pm or
1680:
1672:
1664:
1656:
1648:
1640:
1632:
1624:
1616:
1608:
1592:
1584:
1576:
1559:
1551:
1543:
1535:
1527:
1519:
1511:
1503:
1495:
1487:
1479:
1471:
1463:
1455:
1433:
1425:
1417:
1409:
1401:
1393:
1385:
1377:
1369:
1361:
1353:
1345:
1337:
1329:
1321:
1313:
1203:
1195:
1187:
1179:
1171:
1163:
1155:
1045:
1037:
1029:
1021:
1013:
1005:
997:
892:
884:
876:
868:
860:
852:
652:or 120
628:↓
529: →
488:⁄
314:removed
299:sources
242:is the
36:Element
3485:
3392:
3338:
3307:
3266:
3256:
2316:helium
2268:57.19
2265:56.22
2262:1.988
2249:36.62
2246:31.83
2243:1.208
2239:Oxygen
2230:47.71
2227:39.13
2211:34.53
2208:26.61
1998:where
1758:Border
1686:Legend
630:Period
448:, the
264:points
248:sphere
244:radius
129:Copper
109:Sulfur
79:Oxygen
59:Carbon
3053:2.073
2975:2.307
2823:8.685
2797:1.000
2328:6.022
2271:2.39
2252:2.06
2233:2.25
2214:2.02
527:Group
464:molar
123:1.75
93:1.47
83:1.52
73:1.55
3483:ISBN
3390:PMID
3336:ISBN
3305:ISBN
3264:PMID
2844:The
2808:5.23
2799:0350
2708:The
2687:2.30
2594:18.7
2314:For
2304:The
2293:and
2195:(Å)
2186:(Å)
2161:Gas
2010:and
1600:186
1298:283
1290:348
1275:220
1267:202
1259:197
1251:207
1243:202
1235:196
1227:155
1219:166
1211:175
1140:268
1132:343
1117:216
1109:198
1101:206
1093:206
1085:217
1077:193
1069:158
1061:172
1053:163
987:249
979:303
964:202
956:185
948:190
940:185
932:211
924:187
916:139
908:140
900:163
844:211
834:231
826:275
811:188
803:175
795:180
787:180
779:210
771:184
760:173
752:227
737:154
729:147
721:152
713:155
705:170
697:192
686:153
678:182
663:140
497:1000
491:1000
344:The
297:any
295:cite
240:atom
227:The
133:1.4
113:1.8
103:1.8
63:1.7
3427:doi
3415:109
3380:hdl
3370:doi
3254:PMC
3244:doi
3232:113
3170:doi
3137:doi
3133:100
2578:is
2576:atm
2570:or
2345:):
1794:to
650:110
359:or
308:by
3521::
3425:.
3413:.
3388:.
3378:.
3366:42
3359:.
3284:.
3262:.
3252:.
3242:.
3230:.
3224:.
3182:^
3166:68
3149:^
3131:.
3117:^
2967:10
2726::
2678::
2657:18
2518:.
2338:,
2332:10
2318:,
2171:)
2088:nb
2086:-
2074:nb
1888::
1859:pm
1721:s
1704:)
1677:No
1669:Md
1661:Fm
1653:Es
1645:Cf
1637:Bk
1629:Cm
1621:Am
1613:Pu
1605:Np
1597:U
1589:Pa
1581:Th
1573:Ac
1556:Yb
1548:Tm
1540:Er
1532:Ho
1524:Dy
1516:Tb
1508:Gd
1500:Eu
1492:Sm
1484:Pm
1476:Nd
1468:Pr
1460:Ce
1452:La
1430:Og
1422:Ts
1414:Lv
1406:Mc
1398:Fl
1390:Nh
1382:Cn
1374:Rg
1366:Ds
1358:Mt
1350:Hs
1342:Bh
1334:Sg
1326:Db
1318:Rf
1310:Lr
1295:Ra
1287:Fr
1272:Rn
1264:At
1256:Po
1248:Bi
1240:Pb
1232:Tl
1224:Hg
1216:Au
1208:Pt
1200:Ir
1192:Os
1184:Re
1176:W
1168:Ta
1160:Hf
1152:Lu
1137:Ba
1129:Cs
1114:Xe
1106:I
1098:Te
1090:Sb
1082:Sn
1074:In
1066:Cd
1058:Ag
1050:Pd
1042:Rh
1034:Ru
1026:Tc
1018:Mo
1010:Nb
1002:Zr
994:Y
984:Sr
976:Rb
961:Kr
953:Br
945:Se
937:As
929:Ge
921:Ga
913:Zn
905:Cu
897:Ni
889:Co
881:Fe
873:Mn
865:Cr
857:V
849:Ti
841:Sc
831:Ca
823:K
808:Ar
800:Cl
792:S
784:P
776:Si
768:Al
757:Mg
749:Na
734:Ne
726:F
718:O
710:N
702:C
694:B
683:Be
675:Li
660:He
647:H
621:18
616:17
611:16
606:15
601:14
596:13
591:12
586:11
581:10
503:.
476:.
438:.
348:,
270:.
231:,
43:)
3491:.
3460:.
3447:.
3433:.
3429::
3421::
3396:.
3382::
3372::
3344:.
3313:.
3288:.
3270:.
3246::
3238::
3176:.
3172::
3143:.
3139::
3064:w
3061:r
3055:×
3049:w
3046:V
3032:,
3021:0
3010:4
3006:1
3001:=
2995:w
2990:V
2977:×
2971:α
2965:×
2963:7
2959:e
2956:χ
2952:r
2949:ε
2945:e
2942:χ
2938:r
2935:ε
2915:e
2904:p
2900:T
2894:B
2889:k
2883:0
2872:=
2859:e
2856:χ
2849:α
2834:w
2831:r
2825:×
2819:w
2816:V
2810:×
2804:A
2793:n
2776:p
2773:3
2768:)
2765:1
2757:2
2753:n
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2746:T
2743:R
2737:=
2734:A
2720:n
2713:A
2698:w
2695:r
2689:×
2683:w
2680:V
2649:A
2644:N
2635:m
2630:V
2620:=
2614:w
2609:V
2596:×
2590:m
2587:V
2502:d
2497:2
2491:w
2486:r
2479:+
2474:3
2468:w
2463:r
2454:3
2451:4
2446:=
2440:w
2435:V
2424:d
2419:w
2416:r
2414:2
2410:w
2407:r
2403:w
2400:V
2380:A
2375:N
2370:b
2365:=
2359:w
2354:V
2343:A
2340:N
2330:×
2320:b
2309:b
2295:b
2291:d
2282:w
2279:r
2193:w
2190:r
2184:w
2181:V
2175:b
2169:Å
2167:(
2165:d
2153:V
2149:n
2129:2
2124:)
2114:V
2109:n
2104:(
2099:a
2084:V
2079:V
2061:b
2057:b
2053:a
2049:T
2045:R
2025:V
2012:b
2008:a
2004:n
2000:p
1986:,
1983:T
1980:R
1977:n
1974:=
1971:)
1968:b
1965:n
1953:V
1947:(
1943:)
1937:2
1932:)
1922:V
1917:n
1912:(
1907:a
1904:+
1901:p
1897:(
1855:Å
1824:)
1818:(
1813:)
1809:(
1799:.
1719:'
1700:×
1698:1
1281:7
1123:6
970:5
817:4
743:3
669:2
641:1
576:9
571:8
566:7
561:6
556:5
551:4
546:3
539:2
534:1
486:1
474:A
471:N
460:A
453:α
446:b
416:.
411:3
405:w
400:r
391:3
388:4
383:=
377:w
372:V
352:w
350:V
335:)
329:(
324:)
320:(
316:.
302:.
236:w
233:r
216:e
209:t
202:v
149:)
41:Å
20:)
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