Equilibrium concentration of free Na atoms in the atmosphere has been calculated from photo-chemical reactions, diffusion and assuming that. there is a constant influx of Na atoms from either the top or bottom side of the atmosphere. The analysis reveals the direction and magnitude of the flux of Na atoms in the atmosphere and hence settles the question whether these atoms have terrestrial or extraterrestrial origin

Ghosh, S N

Mitra, V

English

IACS Institutional Repository

Indian J. Phya., 48. 1-10 (1974)Origin of sodium in atmosphereS. N. GhoshJ . K. Institvie of Applied Physics and Technology. University of Allahahad.Allahabad, hidia^ANDV. M it r aMofi La,! Nehru Regional Engineering Collsge, Allahabad. U. P. {Received 20 September 1972)Equilibrium concentration of free Na atoms in the atmosphere iias been calculated from photo-chemical reactions, diffusion and assum­ing that. thori3 is a constant influx of Na atoms from either the top or bottom side of the atmosplmro. The analysis reveals the direction and magnitude of the? flux of Na atoms in the atmosphere and hence settles the question whether these atoms have terrestrial or extraterrestrial origin.1. Introduction(Certain metallic atoms and ions have been obseivod in tlie atmosphere. For example, the spectroscopic studies of the night and twilight airglows revealed the presence of Na, K, Li atoms (Blamont & Donahue 1964, Sullivan & Hunten 1964, Dolamioy & Weill 19o8). Mass sj)ectromotors carried in rockets sliowed the presence of Na^, Ca ,^ Mg  ^ and probably' Fo+ (Istomin 1963, Narcisi & Bailey 1965). The twilight of Na. which is comparatively richer in the atmosphere, has l)een extensively studied (Hunten 1967).Many attempts have Ihhui made to interpret tJio sodium distribution in terms of the photo(‘homieal reactions in the upper atmosphere. In these investigations (Blamont & Donahue 1964, Sullivan & Hunten 1964, Gadsden 1964, Jungo et al 1962), it is assumed that there is a constant mixing ratio of sodium (free, com­bined and ionized) to other constituents of the atmosphere, and that the con- iiontration of free Na atoms is modified to different extent at different altitudes by oxidation and ionization processes. According to this assumption, one would expect scale height on the top side of the sodium layer nearly equal to that oi' the atmosphere. This is, however, in disagreement writh recent observations (Donahue 1966, Hunter & Wallace 1967, Donahue & Meier 1967) of height dis­tribution of sodium obtained by rocket measurements. The scale height of sodium on the topside of the layer is observed to l>o about 3 km, whereas the12 S. N- Ghosh and V. Mitraatmoaphw-ic nealo lioinht at tlif« fiamo altitudo ran'j;o is about, (i km. Roocmtly, it. lias boon suggostwl (Donalmo JOtiG. .Ihmtou &■ WalliU’O 19(57. Donahue & Meier I9(>7. Hunfon & CJodsou 1!M57) that sodium is rolea.stxl from d i.st partioos, Gadsden (1967) point.od out certain implications in the dust' bypot]iesi.s and suggested an alternative explanation on the liasis of mdeor alilatiou. Thus, the origin of sodium in tjio at'muspluM'o is still a subjoGt ot controNorsy.Tho hoight distributions of nil motallio atoms and ions (tionos 1906) in tJio atmosphoro rovaal maxima approx imatoly in tlu^  alt it ads rango 90-100 km. This iiidicat(js that tla^ ro is cc^ rtain i (»mnion ]>r(x‘tv^ s th[th‘riv(» in prodiioing thos(  ^maxima. Siiu^ o tho vt r^tical dilTusioii of bva atoms iiaving a constanti’lfiiix in tho atmospiioro cun produc<5 a maxima al a cortain altituds Uu> diffusion process seems to play a role in ostablisiiing thou equilibrium coiicontrations.In tho present paper, tho equilii)rium concoiiiration of tree Na atoms has boon calculated from pJiotochemical reactions, ditfusion and assuming a constant influx of Na atoms from eithoj* top or bottom side of tiio atmospJi<u*(^ . Such an analysis will reveal tho direction and JiiagpJtudo ‘ >f thc^  flux Xa atoms in t}l<^  atmosphere! and Jiencii will settle tlioir origin frv>m tiuaesijial or oxtra-toiTostriai source.2. E quilibrium  P rockssesIn considering the equilibrium propesses, tlio following chemical reacdlonscl oxyg(m atojus i w  cousidonid .M — > XaO^ I M, ... (i«)h 'i\'a+(>3 XaO +  (t ,^ ... (16)k"NaO, 1-0 — > X aO +().., ... (Ic)NaO-f 0k '"— > Xa -I O,. ... (Id)in addition to those, tiio ionization (Pales w Seaton 1950) of Xa atoms and tlieir recoml)inatiou3 (Bates ife Boyd I0r)(>) art^  also "ousidorod, ruumdyNa + h v  N’ a c , 2^a)Na'' I 0 “ —♦ Xa<)-!-/(.' i^b)whoro /c,', fcgh k  , k "', aad are. tho rate coolTicioul.s of tho various reactions.Tl... oqi^brium „■ „r Xa. of .N'aO. molocute, ofNaO moloauloa and r  of N .' i„„a (all (,ho3» oo^apond to ,nOrigin of sodium in atmosphere 3{ivorag(» atmosplioi'o) aro produood by tho joint efibct of tlio reactionH (la. 6, r. d) and (2a, h) and diffusion of various sodium products.3. Equilibium Equations»Siq)pose on tlio average metallic atoms are continuously deposited per unit area per scKJond from a certain agouey (terj'cstrial or oxtra-torre>strial) in some layer of liie at]noS])}uu'e remote iVom the region of maximum sodium con­centration. At tlie steady state of dinusio)i, tl\o not current of the combined sodium products should be cousitint in each layer of tljo atmosphoro and be equalto the fhix S..orThuso f'/> ) r I (i n' \ }/-\-c' -\-(V “  a-' h \ c j d~~ Sf^  0.... (3)... (4)Hero the sign of has been sot such that if S^y is positive, the not flow of the cornhiTUKi sodium products is in tji(> upward direction and the metallic atoms liavo their origin from tlie eartb,.id*  ^ If on the otb.er jiand is negative, su(h atoms liav(i tluur origin from tli<^  outside of the earth. During motion Xa atoms may und >rgo any of tlio reactions —(la, b, c, d) and (2a, b) but since all sodium products invohm only one Na atom, the validity of equation (4) is always main­tained.A numlxT of offe.-ts otlier tlian those considered in the present staidy, may modify the net steady cumuit of sodium products duo to difftision from one hyoT to another. For example, iU<^  dust particles or meteors carrying Xa atoms may Rstain sonu^  of tlioir initial velocity in addition to the diffusive velocity. I^ lio dust particles or meteors may continu(» to travel up to a considerable distance Intforo they release X"a atojns. Hence tliese atoms may bo deposited dirovUly in different amounts in diffennit lavi^ rs. Eddy diffusion du(^  to vertical velocity of wind may also be effective. But all such processes aro likely to subside before Xa atoms roach the n^gion of maximum conc ^itration. Formation of a region of maximum concentration indicates acrcumulation of Xa atoms duo to slow movonumls indicating abscn<*e oi' all rapidly changing proceases iiientiom>d ahovo. TIm^ assunuid procosa .^s should, therefore, be applicable at least in a region close to tlio layer oi' maximum conciuxtratioii.Tf tv\ w", w/" and wl' be the upward vertical diffusion velocities of Xa. XaO^, NaO and Na+, respectively, in any layer of altitude Z then,a v'iv'd =  n*ib\S. N. Ghosh and V. Mitra(»)Kquation (4) then becomesn'w'+n"u-''+n"'i<’’" ~Th, v,tei.y . f  of » y  »>■>» » » • « “ “  °*thtoonh a stabto n»m .tmoaph.r. a t... aUitud. Z ■» P™" >>.vwhere different symbols us<«i in the equation are as follows 1) — coefficient of diffusionf,i'_ molecular mass of diffusing constituent)ti moan inolec.ular mass (tf the main gas _  scale hoight. of the atmosplioro /i — gradient of the atmosplieri(; scale height X — thermal diffusion factor.Equation « shows that ic' can to either m'gative, zero or positive. If the consti­tuent concentration decreases slowly with altitiid ', the second term in tho equa­tion ontweights tho first and tho transport is in the downward direction. If on the other liand the coiwlitnent concentration falls off rapidly with altitude, the first term prodominatos and the transfiort is upward.'I’lio continuity equation under the sti^ ady state of diflusion ol all the sodium products together is given byd(7i"w')  ^ d(n 'W )dz dz '  dz(7)Each term in equation (7) represents the rate of change of cone<nitration of coitaiii sodium products duo to diffuBivi* velocity in a given layer. Ea(*h term is small compariHl to such rate of the prcnhict liy photoc]Lemi(!al reactions particularly in a region closer to tlie maximum of sodium concentration. Thfireforo, it can he approximately assumisd that th ‘ (equilibrium in a layer among various products of sodium is proposed by photoi heinical reactions (la, b, c, d) and (2a, b) Thusandn{0) \-Q^ n’n(iyk,'n'n(i)^) k"n"n(()).(8a)(8b)Since on the averages the concentration of Na and Na*** remain constant in any layer we have also^  Q^n'n(0- (80)Origin of sodium in atmosphereTiie concentration ol various products of sodium in any layer can, therefore, be represented in terms of the concentration of Na atoms of the same layer. Thus■ I *"(«(0 ) J’L jfc"'w(0) >"'»(0) J ’[ O s^b -y]'(9a)(9b)(9c)In tlie absence of any reliable measurement of the concentration of O ■ another simplifying assumption may bo mode. The assumption is that/?' rr- n ... (9d)Thus each product of Na atoms should satisfy equations (9a, b, c, d) as well as equation (5) under the joint effect of the chemical and diffusive equilibrium of the atmosphere. Substituting in equation (5) the values of w\ and w'wo have/>' ■-4; i j r  -i- !)••' .^2ir,, l o ydZ nz z dZ 7IZn Ii r { m j-/il)"'n '" I m'" , , ,, ,,, \H m•2D'n'In case an ion-oJoctron plasma diffuses through a neutral gas, ambipolar diffusion coefTicient (whicli is double of tiie diffusion coefficient of Na‘ ) is used in the ex­pression of tZi' Also for the mass of Na  ^ the mean molecular mass of ion-oloctron /.r., (nVj2) is to bo used. Because Indow F layer of the atmosphere any ion will suifbr collisions mainly with the neutral particles, the diffusion coefficient of Na* (uin be calculated with the help of the same formula which is used for the neutral particles. Again substituting the values of n'" and n' in terms of /T and neglecting the effect of thermal diffusion in equation (10).dn' rdZ [ ! )• + ( k" -(-D"'k7 \nn(0^)T '~ 7 ~ » ( O r ^ L \ Jt' ' k'" I adZ\ n(0) rD '"k M O ,) I gp,1d / » (0 .) Vk’"  n(0) )S. N . Ghosli and V. Mitra( a'"  /*(0 )  ^ k"'n(0) r  I. . .  ( 11)^ mil {f ..ndimit n' (max) is ol)taiiu*cl from tlm followm*- oonwnitratio.i of aoitmin u' ‘ -" '“ I " ' ' 'HTho maximum equation10. ... ( 12)tra4. Vautks and CosiputattonFrom tho ohaorvod l.oighl disirilmtioa of Na atom., Urn maximum conoon- ation of sodium and it.s altitude are known. l>om oquation (12) S„ oanho dotorniinod if oUkt quautitats hoIonuiuR to Ihi.s iiftitudo are known. \ aliios of ,% ohtainod from equation (121 vun Ih> used in miuation (11) for cominitinR t.lu' hoiRht distrilmtion of Na atoms in tho alrnosythmv in a rooion of maximum aodiuin conoontralion viz.. 80 to 120 kmAt Saskatoon tlio avis-ago value of n\nnr may ho taken about 000 atomH/cm‘* and it is at an alliUide of about 03 km {Sullivan t'v Huntioi 1004). Vuluos of //, /dO,). /((()), nf. T. II and // at (lifferent altitncbr’ an available, at an interval of on<‘ kilometer from (JOSPAR Intenuitional TOdbrenee Atmospluiro (Cliampion 1905). Suck values for are albo available (I'.S.A .Xirforee Handbook ofGeophysics 1901). All tliese atmospheric data b(‘lon*.^  to an average atinospben^ The values of n'jnax altitude Mhicl^  are mentioned abo\a) belong to Saska*toon (52^N), therefore all the data of the atmosphere sliould liave also boon taken at tho same latitude. In the lack of sucii precise latiludeuise data, the average atmospheric data is being used here. In tlu^  absfuico of known values of the rate coefficient of reactions botv\een sodium and oxygen, the values of tho corres­ponding reactions between Itydrogon and oxygen may bo used as w^ as done by Blamont & Donahue (1904). Presfmt authors (19Gb) have also used rate coefficient of reactions betw een hydrogen and oxygon for \]\om between lithium and oxygen. • ; ’ ‘ inten (1967) has applied correction to tho rate coefficients of hydrogenand oxygon roactionft to obtain host guosaos for the rato ooofl&oiont of sodium - oxygon rciictions. His values areA * , '  ~  2 x  1 0 '  -''’  ^ c m ®  8 0 C “ ^• ,  A * ./  -  b - 5 > :  1 0 - 1 2  o m 3 s o c  ^F  ^  lO' ii cm  ^soc"i k *"' --  4 y  cm® socTroalijig tho moloculos lo hi) rigid clastic sphoros, tlioir diffusion coofficioiits can be calculated by tho following formula ((. i^iapman vfi: (-owing 1952)Origin of sodium in  atmosphere 7n 3 j lcT(Wy ,^L 27rmj7)L, J (13)whore cr rr,.12 "v arious symbols used arc as Ibllows •o*j, fTo - molocuiar diameter of tho minor and main gasesk — Boltzman constantT — absolute temperaturemj, nio — masses of tho two kinds of moleculesyt — molecular density of tlio main gas.It iuis boon shown (( l^olomb Mcljood I9()()) (hat tluv values of the diffusion (axdHciontH (\stimatod by using th<^  above formula are in good agreement with theses measunul from the radial growth of clunniliimiuous trials deposited in the upper atmosphere.In the absonoo of known values of ooilisional diameters of atoms, molecules and ions (to bo used in (Kpiation (13)), tlioir size is obtained from the knowledge of their clxomicail bond and valency. Tiie diameters of tho sphere which cir­cumscribe their chemically dotormimxl struoturo have boon tentatively taken equal to their ooilisional diamotors.Tho radii of !Na and Ka aio, rospoctivoly, knouii to be 1*572 A and 0*95 A. Their ooilisional diameters may bo taken equal to 3*14 A and 1*90 A rospoctivoly. Tho ()-~0 distauco in tho molecule of NaOa has beou repented to bo 1*28±0*01 A (Pauling 1900). Tho oxygon atom (Is'^  2s2 2p ‘ ) has two unpaired p eloctrons wliioh are oriented at right angles and ihoroforo ono might oxiK c^t Na-0-0 angle to bo nearly 90^ ’ (Stator 1931). Tho approximate shape of NaOg moleoulo can be obtained by drawing two spheres (0 *®“ molooulos) each of radius 1*4 A with a distance 1*28 A  between their centres and ono of which is ioiioluKl in a per- in>ridioular direction by another sphere (Na moleoulo) of radius 0*95 A. Such8 S. N . Ghosh and V. Mitraa molecule will be ciroumsoribod by a sphere of radius 2-54 A. Therefore the collisional diameter of NaOg molecule may b(^  taken equal to 5*62 A. In a com- pletoly ionic linkage NaO moJociile would contain Na  ^ and 0 “ ions. The radius of Na  ^ is (h95 A and in the absence of exact radius of O the radius of (1*4 A) can bo approximately taken. A spJioro circumscribing two touching spheres of th(me radii would give the diameter of NaO molecule equal to 5*42 A for the completely ionic linkage. For a single bond covalent linkage the diameter of NaO molecule would be the sum of the diameters of Na atom (3*144 A) and O atom (1*48 A) and is equal to 4*624 A. As the linkage of NaO is 82 per cent ionic, the diameter of NaO would bo equal to about 5*276 A. Moan collisional diameters of air molecules at different altitudes between 80 and 120 km are obtained by taking the collisional diameters of No, (X, and O equal to 3*15 A. 2*98 A and 1 *49 A respectively.Fig. 1. Diffusion Coefficient, of Na. Na^ NaO. and NaO, at different altitudes.Diffosion coefficients of Na, NaO, NaO and Na as calculated with the help of the above values arc plotted in fipire 1 lK,tween altilnde range 80 to 120 kmR esults and Discussions F W  ,12, th« vah.™ .V.sjgn mdicato, that the toflax „t Na atoms i. ftoa. outaida the earth0 ^  th» va^ ao of S, m aqaati™, (11), th» h.ight diatrtbution of Na atom, totavooh Uia altrtad. ranp, ta  i. ^Origin of sodium in atmosphere 9KMFig, 2. Tho hoiglit distribution of Na atoms obtained from equation (11).TJio extra-torrcstrial souruo of Ka atoms, as revoalod in prosent study, may l>o oilher tJu^  iiitorsiollar dust or m(d(u.)rs. It is assumed that, thoro is a (ionstant current of sodium flenving througli all layers iKdweon 80 and 120 km. This assumption is true only wlnm ail Na atoms are released irom tho dust or meteors soon after their entry into the atmosphere. If meteors are the source of tho atmospheric sodium, following Gadsden’s suggestion, tho release of Na atoms wdll not he complete until considerable depth of tin? atmospliero is pene­trated. Tho assumption of constant vertical current of sodium products flow ing through all layers, as assumed in our analysis, will not l><^ true. However at, 93 km which is tho altitude of maximum sodium C(jncentration tlie release of Na atoms should bo nearly complete. Hence the topside of the computed curve of sodium distribution curve has a stec>]>or rise compared to tJiat of tho observed curve. It is, therefore likely that the atmospheric sodium is of meteoric origin.In any case, the arguments and assumptions of the present study are valid for the region of maximum sodium concentration and therefore, of tho equations (11) and (12), at least the latter is valid. Moreover, substitutions of various quantities in equations (11) and (12) show, that very few terms namely(D’ +2D'), and ^(/>| 2D')have aignifioant contributions. It may be pointed out that all tlie quantities involved in these terms are known. Quantities liaving uncertain values,!(► S. N. Ghosli and V. Mitraj'oat'.tion Goofiticumt, dillusiou oootticii i^ils of NnO  ^aiui NaO inoloculos ari» avoidod. Tliorolon  ^ (rom ari»uinouts, tlioro is no uiicoj'laiiity in llio diroctioti of tlioIlux of Na atoms in aljiiospluao as olilaiuod fn>ni (‘tpiatioii (12) Tlu» prosoiil study, ius])ito of havinu a limited and n^strieted usii al. all altitudes duo to motoor aMatioii, doliiiitoly iiidit-atos tlio origin of atmos])JuTic sodium to l>o froin <ixlra tom^htnal souroe and most likoh' from mo1iu)rsRefehenckslialos L). ii, tS: litn il T .  J .  M. ll)r»a /Vor. I^lufs S o i , A -69, 10<>.IkiO'S 1). K . X' Soa-toii M. .1. 1950 /Vor, /V<//,s’. Sm . B63, iLMtJ . K. ,V: J)(inabn<‘ 'I' M IJHM J  (Ivoplnff;. /iV v. 69. -lOO.*}.( ‘hrtpinaii S. X t ovvling Ct 1951' Thv Mafhanattraf T/norff o f  in fo im  (Uitas, p. 1M5,raiiif)n(lga U n i\ t 'v s i t l'rc•h^ .( 'hainpioti K S \\ liMi.") A u ‘ ( 'ffmf)r/</(ff LahoKtlont s l»rjioi/ A f'('IiJj-(\r)-44',lAfmoxjAtvnt l^iop< An s iu lln Ihnnp  110-*100 kjji.).l>'laminy A k  Weill (i, 105cS ( ’./»*. A r a d .  *>ci. { I\nhA  247, SOO,Donahui' '^ t. M lOOO J  (jtojdiifs. Hm.  71, - 2II7.I >f>iiahue 'I\ cV. Mru'r 1{. HHi7 -/. Urophsjp.  72. I'SOIl.(Ja<ts(l('ii iM. llHil A n n  (Jiopiiys.  20. .‘1811.Gudrtdon M. 1!)07 ./. Ainw.sjih. l*lujs. 30, 151.(Jliosh S. N X- .Mill’d V . 1001) A n n  (.)ro})hjiti. 22, 000.(tuloinl) 1). k  ^Vlac](‘od M. A. 1900 J .  (hophpfi. Jivy.  71, 22110,Huiilon 1). M 1007 Sparc S r i .  J*rr. 6 . 510.Hiinteji J) \\. k  CJod.sfjii W . Jv. 1907 J .  .U m oyph. S r^  24, so Hnnlnn I). M X VValliicr (^ , 1067 ./. (Uophifi^ llrfi. 72. 09 Istomin \'. (J, lOOil Ahmet S p a n  S r i  11, I 7,’l. dories 1966 A n n .  Geophps. 2 , ISO.dimgn C. E ., Oldeubidg O. k  VVa.sson d. 'V. 1062 J  Ireophp.^ J h s .  67, 1027.Mange I'. 1955 A)ui .  Cico})hys. 11, 1,57.Xai'sist U. S A: \UWv\ A. I). 1065 Lahoratorn s Aejnnt A t 'C J iL - in n S l  S p e rt ia w e iiy  in Hu1) fiCijion Ionnspherr-A])jinrfitn,s, Terhnnpu and first Alen sifrem od) .  Pauling L. I 960 Idir Sa/nrr of the Chnnicat Bond  p. .‘152, ( ornrll rni\crsit\ I'ress, IthocnNew Y o rkKatcliffe d A. VVenkf*^  K \\H)a itf the A p p n  .Mwosjdu ri (d A . KmOcliffe fi. 391./Vcudemic Pr('s,s. Nc'w York and London.Slaler d. C lOIll /Vr//.v 37. 481Sullivan H . M. k  Huntcii 1). .M. 1064 Cam nl.  J .  Ahy^. 42, 9.‘17. r  S. A i r  Force i iandhool  of a<opUn.sirs 1961 Macnullan. Ni»v\ Y m k , llexisod Ed-

Origin of Sodium in Atmosphere

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Origin of Sodium in Atmosphere

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