Transfer of excitation energy from nitrogen molecules to sodium atom

Fite, W. L.

Krause, H. F.

Mentall, J. E.

English

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https://ntrs.nasa.gov/search.jsp?R=19680016513 2020-03-12T10:51:12+00:00Z
! t 
' J. E, Megtall, H, F. Krause-aad W, L, Fihe 
?~petpqn%ubnt of p h y s i c s ~  and Spwce Research Coordination Center 
/ University of PiOtsburgh 
Pittsburgh, pennsylvania 15213 
USA 2 
For presentaOion at tbe Faretdw Society's General Piscnssh~ on Molecular 
Wpwics o f  tha Chemical. Reactions in Gases Toronto University S C ~ + ~ ~ U ~ Q T ,  1967. 
?Ehis regearch was suppqrted in part by the National A@ronautics and Space 
e@inis$ra*ion snd in part by the Advanced Research Projects Agency. 
Transfer of Excitation b e r i g  from Nitrogen Molecules t o  Sodium Atoms 
J, E. Mentall, H. F. Krause andW. L. F i t e  
Department of Physics and Space Research Coordination Center 
University of Pf t tsbwgh 
Pitesburgh, Pennsylvania 15213 
USA 
ABSTRACT 
apcrimcsnta have been performed i n  which a beam of N2, issuing from 
a furnace! sc?urce operating at  temperatures from 2000 t o  3000°K, crossed a 
beam of sodium atoms. 
the coklisions of the  two bsamg. 
f romthe transfer of in te rna l  energy i n  t he  diatomic molecrz2e, which because 
8odium D-line radiation was observed ss a product of 
The radiation appears t o  occur primarily 
of the nature of the molecules must be vibrat ional  and rotationaJ only, i n to  
eletctroaio energy i n  the sodium, presmab2y through the  formation of a 
t rans i tory  NaN2* complex. 
i s  involved, rate coeff ic ients  of approximately 
t h s e  molecules wi%h suf f ic ien t  in te rna l  energy t o  exci te  the sodium. 
.temperature dependences of the observed,rate coeff ic ients  are discussed. 
On the assumption $ha% on3.y in te rna l  energy t ransfer  
3 ern /see are found for  
Weak 
"he quenching of sodium resonance radiation by diatomic molecules is well- 
1 known and has been studied extensively under a variety of laboratory conditions, 
In the case of Nz as the quenching gas, the first electronic state is more thaa 
6 eV above the groundstate and ,the transfer must therefore involve the conversion 
of 2.10 eV of electronic energy in the Na into vibrational and rotational energy 
in the N2 and kinetic energy. The effective cross sections are large, typical 
values published ranging from 6 to 40 x cm20 
excitation levels which are nearly resonant with the energy of the sodium excitation, 
it is often assumed that quenching OCCUPS primarily through the excitation of 
Because one can find vibrational 
vibrational energy in the N2. 
of the NaN2 complex, which might, however, give products with low internal 
energy and large kinetic energies, 
This presumably must proceed through the formation 
36 
Wbsther the excitation is transferred with little involvement of kinetic 
energy is of considerable interest to the understanding of certain types af 
aurora in which very strong sodium radiation fs observed. D. M. Hunten has 
considered the auroral sodium excitation problem in detail and has concluded that 
2 
direct excitation of the sodium by energetic electrons fs untenable; the 
competition for these electrons is overwhelmingly won at the auroral altitudes 
by the much more abundant N2 molecules, which become vibrationally excited to 
the v = 8 state with large cross sectione3 Huntan propose4 that the excitation 
of the sodium arises through transfer of thfs vibrational energy in the N2 to 
electronic excitation in the Na, a process which has been observed to occur 
and for which & lower limit to the cross section has come from shock tube data. 
4 
5 
Whether this proposal is tenable depends on the cross section for such B 
transfer process. 
sections are not fully satisfactory in the absence of a guarantee that quenching 
does not result in products with l o w  internal excitation m d  large kinetic energies. 
A direct quantitative eqeriment on transfer of energy from N 
called for, 
Detailed balancing arguments applied to the Na quenching cross 
to Na is clearly 2 
This paper describes such an experiment. 
2 
The experiment, which u t i l i z e s  beams crossed at  90' is shown schematically 
i n  Fig. 1, 
between 2000 and 30OO0K0 
would make on the average approximately 10 
escaping in to  the  beam and the use of tungsten wire wadding inside the furnace 
m t h e r  increases contact of the  gas w i t h  the  hot surfaces of' t he  furnaoe!, it 
i s  assumed that the gas reaches equilibrium w i t h  the furnace w a l l s  and the degree 
of excitation of in te rna l  energy s t a t e s  is t h a t  given by the Boltzmann dis t r ibut ion.  
Typically, therefore,  only about one molecule i n  1 0  has suff ic ient  in te rna l  
energy t o  excite the 2,lO e Y  sodium excited s t a t e ,  The slow relaxation rate 
f o r  vibrat icpal  exaitation i n  N2 implies t h a t  the  vibrat ional  population remains 
very nearly that i n  the furnace even a f t e r  the gas emerges and foms the 
molecular beam, 
The diatomic gas is  excited by heating i n  a tungsten furnace operating 
Since the h r n a c e  geometry i s  such that each molecule 
3 col l is ions w i t h  the walls before 
4 
The sodium atom beam i s  produced i n  a double-chamber oven, t h e  temperatwe 
of the  rear chamber governing the beam intensi ty  and the temperature of the 
front  chamber d e t e m i n i q  the beam speed., 
Sodium D-line photons produced by t h e  interact ion of t he  N2 and N a  beams 
%re detected w i t h  an EM1 9558A photomultiplier which views the interaction 
region.. Wavelength discrimination is achieved us- a 10 8 bandpass interference 
f i l t e r  preceded by a collimating lens ,  
signal due t o  radiation from the hot furnace ref lect ing from the blackened w a l l s  
This bandwidth s t i l l  admits a h r g e  
of' the vacuum chambero 
radiation from radiation ar is ing from the intersect ing beams, the sodium beam 
i s  modulated at  1440 cps by a rotat ing chopper wheel. 
the desired s ignal  i s  ident i f ied  by i t s  occurring at the  sodium beam modulation 
As a matter of' convenience i n  separating such ref lected 
Under these circumstaaces 
frequency and i n  specified phase. The signal from the  photomultiplier is  fed 
3 
t o  a cathode follower and a, condenser blocks out the d,c.  
ref lected radiation. The remaining a.c. s ignal  i s  passed 
band-amplifier and then t o  a phase-sensitive detector and 
is  displayed on a pen recorder. 
signal. from t h e  
through a narrow- 
integrator.  Output 
Modulated signals i n  addition t o  those from the  interaction of the  excited 
N2 molecules w i t h  the Na atoms are obtained by resonant scattering of the  
thermal LighC Prom the  furnace. 
t ha t  about 90% of the  l i gh t  intersecting the Na beam comes from the hole i n  
$he furnace, the l i gh t  can t o  good approximation.be taken as conforming t o  the 
Planck black-body radiation formula. Sfnce the resonant acattering cross sectiQn 
for D-line radiation is w e l l  known, the  experiment can therefore proceed by 
comparing the  scat tered black-body-light s ignal  t o  the signal produced by the  
pa r t i c l e  interaotion, both detected by the  same opt ica l  system. Effectively, 
black-body radiation scat ter ing by sodium atoms cal ibrates  i n  one step both the 
intensi ty  gf t he  N a  beam and the character is t ics  of the opt ica l  system, 
By making the collimation suff ic ient ly  t i g h t  
Tn pract ice  the  s i tua t ion  is s l igh t ly  more complex being so rendered by 
Che very large in tens i ty  of the  resonantly scattered black-body-light compared 
t o  the l i gh t  from t he  pa r t i c l e  interaction, 
interaction simals it is necessary t o  attenuate the black-body-light by about 
three orders of magnitude. 
c e l l  containing sodium vapor shown 9n Fig. 1 immediately before the sodium cross 
beam. 
is about 5 x 
approximately 10-l' cm2, t h i s  pressure i s  adequate t o  provide the needed attenuation. 
A t  t h e  same $he ,  a pressure of 5 x 
t he  N2 molecules passing thropgh the  ce l l .  
I n  order t o  detect the pa r t i c l e  
This is accomplished by the  insertion of the abswptfon 
Operating at a temperature of about 490°K, the vapor pressure i n  t h i s  c e l l  
t o r r ,  Because the cross section f o r  resonant absorption is  
t o r r  a f fec ts  only approximately 1% of 
The experimental procedure is  as follows.. F i r s t  the  sodium oven temperatures 
are set and t h e  sodium beam established. A hot w i r e  surface ionization detector 
4 
(not show i n  Fig. 1) indicates the  presence of an adequately intense sodium 
beam 
using an opt ical  pyrometer looking in to  the furnace aperture. 
Second, the  tungsten oven i s  turned on and i t s  temperature measured 
The signal. from 
the  resonantly scaktered furnace l ight  i s  noted. 
The sodium vapor absorption c e l l  i s  then heated t o  i t s  temperature and 
the scattered l i g h t  aignal drops. 
rise of signal of sodium llghk i s  noted, 
Gas i s  then admitted t o  the furnace and the 
LastJy, the  ohange i n  pressure i n  the f i n a l  vacuum chamber on turning on 
and off tihe molecul&r beam is noted, 
beam gas (abtained from a separate measurement of the  pressure time constant 
of t he  sys2;m) and the pressure change on admission of the beam, the current 
carried by the molecular beam i s  obtained, 
From the pumping speed f a r  the  molecular 
Since *he attenuation of the sodium c e l l  is  known and is  kept constant, 
the  furnace temperature can be changed and the  signals before and a f t e r  addition 
of %he molecular gas t o  the furnace can be noted, giving data at  a second 
tempera$we 
From the measured geometry of t he  apparatus, the  measured l i g h t  signals 
and the measured molecular beam current, and using the known sodium resonant 
scat ter ing cross section and Planck's dis t r ibut ion l a w  f o r  the in tens i ty  of 
radiation resonantly scat tered by the  sodium beam, a r a t e  coefficient i q  obtrained. 
me rate so obtiained i s  appropriate t o  t h e  assumption tha t  the l i gh t  produced 
I 
i n  t h e  pa r t i c l e  co l l i s ions  is isotropical ly  distributed. 
of the resonantly scat tered l i gh t  is an2y 2% away from being isotropic 
t h i s  correction w a s  not 
(The angular dis t r iqut ion 
6 and 
e i n  treqting the data.) 
5 
The dire& sutput gf the experiment is  a Tate coeff ic ient  defined i n  the  
llsurpl WW, 
S i a n n  (1) 1 2  
wbere S I s  $he tQ$%,l signal per wit t i m e  and volume, nl and g are the  t o t a l  
number densi t ies  of the sodium atoms and the  diatomic gas moleculesq respectively, 
and a is  $he re%@ coeff ia ient ,  When the two beams have Mawell-Bal~zmann 
2 
.7 
velocity ais$ribut&Qns, the rate constent i s  given by 
velocity i n  the; center of maw, and I1(x) is  the first order modified BesseZ 'p  
function of the first kind, I n  the quantity i n  brackets i n  the integrapd 
Q(E,v) is the cross section for the  energy t ransfer  which depends i n  general 
on both *he rel.ative velocity and the energy of internal excilmtion, E. 
is the  s t a t i s t i c a l  weight density of states of in te rna l  energy E. 
population of' PnDernal. energy states depends only on the  temperature of the 
molecaar be- furnace sowce, T2, t h i s  temperature appears i n  the-Boltmmn 
factor ,  The t;otal quantity i n  brackets i s ,  of course, t h e  reaction-cross section 
fo r  a given r e l a t ive  velocity averaged over a13 internal. energy states thermally 
populated , 
@;(E) 
Sgnce the  
It is aonvenient t o  re-write (2)  i n  terms no% of the  r e l a t ive  velocity,  v, 
1 5 uv2, where 1.1 is  the but of' k inet ic  energy i n  the center of mass systems E 
reduced masa, The expression becomes 
6 
Conservation of energy requires of course that Q(c,E)  vanish for E + E c Eo, the 
threshold energy for excitation of the sodium (2.10 eV. ) 
Since a itself is stron@;ly dependent, on the temperature T2 through the 
Boltzmann factor, it is convenient to introduce a second quantity, n, given by 
- EO 
kT2 q = ae (4 )  
The quantity n is plotted as a function of T2 in Fig. 2. 
points to note are the weak dependence of q on temperature and the large 
The most striking 
magnitudes. 
In the absence of more detailed information than that provided by the 
thermal beam experiments, the physical interpretation of the results must 
necessarily be semi-quantitative6 Nonetheless some consideration of the results 
reveal the main essentials of tho basic processes involved. These considerations 
are based upon the extent to which tho excitation of the sodium depends on the 
kinetic energy as opposed to internal energy in the molecule. 
It is of interest to consider two extreme cases, %he first assuming that 
internal energy is irrelevant and all the effect comes from the kinetic energy 
of the molecules. 
&(E) so that 
In this case, the term in brackets in Eq. ( 3 )  becomes simply 
2SEo 
Under conditions of the experiment the value of - is 
lJ 
where Eo = 2.10 eV. 
7 
about 20, so that the asymptotic form of the Bessel f thct ion can be used, mad 
the expression simplifies t o  
2 m 
M Since the minimum value of E i s  Eo and m2 
posit ive.  
1.1, - E  - Eo must always be 
For nitrogen where the r a t i o  of the  mass t o  the reduced mas8 is 
about 2.2 the exponential i n  t he  in tegra l  must give a temperature dependence 
f o r  II at least as strong as 1 2Eo 
e kT2 ., 
- -  
(5) 
This would require a factor  i n  excess of 10 difference i n  the values of rl a t  
2200 and 2 8 0 0 ~ ~ .  Fig. 2 shows a much weaker temperature dependence, from which 
we can conclude t h a t  kinet ic  energy cannot be the major cause of the  sodium 
excitation. 
It can also be shown tha t  t h e  cross sections fo r  those molecules having 
sufficie’rit k inet ic  energy t o  produce the observed signals would have t o  be of 
t h e  order of cm which is unreasonably high. 2 
Turning t o  t h e  oaher extreme, i f  it fs assumed tha t  kinekic energy plays 
no role  whBtever, then Q(e,E) = Q ( E )  and the expression for II reduces t o  
E - -  
de kT2 
W - [ Q(Eo+E) g(Eo+c)e 
n = v  10 e (6) 
E - -  
d E  
rg( c ) e  kT2 
0 
Since fo r  the molecules of i n t e re s t  here only vibrat ional  and rotat ional  states 
are available, the cross section f o r  the n-th vibrational s t a t e  and rotat ional  
energy, u, can be writ ten Q !u). The rotat ional  weight density, 1/33, where 
3 i s  the  rotat ional  constant, and the vibrat ional  weight density CG(E-nhwo) 
n 
8 
(using the simple harmonic oscillator approximation) can be inserted to yield 
. 2hw0 - -  - -  huO - ( nohuo-Eo ) - -  hwO 
+ . . * I  (7)  kT2 * cn 4.2' kT2 'Cn * cn +p kT2 )e n = + 4 l - e  -c kT2 
0 0 0 
where no is the quantum number of the 
exceeds Eo, v is the aver8ge relative 
- 
1 - 
Q n = q  
lowest vibrational state whose energy 
velocity and, 
is the cross section for a given vibrational level averaged over the rotational 
"- 
levels 
Now, ;varies by less than 10% over the temperature range of the exper4ments 
and for no = 8 the energy difference in the third factor of Eq, (7) is but 0,ll eV 
giving a weak temperature dependence, 
increases with temperature the second term decreases with temperature such that 
the product of the two is very nearly temperature-independent. 
temperatwe dependence must arise from the series. 
Further, while the thfrd factor weakly 
Thus any appreciable 
The temperature dependence 
in Fig. 2 can be quite consistent wfth the assumption of internal energy counting 
for the entire energy transfer. 
the cross sections, qn, averaged over the rotatfdnal energy states, little more 
a m  be said, except to note that the increase of cn with-temperature offers the 
possibility that the cross sections for transfer from vibrational states of 
n > 8, may be quite large. 
In the absence of detailed information about 
In this extreme case, where only internal energy is considered important, 
q takes on the physical significance of being the reaction rete constant for 
those molecules with sufficient energy to cause the excitation of the sodium. 
One can then deduce that for these molecules the effective cross section for 
the excitation is about 2 x cm2, which is of the correct magnitude to 
9 
explain the auroral phenomena. The number also exceeds the lower l i m i t  of 
2 5 cm given by Hurle based on shock tube data. 
One fur ther  exercise w a s  performed on the dkta of t h i s  experiment. 
balancing was exmined fo r  ttre sodium excitation a d  sodium quenching cross 
sections. The sodium exci ta t ion cross section-was taken-to be the rate ooefficient 
measured i n  th i s  experiment simply divided by the mean relat ive.valoci ty  of the  
molecules and detai led balancing was used t o  derive quenching cross sections 
of differing f i n a l  kinet ic  energy and vibrational energy of the  I?:! molecule, 
It was found that i n  order t o  obtain quenching CPOSS sections within the range 
of experimental vaaues which have been reported, it appears necessary t o  have 
the molecule l e f t  i n  vibrations1 s t a t e s  of a t  l ea s t  n = 6, 
is  injected in to  this argument i n  the manner i n  which an excitation CPOSS section 
i s  obtained, we regard the consistency obtained 8s supporting the bel ief  tha t  
in te rna l  energy i s  more important than k ine t ie  energy i n  the interactions 
leading e i ther  t o  excitation or t o  quenching of sodium atoms i n  col l is ions 
w i t h  nitrogen molecules. 
Detailed 
Although some bias 
FIGURE CAPTIONS 
1. Sketch of experimental arrangement, For discussion see text, The 
figure does not show the hot-wire detector for the sodium beam nor the light 
baffles used to cut down scattered light originating from the tungsten furnace. 
2. Plot of PS. T2, the temperature of furrrace from which the N2 
bean issues. 
nitrogen molecules with sufficient energy to effect the exeftation of.the sodirpm, 
n can be thought of crudely as a rate coefficient for those 
RE'FEREEICES 
1. 
2. 
3. 
4. 
5. 
6. 
Pork, 19611 p. 448. 
D. R. Jenkins, Proc, Roy. SOC., 1966, - A293, 493. 
D. M. Hunten, J. Atm. Terr. Physics, 1965, 27, 538. 
G. J. Schulz, Phys. Rev., 1962, a, 229. 
W. L, Starr, J. Chem. Phys , ,  1965, 43, 73. 
I. R. Hurla, J. Chem, Phys., 1964, 41, 3911. 
J, W e  Chamberlain, Physics of the Aurora and Airglow (Academic Press, New 
CELL 
0 
n 
N 
00 
0 
0 
b 
*P 
w. 


Transfer of excitation energy from nitrogen molecules to sodium atoms

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