3075:
699:
563:
939:
3087:
40:
3123:
334:
3147:
3099:
3135:
3111:
662:, and a mean lifetime of the excited state of around 11 million years. Collisions of neutral hydrogen atoms with electrons or other atoms can help promote the emission of 21 cm photons. A spontaneous occurrence of the transition is unlikely to be seen in a laboratory on Earth, but it can be artificially induced through
917:, so they must be made from very secluded sites with care taken to eliminate interference. Space based experiments, even on the far side of the Moon (where they would be sheltered from interference from terrestrial radio signals), have been proposed to compensate for this. Little is known about other foreground effects, such as
558:{\displaystyle \lambda ={\frac {1}{\nu }}\cdot c={\frac {h}{E}}\cdot c\approx {\frac {\;4.135\,67\cdot 10^{-15}\ \mathrm {eV} \cdot {\text{s}}\;}{5.874\,33\cdot 10^{-6}\ \mathrm {eV} }}\,\cdot \,2.997\,92\cdot 10^{8}\ \mathrm {m} \cdot \mathrm {s} ^{-1}\approx 0.211\,06\ \mathrm {m} =21.106\ \mathrm {cm} \;}
958:
spacecraft, portrays the hyperfine transition of neutral hydrogen and used the wavelength as a standard scale of measurement. For example, the height of the woman in the image is displayed as eight times 21 cm, or 168 cm. Similarly the frequency of the hydrogen spin-flip transition was used
308:
just as two magnets will align so that the north pole of one is closest to the south pole of the other. This logic fails here because the wave functions of the electron and the proton overlap; that is, the electron is not spatially displaced from the proton, but encompasses it. The magnetic dipole
991:
published "Searching for interstellar communications", a paper proposing the 21 cm hydrogen line and the potential of microwaves in the search for interstellar communications. According to George
Basalla, the paper by Cocconi and Morrison "provided a reasonable theoretical basis" for the
2942:
Wang, Jingying; Xu, Haiguang; An, Tao; Gu, Junhua; Guo, Xueying; Li, Weitian; Wang, Yu; Liu, Chengze; Martineau-Huynh, Olivier; Wu, Xiang-Ping (2013-01-14). "Exploring the cosmic reionization epoch in frequency space: An improved approach to remove the foreground in 21 cm tomography".
821:. Assuming that the hydrogen atoms are uniformly distributed throughout the galaxy, each line of sight through the galaxy will reveal a hydrogen line. The only difference between each of these lines is the Doppler shift that each of these lines has. Hence, by assuming
833:
hydrogen line. It is then possible to use the plot of the rotation curve and the velocity to determine the distance to a certain point within the galaxy. However, a limitation of this method is that departures from circular motion are observed at various scales.
712:
During the 1930s, it was noticed that there was a radio "hiss" that varied on a daily cycle and appeared to be extraterrestrial in origin. After initial suggestions that this was due to the Sun, it was observed that the radio waves seemed to propagate from the
971:
whose rotation period circa 1977 is given as a multiple of the frequency of the hydrogen spin-flip transition. It is theorized by the plaque's creators that an advanced civilization would then be able to use the locations of these pulsars to locate the
868:
Deuterium has a similar hyperfine spectral line at 91.6 cm (327 MHz), and the relative strength of the 21 cm line to the 91.6 cm line can be used to measure the deuterium-to-hydrogen (D/H) ratio. One group in 2007 reported D/H ratio in the
1746:
Skywaves are not used in the UHF band because the ionosphere is not sufficiently dense to reflect the waves, which pass through it into space. ... Reception of UHF signals is virtually free from fading and interference from atmospheric
909:
in the period after recombination. Second, it can provide a picture of how the universe was re‑ionized, as neutral hydrogen which has been ionized by radiation from stars or quasars will appear as holes in the 21 cm background.
993:
808:
to be exact). Electromagnetic energy in this range can easily pass through the Earth's atmosphere and be observed from the Earth with little interference. The hydrogen line can readily penetrate clouds of interstellar
925:
on the galaxy. Despite these problems, 21 cm observations, along with space-based gravitational wave observations, are generally viewed as the next great frontier in observational cosmology, after the
295:, whose interaction results in a slight increase in energy when the spins are parallel, and a decrease when antiparallel. The fact that only parallel and antiparallel states are allowed is a result of the
1156:, so it is pronounced "H one". It is also called the "neutral hydrogen" line, with the listener obliged to infer from context that "cold neutral hydrogen" at 1420.4 MHz or 0.211 m is meant.
303:
of the system. When the spins are parallel, the magnetic dipole moments are antiparallel (because the electron and proton have opposite charge), thus one would expect this configuration to actually have
2787:
Loeb, A.; Zaldarriaga, M. (2004). "Measuring the small-scale power spectrum of cosmic density fluctuations through 21 cm tomography prior to the epoch of structure formation".
913:
However, 21 cm observations are very difficult to make. Ground-based experiments to observe the faint signal are plagued by interference from television transmitters and the
309:
moments are therefore best thought of as tiny current loops. As parallel currents attract, the parallel magnetic dipole moments (i.e., antiparallel spins) have lower energy.
43:
A hydrogen atom with proton and electron spins aligned (top) undergoes a flip of the electron spin, resulting in emission of a photon with a 21 cm wavelength (bottom)
2736:
1262:
Mhaske, Ashish A.; et al. (August 2022). "A Bose horn antenna radio telescope (BHARAT) design for 21 cm hydrogen line experiments for radio astronomy teaching".
1666:
van de Hulst, H. C.; et al. (May 1954). "The spiral structure of the outer part of the
Galactic System derived from the hydrogen emission at 21 cm wavelength".
1305:
1924:
Verschuur, G. L. (September 1968). "Positive
Determination of an Interstellar Magnetic Field by Measurement of the Zeeman Splitting of the 21-cm Hydrogen Line".
775:
and
Hindman in Australia. After 1952 the first maps of the neutral hydrogen in the Galaxy were made, and revealed for the first time the spiral structure of the
3020:
Pen, Ue-Li; Wu, Xiang-Ping; Peterson, Jeff (5 April 2004). "Forecast for Epoch-of-Reionization as viewable by the PrimevAl
Structure Telescope (PAST)".
2223:
Kohler, Katharina; et al. (November 2005). "Redshifted 21 cm
Emission from the Pre-Reionization Era. II. H II Regions around Individual Quasars".
254:
1088:, and would clearly signify its artificial origin. Such a signal would not be overwhelmed by the H I line itself, or by any of its harmonics.
3074:
2537:
927:
901:, this line will be observed at frequencies from 200 MHz to about 15 MHz on Earth. It potentially has two applications. First, by
3012:
1727:
1621:
Muller, C.A.; Oort, J.H. (September 1951). "The interstellar hydrogen line at 1,420 Mc./sec., and an estimate of galactic rotation".
837:
Hydrogen line observations have been used indirectly to calculate the mass of galaxies, to put limits on any changes over time of the
1770:
1576:(September 1951). "Observation of a line in the galactic radio spectrum: Radiation from galactic hydrogen at 1,420 Mc./sec".
2278:"Transformative science from the lunar farside: observations of the dark ages and exoplanetary systems at low radio frequencies"
2844:
Santos, M.G.; Cooray, A.; Knox, L. (2005). "Multifrequency analysis of 21 cm fluctuations from the era of reionization".
2055:
Peters, Wendy M.; et al. (January 2011). "Radio
Recombination Lines at Decameter Wavelengths: Prospects for the Future".
3172:
2464:
78:-flip transition, which means the direction of the electron's spin is reversed relative to the spin of the proton. This is a
2679:
Zaldarriaga, M.; Furlanetto, S.; Hernquist, L. (2004). "21 centimeter fluctuations from cosmic gas at high redshifts".
3065:
145:
253:
because it can be used to study the early
Universe. Due to its fundamental properties, this line is of interest in the
3182:
1224:
183:
2628:
Ciardi, B.; Madau, P. (2003). "Probing beyond the epoch of hydrogen reionization with 21 centimeter radiation".
2893:
Barkana, R.; Loeb, A. (2005). "Detecting the earliest galaxies through two new sources of 21 cm fluctuations".
1103:
772:
3167:
2945:
2895:
2846:
2681:
2630:
2579:
2577:
Madau, P.; Meiksin, A.; Rees, M.J. (1997). "21 cm tomography of the intergalactic medium at high redshift".
1185:
890:
97:
3177:
1407:
1132:
1113:
1108:
206:
90:
87:
31:
3044:
983:
program in their search for signals from potential extraterrestrial civilizations. In 1959, Italian physicist
698:
3187:
2789:
2525:
838:
246:
2166:"Simulating cosmic reionization at large scales - II. The 21-cm emission features and statistical signals"
862:
288:
2487:"Introducing Humans to the Extraterrestrials: the Pioneering Missions of the Pioneer and Voyager Probes"
2108:
Fialkov, A.; Loeb, A. (November 2013). "The 21-cm Signal from the cosmological epoch of recombination".
918:
906:
886:
675:
905:
of redshifted 21 centimeter radiation it can, in principle, provide a very precise picture of the
2964:
2914:
2865:
2808:
2755:
2700:
2649:
2598:
2419:
2362:
2299:
2242:
2187:
2127:
2074:
2013:
1972:
1933:
1888:
1837:
1798:
1705:
1675:
1632:
1587:
1573:
1534:
1492:
1426:
1411:
1371:
1314:
1233:
1190:
801:
764:
726:
234:
230:
68:
3151:
870:
854:
663:
270:
3139:
3127:
3021:
2988:
2954:
2930:
2904:
2881:
2855:
2832:
2798:
2773:
2745:
2716:
2690:
2665:
2639:
2614:
2588:
2409:
2378:
2352:
2289:
2258:
2232:
2205:
2177:
2143:
2117:
2090:
2064:
2037:
1906:
1878:
1723:
1648:
1603:
1554:
1516:
1482:
1442:
1389:
1361:
1271:
846:
768:
760:
238:
2529:
2519:
771:, and published after their data was corroborated by Dutch astronomers Muller and Oort, and by
3192:
2980:
2824:
2533:
2445:
2325:
2029:
1766:
1508:
1330:
1081:
902:
604:. In a laboratory setting, the hydrogen line parameters have been more precisely measured as:
296:
1760:
1696:(May 1957). "The distribution of atomic hydrogen in the outer parts of the Galactic System".
3103:
3091:
2972:
2922:
2873:
2816:
2763:
2708:
2657:
2606:
2498:
2435:
2427:
2370:
2315:
2307:
2250:
2195:
2135:
2082:
2078:
2021:
1980:
1941:
1896:
1845:
1806:
1802:
1640:
1623:
1595:
1578:
1546:
1500:
1434:
1379:
1322:
1281:
1241:
1198:
984:
814:
805:
300:
245:, to calculate the mass and dynamics of individual galaxies, and to test for changes to the
241:
in 1951. Observations of the hydrogen line have been used to reveal the spiral shape of the
222:
83:
1961:"The 21 cm absorption line profile as a tool for the search for antimatter in the universe"
1786:
1693:
1127:
1039:
988:
822:
730:
714:
593:
325:
313:
210:
191:
2001:
2968:
2918:
2869:
2812:
2759:
2704:
2653:
2602:
2423:
2366:
2303:
2246:
2191:
2139:
2131:
2017:
1976:
1937:
1892:
1841:
1810:
1709:
1679:
1636:
1591:
1504:
1496:
1430:
1375:
1318:
1237:
1194:
942:
The hyperfine transition of hydrogen, as depicted on the
Pioneer and Voyager spacecraft.
938:
3079:
2440:
2397:
2320:
2277:
1901:
1866:
947:
922:
842:
826:
793:
667:
651:
601:
292:
258:
75:
3008:
3161:
2992:
2976:
2768:
2731:
2720:
2618:
2382:
2200:
2165:
2147:
1735:
The
American Practical Navigator: An Epitome of Navigation. 2002 Bicentennial Edition
1446:
1384:
1349:
1153:
1098:
850:
818:
753:
722:
687:
683:
679:
226:
162:
79:
71:
64:
60:
2885:
2836:
2669:
2262:
2209:
2094:
2041:
1652:
1607:
1520:
1438:
1393:
705:
used by Ewen and Purcell for the first detection of hydrogen line emission from the
3115:
2934:
2777:
1910:
973:
894:
858:
749:
702:
284:
178:
93:
2820:
2086:
1300:
959:
for a unit of time in a map to Earth included on the Pioneer plaques and also the
2343:
Wang, Xiaomin; et al. (October 2006). "21 cm Tomography with Foregrounds".
810:
218:
39:
2431:
1945:
1222:
Griffiths, D.J. (1982). "Hyperfine splitting in the ground state of hydrogen".
17:
2503:
2486:
967:
probes. On this map, the position of the Sun is portrayed relative to 14
955:
951:
914:
671:
573:
214:
123:
2984:
2033:
1865:
Drinkwater, M. J.; Webb, J. K–; Barrow, J. D.; Flambaum, V. V. (April 1998).
1334:
1202:
1301:"Accurate atomic transition probabilities for hydrogen, helium, and lithium"
1122:
964:
960:
776:
737:
721:
who knew that significant advances could be made in astronomy if there were
706:
581:
250:
242:
202:
118:
101:
2828:
2449:
2329:
2311:
1512:
1985:
1960:
3026:
2909:
2860:
2803:
2750:
2695:
2644:
2593:
2357:
2237:
2182:
1883:
1470:
1366:
1350:"The spin temperature of neutral hydrogen during cosmic pre-reionization"
1177:
1085:
898:
882:
733:
718:
283:. The lowest stationary energy state of the bound electron is called its
276:
1558:
1178:"Measurement of the unperturbed hydrogen hyperfine transition frequency"
1084:, such a frequency could not possibly be produced in a natural way as a
979:
The 21 cm hydrogen line is considered a favorable frequency by the
2732:"Observing the reionization epoch through 21 centimeter radiation"
2398:"Peering into the dark (ages) with low-frequency space interferometers"
1118:
1326:
1285:
885:
cosmology because it is the only known way to probe the cosmological "
825:, one can calculate the relative speed of each arm of our galaxy. The
690:
caused by bulk motion or nonzero temperature of the emitting regions.
1644:
1599:
1550:
968:
797:
280:
198:
158:
141:
1245:
759:
The 21 cm line (1420.4 MHz) was first detected in 1951 by
3110:
3048:
2926:
2877:
2712:
2661:
2610:
2414:
2374:
2294:
2254:
2025:
1850:
1825:
1276:
27:
Spectral line of hydrogen state transition in UHF radio frequencies
3009:"The story of Ewen and Purcell's discovery of the 21 cm line"
2959:
2554:
2122:
2069:
1789:(1969). "The Large-Scale Distribution of Hydrogen in the Galaxy".
1487:
937:
697:
38:
980:
3056:
1121:, the visible red spectral line with wavelength of 656.28
229:. The existence of this line was predicted by Dutch astronomer
2000:
Rogers, A. E. E.; Dudevoir, K. A.; Bania, T. M. (2007-03-09).
717:. These discoveries were published in 1940 and were noted by
2002:"Observations of the 327 MHz Deuterium Hyperfine Transition"
1867:"New limits on the possible variation of physical constants"
1075:
670:. It is commonly observed in astronomical settings such as
1698:
Bulletin of the Astronomical Institutes of the Netherlands
1668:
Bulletin of the Astronomical Institutes of the Netherlands
853:
on the 21-cm line; a task that was first accomplished by
316:
between these aligned states has an energy difference of
3036:
1539:
Proceedings of the American Academy of Arts and Sciences
841:, and to study the dynamics of individual galaxies. The
996:
proposed SETI use a frequency which is equal to either
725:
in the radio part of the spectrum. He referred this to
1826:"Integral Properties of Spiral and Irregular Galaxies"
1473:(August 2012). "21 cm cosmology in the 21st century".
934:
Relevance to the search for non-human intelligent life
3063:
2465:"The Pioneer Plaque: Science as a Universal Language"
2159:
2157:
1959:
Solovyev, Dmitry; Labzowsky, Leonti (November 2014).
1464:
1462:
857:
in 1968. In theory, it may be possible to search for
337:
2730:
Furlanetto, S.; Sokasian, A.; Hernquist, L. (2004).
1186:
IEEE Transactions on Instrumentation and Measurement
1257:
1255:
63:that is created by a change in the energy state of
1737:. National Imagery and Mapping Agency. p. 158
557:
287:. Both the electron and the proton have intrinsic
2737:Monthly Notices of the Royal Astronomical Society
2282:Philosophical Transactions of the Royal Society A
2170:Monthly Notices of the Royal Astronomical Society
1871:Monthly Notices of the Royal Astronomical Society
1354:Monthly Notices of the Royal Astronomical Society
865:of the 21-cm line in an external magnetic field.
1965:Progress of Theoretical and Experimental Physics
792:The 21 cm spectral line appears within the
2396:Koopmans, Léon V. E.; et al. (June 2021).
1306:Journal of Physical and Chemical Reference Data
748:due to two closely spaced energy levels in the
217:can penetrate the large clouds of interstellar
2164:Mellema, Garrelt; et al. (October 2006).
2110:Journal of Cosmology and Astroparticle Physics
893:(when stable hydrogen atoms first formed) to
249:over time. It is of particular importance to
8:
829:of our galaxy has been calculated using the
257:. This line is the theoretical basis of the
1791:Annual Review of Astronomy and Astrophysics
1537:(1953). "Line Spectra in Radio Astronomy".
654:with an extremely small transition rate of
275:An atom of neutral hydrogen consists of an
201:, which is located in the lower end of the
1765:. Cambridge University Press. p. 36.
976:at the time the spacecraft were launched.
554:
428:
385:
122:(1.42 GHz), which is equivalent to a
3025:
2958:
2908:
2859:
2802:
2767:
2749:
2694:
2643:
2592:
2502:
2439:
2413:
2356:
2319:
2293:
2236:
2199:
2181:
2121:
2068:
1984:
1900:
1882:
1849:
1486:
1383:
1365:
1275:
674:in our galaxy and others. Because of the
546:
532:
525:
510:
505:
496:
487:
476:
472:
468:
457:
445:
434:
423:
412:
400:
389:
382:
363:
344:
336:
2557:[Look at the root] (in Russian).
928:cosmic microwave background polarization
255:search for extraterrestrial intelligence
197:The hydrogen line frequency lies in the
3070:
2485:Capova, Klara Anna (October 18, 2021).
1168:
1145:
1299:Wiese, W.L.; Fuhr, J.R. (2009-06-24).
992:then-nascent SETI program. Similarly,
1824:Roberts, Morton S. (September 1969).
1176:Hellwig, Helmut; et al. (1970).
7:
3045:"Mileura Widefield Array experiment"
3013:National Radio Astronomy Observatory
2463:Rosenthal, Jake (January 20, 2016).
3057:"Square kilometer array experiment"
1811:10.1146/annurev.aa.07.090169.000351
233:in 1944, then directly observed by
30:For hydrogen lines in general, see
1902:10.1046/j.1365-8711.1998.2952457.x
550:
547:
533:
506:
497:
461:
458:
416:
413:
161:emitted by this transition has an
25:
881:The line is of great interest in
849:can be measured by observing the
3145:
3133:
3121:
3109:
3097:
3085:
3073:
2769:10.1111/j.1365-2966.2004.07187.x
2201:10.1111/j.1365-2966.2006.10919.x
1385:10.1111/j.1365-2966.2005.08894.x
873:to be 21 ± 7 parts per million.
2276:Burns, Jack O. (January 2021).
686:, so most broadening is due to
209:. It is frequently observed in
3047:(main website). Archived from
2521:Civilized Life in the Universe
1759:Wynn-Williams, Gareth (1992).
1475:Reports on Progress in Physics
678:, its long lifetime gives the
1:
3032:— PAST experiment description
2821:10.1103/PhysRevLett.92.211301
2140:10.1088/1475-7516/2013/11/066
1505:10.1088/0034-4885/75/8/086901
736:could produce radiation at a
729:who, in 1944, predicted that
2057:Astronomy & Astrophysics
299:discretization of the total
2491:Frontiers in Human Dynamics
2087:10.1051/0004-6361/201014707
1412:"The Atomic Hydrogen Maser"
1264:American Journal of Physics
1225:American Journal of Physics
184:constant of proportionality
3209:
2977:10.1088/0004-637X/763/2/90
2432:10.1007/s10686-021-09743-7
1946:10.1103/PhysRevLett.21.775
1104:Chronology of the universe
650:This transition is highly
268:
100:producing this line has a
29:
2946:The Astrophysical Journal
2896:The Astrophysical Journal
2847:The Astrophysical Journal
2682:The Astrophysical Journal
2631:The Astrophysical Journal
2580:The Astrophysical Journal
2504:10.3389/fhumd.2021.714616
2345:The Astrophysical Journal
2225:The Astrophysical Journal
1439:10.1088/0026-1394/1/1/004
1152:The "I" in H I is a
312:In the ground state, the
98:electromagnetic radiation
2518:Basalla, George (2006).
2006:The Astronomical Journal
1469:Pritchard, Jonathan R.;
1348:Nusser, Adi (May 2005).
1203:10.1109/TIM.1970.4313902
1133:Timeline of the Big Bang
1114:Hydrogen spectral series
1109:Dark Ages Radio Explorer
207:electromagnetic spectrum
146:Planck–Einstein relation
32:hydrogen spectral series
2790:Physical Review Letters
2526:Oxford University Press
2497:. Frontiers Media S.A.
2467:. The Planetary Society
2079:2011A&A...525A.128P
1926:Physical Review Letters
1803:1969ARA&A...7...39K
987:and American physicist
861:atoms by measuring the
839:fine-structure constant
289:magnetic dipole moments
247:fine-structure constant
82:change between the two
53:21 centimeter line
2402:Experimental Astronomy
2312:10.1098/rsta.2019.0564
943:
709:
588:is the photon energy,
576:of an emitted photon,
559:
324:. When applied to the
74:. It is produced by a
44:
3173:Emission spectroscopy
1762:The Fullness of Space
941:
907:matter power spectrum
903:mapping the intensity
701:
676:uncertainty principle
560:
269:Further information:
42:
1830:Astronomical Journal
919:synchrotron emission
727:Hendrik van de Hulst
715:centre of the Galaxy
335:
314:spin-flip transition
69:electrically neutral
2969:2013ApJ...763...90W
2919:2005ApJ...626....1B
2870:2005ApJ...625..575S
2813:2004PhRvL..92u1301L
2760:2004MNRAS.347..187F
2705:2004ApJ...608..622Z
2654:2003ApJ...596....1C
2603:1997ApJ...475..429M
2424:2021ExA....51.1641K
2367:2006ApJ...650..529W
2304:2021RSPTA.37990564B
2247:2005ApJ...633..552K
2192:2006MNRAS.372..679M
2132:2013JCAP...11..066F
2018:2007AJ....133.1625R
1986:10.1093/ptep/ptu142
1977:2014PTEP.2014k1E01S
1938:1968PhRvL..21..775V
1893:1998MNRAS.295..457D
1842:1969AJ.....74..859R
1724:Bowditch, Nathaniel
1710:1957BAN....13..201W
1680:1954BAN....12..117V
1637:1951Natur.168..357M
1592:1951Natur.168..356E
1497:2012RPPh...75h6901P
1431:1965Metro...1....7R
1376:2005MNRAS.359..183N
1319:2009JPCRD..38..565W
1238:1982AmJPh..50..698G
1195:1970ITIM...19..200H
871:galactic anticenter
682:an extremely small
664:stimulated emission
271:Hyperfine structure
144:. According to the
3183:Physical cosmology
3037:"LOFAR experiment"
1189:. IM-19 (4): 200.
950:, attached to the
944:
923:free–free emission
847:interstellar space
788:In radio astronomy
769:Harvard University
710:
555:
297:quantum mechanical
291:ascribed to their
190:, is known as the
45:
2555:"Смотри в корень"
2539:978-0-19-517181-5
1728:"10. Radio Waves"
1631:(4270): 357–358.
1408:Ramsey, Norman F.
1327:10.1063/1.3077727
1286:10.1119/5.0065381
1082:irrational number
545:
531:
495:
466:
456:
426:
411:
371:
352:
16:(Redirected from
3200:
3168:Hydrogen physics
3150:
3149:
3148:
3138:
3137:
3136:
3126:
3125:
3124:
3114:
3113:
3102:
3101:
3100:
3090:
3089:
3088:
3078:
3077:
3069:
3060:
3052:
3040:
3031:
3029:
3027:astro-ph/0404083
3016:
2996:
2962:
2938:
2912:
2910:astro-ph/0410129
2889:
2863:
2861:astro-ph/0408515
2840:
2806:
2804:astro-ph/0312134
2781:
2771:
2753:
2751:astro-ph/0305065
2724:
2698:
2696:astro-ph/0311514
2673:
2647:
2645:astro-ph/0303249
2622:
2596:
2594:astro-ph/9608010
2559:
2558:
2550:
2544:
2543:
2515:
2509:
2508:
2506:
2482:
2476:
2475:
2473:
2472:
2460:
2454:
2453:
2443:
2417:
2408:(3): 1641–1676.
2393:
2387:
2386:
2360:
2358:astro-ph/0501081
2340:
2334:
2333:
2323:
2297:
2273:
2267:
2266:
2240:
2238:astro-ph/0501086
2220:
2214:
2213:
2203:
2185:
2183:astro-ph/0603518
2161:
2152:
2151:
2125:
2105:
2099:
2098:
2072:
2052:
2046:
2045:
2012:(4): 1625–1632.
1997:
1991:
1990:
1988:
1956:
1950:
1949:
1921:
1915:
1914:
1904:
1886:
1884:astro-ph/9711290
1862:
1856:
1855:
1853:
1821:
1815:
1814:
1783:
1777:
1776:
1756:
1750:
1749:
1743:
1742:
1732:
1720:
1714:
1713:
1690:
1684:
1683:
1663:
1657:
1656:
1645:10.1038/168357a0
1618:
1612:
1611:
1600:10.1038/168356a0
1569:
1563:
1562:
1551:10.2307/20023736
1531:
1525:
1524:
1490:
1466:
1457:
1456:
1454:
1453:
1416:
1410:(January 1965).
1404:
1398:
1397:
1387:
1369:
1367:astro-ph/0409640
1345:
1339:
1338:
1296:
1290:
1289:
1279:
1259:
1250:
1249:
1219:
1213:
1212:
1210:
1209:
1182:
1173:
1157:
1150:
1078:
1070:
1068:
1065:
1059:
1057:
1054:
1050:
1043:
1031:
1029:
1026:
1020:
1018:
1015:
1011:
1005:
1002:
994:Pyotr Makovetsky
985:Giuseppe Cocconi
897:. Including the
832:
806:microwave window
747:
745:
661:
659:
643:
641:
638:
635:
624:
622:
619:
616:
599:
591:
587:
579:
571:
564:
562:
561:
556:
553:
543:
536:
529:
518:
517:
509:
500:
493:
492:
491:
467:
465:
464:
454:
453:
452:
429:
427:
424:
419:
409:
408:
407:
383:
372:
364:
353:
345:
323:
321:
301:angular momentum
237:and his student
189:
181:
176:
173:
170:
156:
139:
137:
134:
131:
121:
116:
113:
109:
86:of the hydrogen
84:hyperfine levels
21:
3208:
3207:
3203:
3202:
3201:
3199:
3198:
3197:
3178:Radio astronomy
3158:
3157:
3156:
3146:
3144:
3134:
3132:
3122:
3120:
3108:
3098:
3096:
3086:
3084:
3072:
3064:
3059:(main website).
3055:
3043:
3039:(main website).
3035:
3019:
3007:
3004:
2999:
2941:
2892:
2843:
2786:
2729:
2678:
2627:
2576:
2572:
2567:
2565:Further reading
2562:
2553:Makovetsky, P.
2552:
2551:
2547:
2540:
2517:
2516:
2512:
2484:
2483:
2479:
2470:
2468:
2462:
2461:
2457:
2395:
2394:
2390:
2342:
2341:
2337:
2275:
2274:
2270:
2222:
2221:
2217:
2163:
2162:
2155:
2107:
2106:
2102:
2054:
2053:
2049:
1999:
1998:
1994:
1958:
1957:
1953:
1932:(11): 775–778.
1923:
1922:
1918:
1864:
1863:
1859:
1823:
1822:
1818:
1785:
1784:
1780:
1773:
1758:
1757:
1753:
1740:
1738:
1730:
1722:
1721:
1717:
1692:
1691:
1687:
1665:
1664:
1660:
1620:
1619:
1615:
1571:
1570:
1566:
1533:
1532:
1528:
1468:
1467:
1460:
1451:
1449:
1414:
1406:
1405:
1401:
1347:
1346:
1342:
1298:
1297:
1293:
1270:(12): 948–960.
1261:
1260:
1253:
1246:10.1119/1.12733
1221:
1220:
1216:
1207:
1205:
1180:
1175:
1174:
1170:
1166:
1161:
1160:
1151:
1147:
1142:
1137:
1128:Rydberg formula
1094:
1076:
1066:
1063:
1061:
1055:
1052:
1048:
1046:
1041:
1027:
1024:
1022:
1016:
1013:
1009:
1007:
1003:
1000:
989:Philip Morrison
936:
879:
855:G. L. Verschuur
830:
823:circular motion
790:
785:
743:
741:
696:
672:hydrogen clouds
657:
655:
642:.768(2) Hz
639:
636:
633:
631:
620:
617:
614:
612:
597:
594:Planck constant
589:
585:
577:
569:
504:
483:
441:
430:
396:
384:
333:
332:
326:Planck relation
319:
317:
273:
267:
231:H. van de Hulst
211:radio astronomy
192:Planck constant
187:
174:
171:
168:
166:
148:
135:
132:
129:
127:
114:
111:
107:
105:
35:
28:
23:
22:
18:21 cm radiation
15:
12:
11:
5:
3206:
3204:
3196:
3195:
3190:
3188:Astrochemistry
3185:
3180:
3175:
3170:
3160:
3159:
3155:
3154:
3142:
3130:
3118:
3106:
3094:
3082:
3062:
3061:
3053:
3051:on 2005-02-11.
3041:
3033:
3017:
3003:
3002:External links
3000:
2998:
2997:
2939:
2927:10.1086/429954
2890:
2878:10.1086/429857
2854:(2): 575–587.
2841:
2797:(21): 211301.
2783:
2782:
2744:(1): 187–195.
2726:
2725:
2713:10.1086/386327
2689:(2): 622–635.
2675:
2674:
2662:10.1086/377634
2624:
2623:
2611:10.1086/303549
2587:(2): 429–444.
2573:
2571:
2568:
2566:
2563:
2561:
2560:
2545:
2538:
2510:
2477:
2455:
2388:
2375:10.1086/506597
2351:(2): 529–537.
2335:
2268:
2255:10.1086/444370
2231:(2): 552–559.
2215:
2176:(2): 679–692.
2153:
2100:
2047:
2026:10.1086/511978
1992:
1971:(11): 111E01.
1951:
1916:
1877:(2): 457–462.
1857:
1851:10.1086/110874
1816:
1787:Kerr, Frank J.
1778:
1771:
1751:
1715:
1694:Westerhout, G.
1685:
1658:
1613:
1564:
1545:(7): 347–349.
1535:Purcell, E. M.
1526:
1458:
1399:
1360:(1): 183–190.
1340:
1313:(3): 565–720.
1291:
1251:
1232:(8): 698–703.
1214:
1167:
1165:
1162:
1159:
1158:
1144:
1143:
1141:
1138:
1136:
1135:
1130:
1125:
1116:
1111:
1106:
1101:
1095:
1093:
1090:
1072:
1071:
1033:
1032:
948:Pioneer plaque
935:
932:
878:
875:
843:magnetic field
827:rotation curve
794:radio spectrum
789:
786:
784:
781:
746:.4058 MHz
723:emission lines
695:
692:
688:Doppler shifts
668:hydrogen maser
645:
644:
625:
602:speed of light
566:
565:
552:
549:
542:
539:
535:
528:
524:
521:
516:
513:
508:
503:
499:
490:
486:
482:
479:
475:
471:
463:
460:
451:
448:
444:
440:
437:
433:
422:
418:
415:
406:
403:
399:
395:
392:
388:
381:
378:
375:
370:
367:
362:
359:
356:
351:
348:
343:
340:
328:, this gives:
266:
263:
259:hydrogen maser
213:because those
205:region of the
72:hydrogen atoms
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
3205:
3194:
3191:
3189:
3186:
3184:
3181:
3179:
3176:
3174:
3171:
3169:
3166:
3165:
3163:
3153:
3143:
3141:
3131:
3129:
3119:
3117:
3112:
3107:
3105:
3095:
3093:
3083:
3081:
3076:
3071:
3067:
3058:
3054:
3050:
3046:
3042:
3038:
3034:
3028:
3023:
3018:
3014:
3010:
3006:
3005:
3001:
2994:
2990:
2986:
2982:
2978:
2974:
2970:
2966:
2961:
2956:
2952:
2948:
2947:
2940:
2936:
2932:
2928:
2924:
2920:
2916:
2911:
2906:
2902:
2898:
2897:
2891:
2887:
2883:
2879:
2875:
2871:
2867:
2862:
2857:
2853:
2849:
2848:
2842:
2838:
2834:
2830:
2826:
2822:
2818:
2814:
2810:
2805:
2800:
2796:
2792:
2791:
2785:
2784:
2779:
2775:
2770:
2765:
2761:
2757:
2752:
2747:
2743:
2739:
2738:
2733:
2728:
2727:
2722:
2718:
2714:
2710:
2706:
2702:
2697:
2692:
2688:
2684:
2683:
2677:
2676:
2671:
2667:
2663:
2659:
2655:
2651:
2646:
2641:
2637:
2633:
2632:
2626:
2625:
2620:
2616:
2612:
2608:
2604:
2600:
2595:
2590:
2586:
2582:
2581:
2575:
2574:
2569:
2564:
2556:
2549:
2546:
2541:
2535:
2531:
2527:
2523:
2522:
2514:
2511:
2505:
2500:
2496:
2492:
2488:
2481:
2478:
2466:
2459:
2456:
2451:
2447:
2442:
2437:
2433:
2429:
2425:
2421:
2416:
2411:
2407:
2403:
2399:
2392:
2389:
2384:
2380:
2376:
2372:
2368:
2364:
2359:
2354:
2350:
2346:
2339:
2336:
2331:
2327:
2322:
2317:
2313:
2309:
2305:
2301:
2296:
2291:
2287:
2283:
2279:
2272:
2269:
2264:
2260:
2256:
2252:
2248:
2244:
2239:
2234:
2230:
2226:
2219:
2216:
2211:
2207:
2202:
2197:
2193:
2189:
2184:
2179:
2175:
2171:
2167:
2160:
2158:
2154:
2149:
2145:
2141:
2137:
2133:
2129:
2124:
2119:
2115:
2111:
2104:
2101:
2096:
2092:
2088:
2084:
2080:
2076:
2071:
2066:
2062:
2058:
2051:
2048:
2043:
2039:
2035:
2031:
2027:
2023:
2019:
2015:
2011:
2007:
2003:
1996:
1993:
1987:
1982:
1978:
1974:
1970:
1966:
1962:
1955:
1952:
1947:
1943:
1939:
1935:
1931:
1927:
1920:
1917:
1912:
1908:
1903:
1898:
1894:
1890:
1885:
1880:
1876:
1872:
1868:
1861:
1858:
1852:
1847:
1843:
1839:
1835:
1831:
1827:
1820:
1817:
1812:
1808:
1804:
1800:
1796:
1792:
1788:
1782:
1779:
1774:
1772:9780521426381
1768:
1764:
1763:
1755:
1752:
1748:
1736:
1729:
1725:
1719:
1716:
1711:
1707:
1703:
1699:
1695:
1689:
1686:
1681:
1677:
1673:
1669:
1662:
1659:
1654:
1650:
1646:
1642:
1638:
1634:
1630:
1626:
1625:
1617:
1614:
1609:
1605:
1601:
1597:
1593:
1589:
1586:(4270): 356.
1585:
1581:
1580:
1575:
1574:Purcell, E.M.
1568:
1565:
1560:
1556:
1552:
1548:
1544:
1540:
1536:
1530:
1527:
1522:
1518:
1514:
1510:
1506:
1502:
1498:
1494:
1489:
1484:
1481:(8): 086901.
1480:
1476:
1472:
1471:Loeb, Abraham
1465:
1463:
1459:
1448:
1444:
1440:
1436:
1432:
1428:
1424:
1420:
1413:
1409:
1403:
1400:
1395:
1391:
1386:
1381:
1377:
1373:
1368:
1363:
1359:
1355:
1351:
1344:
1341:
1336:
1332:
1328:
1324:
1320:
1316:
1312:
1308:
1307:
1302:
1295:
1292:
1287:
1283:
1278:
1273:
1269:
1265:
1258:
1256:
1252:
1247:
1243:
1239:
1235:
1231:
1227:
1226:
1218:
1215:
1204:
1200:
1196:
1192:
1188:
1187:
1179:
1172:
1169:
1163:
1155:
1154:roman numeral
1149:
1146:
1139:
1134:
1131:
1129:
1126:
1124:
1120:
1117:
1115:
1112:
1110:
1107:
1105:
1102:
1100:
1099:Balmer series
1097:
1096:
1091:
1089:
1087:
1083:
1079:
1044:
1038:
1037:
1036:
999:
998:
997:
995:
990:
986:
982:
977:
975:
970:
966:
962:
957:
953:
949:
940:
933:
931:
929:
924:
920:
916:
911:
908:
904:
900:
896:
892:
891:recombination
888:
884:
876:
874:
872:
866:
864:
860:
856:
852:
851:Zeeman effect
848:
844:
840:
835:
828:
824:
820:
819:visible light
816:
812:
807:
803:
799:
795:
787:
782:
780:
778:
774:
770:
766:
762:
757:
755:
754:hydrogen atom
751:
739:
735:
732:
728:
724:
720:
716:
708:
704:
700:
693:
691:
689:
685:
684:natural width
681:
680:spectral line
677:
673:
669:
665:
653:
648:
647:in a vacuum.
629:
626:
610:
607:
606:
605:
603:
595:
583:
575:
540:
537:
526:
522:
519:
514:
511:
501:
488:
484:
480:
477:
473:
469:
449:
446:
442:
438:
435:
431:
420:
404:
401:
397:
393:
390:
386:
379:
376:
373:
368:
365:
360:
357:
354:
349:
346:
341:
338:
331:
330:
329:
327:
315:
310:
307:
302:
298:
294:
290:
286:
282:
278:
272:
264:
262:
260:
256:
252:
248:
244:
240:
236:
235:E. M. Purcell
232:
228:
227:visible light
224:
220:
216:
212:
208:
204:
200:
195:
193:
185:
180:
164:
160:
155:
151:
147:
143:
125:
120:
103:
99:
95:
92:
89:
85:
81:
80:quantum state
77:
73:
70:
66:
62:
61:spectral line
58:
57:H I line
54:
50:
49:hydrogen line
41:
37:
33:
19:
3152:Solar System
3049:the original
2950:
2944:
2900:
2894:
2851:
2845:
2794:
2788:
2741:
2735:
2686:
2680:
2635:
2629:
2584:
2578:
2548:
2520:
2513:
2494:
2490:
2480:
2469:. Retrieved
2458:
2405:
2401:
2391:
2348:
2344:
2338:
2285:
2281:
2271:
2228:
2224:
2218:
2173:
2169:
2113:
2109:
2103:
2060:
2056:
2050:
2009:
2005:
1995:
1968:
1964:
1954:
1929:
1925:
1919:
1874:
1870:
1860:
1833:
1829:
1819:
1794:
1790:
1781:
1761:
1754:
1745:
1739:. Retrieved
1734:
1718:
1701:
1697:
1688:
1671:
1667:
1661:
1628:
1622:
1616:
1583:
1577:
1572:Ewen, H.I.;
1567:
1542:
1538:
1529:
1478:
1474:
1450:. Retrieved
1422:
1418:
1402:
1357:
1353:
1343:
1310:
1304:
1294:
1267:
1263:
1229:
1223:
1217:
1206:. Retrieved
1184:
1171:
1148:
1073:
1034:
978:
974:Solar System
945:
912:
895:reionization
880:
877:In cosmology
867:
863:polarization
859:antihydrogen
845:strength of
836:
791:
773:Christiansen
758:
750:ground state
711:
703:Horn antenna
649:
646:
627:
623:(30) cm
608:
567:
311:
306:lower energy
305:
285:ground state
274:
196:
153:
149:
138:(30) cm
94:ground state
56:
52:
48:
46:
36:
3140:Outer space
3128:Spaceflight
2903:(1): 1–11.
2528:. pp.
2332:. 20190564.
2116:(11): 066.
1836:: 859–876.
1425:(1): 7–15.
811:cosmic dust
798:L band
279:bound to a
219:cosmic dust
215:radio waves
177:(81) μ
3162:Categories
2638:(1): 1–8.
2471:2023-04-26
2415:1908.04296
2295:2003.06881
1989:. 111E016.
1741:2023-04-28
1452:2023-04-27
1419:Metrologia
1277:2208.06070
1208:2023-04-30
1164:References
1123:nanometers
956:Pioneer 11
952:Pioneer 10
915:ionosphere
831:21 cm
574:wavelength
239:H. E. Ewen
124:wavelength
3104:Astronomy
3092:Chemistry
2993:118712522
2985:0004-637X
2960:1211.6450
2953:(2): 90.
2721:119439713
2619:118239661
2570:Cosmology
2383:119595472
2148:250754168
2123:1311.4574
2070:1010.0292
2034:1538-3881
1523:. 086901.
1488:1109.6012
1447:250873158
1335:0047-2689
1140:Footnotes
1069: GHz
1058: MHz
1030: GHz
1019: MHz
965:Voyager 2
961:Voyager 1
887:dark ages
813:that are
777:Milky Way
738:frequency
707:Milky Way
694:Discovery
660:10 s
652:forbidden
582:frequency
520:≈
512:−
502:⋅
481:⋅
470:⋅
447:−
439:⋅
421:⋅
402:−
394:⋅
380:≈
374:⋅
355:⋅
350:ν
339:λ
322: μeV
251:cosmology
243:Milky Way
221:that are
203:microwave
117:(2)
102:frequency
3193:Hydrogen
2886:15464776
2837:30510359
2829:15245272
2670:10258589
2450:34511720
2330:33222645
2288:(2188).
2263:15210736
2210:16389221
2095:53582482
2042:15541399
1726:(2002).
1653:32329393
1608:27595927
1559:20023736
1521:41341641
1513:22828208
1394:11547883
1092:See also
1086:harmonic
899:redshift
883:Big Bang
802:UHF band
796:(in the
734:hydrogen
719:Jan Oort
666:using a
277:electron
65:solitary
3080:Physics
3066:Portals
3015:(NRAO).
2965:Bibcode
2935:7343629
2915:Bibcode
2866:Bibcode
2809:Bibcode
2778:6474189
2756:Bibcode
2701:Bibcode
2650:Bibcode
2599:Bibcode
2530:133–135
2441:8416573
2420:Bibcode
2363:Bibcode
2321:7739898
2300:Bibcode
2243:Bibcode
2188:Bibcode
2128:Bibcode
2097:. A128.
2075:Bibcode
2014:Bibcode
1973:Bibcode
1934:Bibcode
1911:5938714
1889:Bibcode
1838:Bibcode
1799:Bibcode
1706:Bibcode
1704:: 201.
1676:Bibcode
1674:: 117.
1633:Bibcode
1588:Bibcode
1493:Bibcode
1427:Bibcode
1372:Bibcode
1315:Bibcode
1234:Bibcode
1191:Bibcode
1119:H-alpha
969:pulsars
889:" from
804:of the
800:of the
765:Purcell
752:of the
731:neutral
600:is the
592:is the
580:is its
572:is the
2991:
2983:
2933:
2884:
2835:
2827:
2776:
2719:
2668:
2617:
2536:
2448:
2438:
2381:
2328:
2318:
2261:
2208:
2150:. 066.
2146:
2093:
2040:
2032:
1909:
1797:: 39.
1769:
1747:noise.
1651:
1624:Nature
1606:
1579:Nature
1557:
1519:
1511:
1445:
1392:
1333:
1080:is an
1074:Since
815:opaque
613:21.106
596:, and
568:where
544:
541:21.106
530:
494:
455:
410:
281:proton
223:opaque
199:L band
182:. The
163:energy
159:photon
157:, the
142:vacuum
128:21.106
96:. The
3116:Stars
3022:arXiv
2989:S2CID
2955:arXiv
2931:S2CID
2905:arXiv
2882:S2CID
2856:arXiv
2833:S2CID
2799:arXiv
2774:S2CID
2746:arXiv
2717:S2CID
2691:arXiv
2666:S2CID
2640:arXiv
2615:S2CID
2589:arXiv
2410:arXiv
2379:S2CID
2353:arXiv
2290:arXiv
2259:S2CID
2233:arXiv
2206:S2CID
2178:arXiv
2144:S2CID
2118:arXiv
2091:S2CID
2065:arXiv
2038:S2CID
1907:S2CID
1879:arXiv
1731:(PDF)
1649:S2CID
1604:S2CID
1555:JSTOR
1517:S2CID
1483:arXiv
1443:S2CID
1415:(PDF)
1390:S2CID
1362:arXiv
1272:arXiv
1181:(PDF)
1062:8.924
1023:4.462
523:0.211
474:2.997
432:5.874
387:4.135
318:5.874
265:Cause
167:5.874
140:in a
59:is a
55:, or
2981:ISSN
2825:PMID
2534:ISBN
2446:PMID
2326:PMID
2114:2013
2030:ISSN
1969:2014
1767:ISBN
1509:PMID
1331:ISSN
1051:.405
1012:.405
981:SETI
963:and
954:and
946:The
921:and
783:Uses
763:and
761:Ewen
293:spin
175:1116
110:.405
76:spin
47:The
2973:doi
2951:763
2923:doi
2901:626
2874:doi
2852:625
2817:doi
2764:doi
2742:347
2709:doi
2687:608
2658:doi
2636:596
2607:doi
2585:475
2499:doi
2436:PMC
2428:doi
2371:doi
2349:650
2316:PMC
2308:doi
2286:379
2251:doi
2229:633
2196:doi
2174:372
2136:doi
2083:doi
2061:525
2022:doi
2010:133
1981:doi
1942:doi
1897:doi
1875:295
1846:doi
1807:doi
1641:doi
1629:168
1596:doi
1584:168
1547:doi
1501:doi
1435:doi
1380:doi
1358:359
1323:doi
1282:doi
1242:doi
1199:doi
1064:672
1053:751
1049:420
1035:or
1025:336
1014:751
1010:420
817:to
767:at
744:420
740:of
656:2.9
640:751
637:405
634:420
621:160
618:054
615:114
225:to
172:184
169:326
165:of
136:160
133:054
130:114
126:of
119:MHz
115:768
112:751
108:420
104:of
3164::
3011:.
2987:.
2979:.
2971:.
2963:.
2949:.
2929:.
2921:.
2913:.
2899:.
2880:.
2872:.
2864:.
2850:.
2831:.
2823:.
2815:.
2807:.
2795:92
2793:.
2772:.
2762:.
2754:.
2740:.
2734:.
2715:.
2707:.
2699:.
2685:.
2664:.
2656:.
2648:.
2634:.
2613:.
2605:.
2597:.
2583:.
2532:.
2524:.
2493:.
2489:.
2444:.
2434:.
2426:.
2418:.
2406:51
2404:.
2400:.
2377:.
2369:.
2361:.
2347:.
2324:.
2314:.
2306:.
2298:.
2284:.
2280:.
2257:.
2249:.
2241:.
2227:.
2204:.
2194:.
2186:.
2172:.
2168:.
2156:^
2142:.
2134:.
2126:.
2112:.
2089:.
2081:.
2073:.
2063:.
2059:.
2036:.
2028:.
2020:.
2008:.
2004:.
1979:.
1967:.
1963:.
1940:.
1930:21
1928:.
1905:.
1895:.
1887:.
1873:.
1869:.
1844:.
1834:74
1832:.
1828:.
1805:.
1793:.
1744:.
1733:.
1702:13
1700:.
1672:12
1670:.
1647:.
1639:.
1627:.
1602:.
1594:.
1582:.
1553:.
1543:82
1541:.
1515:.
1507:.
1499:.
1491:.
1479:75
1477:.
1461:^
1441:.
1433:.
1421:.
1417:.
1388:.
1378:.
1370:.
1356:.
1352:.
1329:.
1321:.
1311:38
1309:.
1303:.
1280:.
1268:90
1266:.
1254:^
1240:.
1230:50
1228:.
1197:.
1183:.
1067:55
1060:≈
1056:77
1045:×
1028:27
1021:≈
1017:77
1006:×
930:.
779:.
756:.
630:=
611:=
584:,
527:06
485:10
478:92
443:10
436:33
405:15
398:10
391:67
320:33
261:.
194:.
186:,
179:eV
154:hν
152:=
67:,
51:,
3068::
3030:.
3024::
2995:.
2975::
2967::
2957::
2937:.
2925::
2917::
2907::
2888:.
2876::
2868::
2858::
2839:.
2819::
2811::
2801::
2780:.
2766::
2758::
2748::
2723:.
2711::
2703::
2693::
2672:.
2660::
2652::
2642::
2621:.
2609::
2601::
2591::
2542:.
2507:.
2501::
2495:3
2474:.
2452:.
2430::
2422::
2412::
2385:.
2373::
2365::
2355::
2310::
2302::
2292::
2265:.
2253::
2245::
2235::
2212:.
2198::
2190::
2180::
2138::
2130::
2120::
2085::
2077::
2067::
2044:.
2024::
2016::
1983::
1975::
1948:.
1944::
1936::
1913:.
1899::
1891::
1881::
1854:.
1848::
1840::
1813:.
1809::
1801::
1795:7
1775:.
1712:.
1708::
1682:.
1678::
1655:.
1643::
1635::
1610:.
1598::
1590::
1561:.
1549::
1503::
1495::
1485::
1455:.
1437::
1429::
1423:1
1396:.
1382::
1374::
1364::
1337:.
1325::
1317::
1288:.
1284::
1274::
1248:.
1244::
1236::
1211:.
1201::
1193::
1077:π
1047:1
1042:π
1040:2
1008:1
1004:π
1001:0
742:1
658:×
632:1
628:ν
609:λ
598:c
590:h
586:E
578:ν
570:λ
551:m
548:c
538:=
534:m
515:1
507:s
498:m
489:8
462:V
459:e
450:6
425:s
417:V
414:e
377:c
369:E
366:h
361:=
358:c
347:1
342:=
188:h
150:E
106:1
91:s
88:1
34:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
