Mercury 2537–Å Emission as a Test for N 2 (A 3 Σ u + ) in Active NitrogenD. H. Stedman, J. A. Meyer, and D. W. Setser Citation: The Journal of Chemical Physics 48, 4320 (1968); doi: 10.1063/1.1669779 View online: http://dx.doi.org/10.1063/1.1669779 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/48/9?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Emission of phosphorescence from biacetyl surface by collision of N2(A 3Σ+ u ) J. Chem. Phys. 84, 4031 (1986); 10.1063/1.450063 Electronically Excited O2 in O3 Photolysis at 2537 Å J. Chem. Phys. 50, 4594 (1969); 10.1063/1.1670938 Kinetic Behavior of N2(A 3Σ u +) in Active Nitrogen J. Chem. Phys. 47, 3691 (1967); 10.1063/1.1712458 Quenching of the 2537Å Resonance Radiation of Mercury J. Chem. Phys. 41, 1705 (1964); 10.1063/1.1726150 CrossSection Measurements for the Quenching of the 2537Å Resonance Radiation of Mercury J. Chem. Phys. 41, 768 (1964); 10.1063/1.1725959

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4320 LETTERS TO THE EDITOR J. CHEM. PHYS., VOL. 48, 1968

Fr~m the data, the translational exoergicity of the reaction may be computed. This quantity is defined as the net conversion of internal to translational energy: Q= T4 - T I , where T4 is the kinetic energy of the prod­ucts and TI that of the reactants (both in the center­of-mass system). TI is known from the initial condi­tions and T4 is computed from the measured velocity o~ A~D+~ArH+) at the peak in the angular and velocity dIstnbutIOns. Values of Q thus determined for the posi­tion of maximum intensity4 are shown in Fig. 1. The remarkable conclusion emerges that the translational exoergicity is not only highly energy dependent, but changes sign: at low reactant velocities there is a net conversion of internal to translational energy of prod­ucts, while at higher velocities an increasing portion of the kinetic energy of the reactants appears as internal energy of products.

According to the simple polarization theory postu­lated earlier, the approaching reactants are accelerated towards each other by the ion-induced-dipole force between them. After atom transfer occurs, the products are similarly decelerated. Using this model, it can readily be shown2 that for a relatively heavy ion react­ing with homonuclear hydrogen the translational exo­ergicity is Q:::~P - pI - ~ TI . P and pI are ion-induced­dipole energies of the reactant and product pairs, re­spectively (having the form ae2/2fc4, where a is the appropriate polarizability and fc the distance of closest approach). The single5 adjustable parameter fc is fitted for the lowest energy. It corresponds to a closest Ar+-D distance of about 1.44±O.lS 1.6 (This agrees reasonably well with the known bond distance of 1.27 1 for the isoelectronic molecule DCl.)

Predictions of this model as to Q at all energies are shown as the solid line in Fig. 1. The agreement of theory and experiment for both isotopic systems sup­ports the proposed mechanism and indicates that long-range forces dominate the dynamics of these direct reactions.

This work was supported by the U.S. Atomic Energy Commission and the National Aeronautics and Space Administration. We greatly appreciate the help of Alfred Lee in all phases of this work.

* Present address: Institute of Physical Chemistry, Czechoslo­vak Academy of Science, Prague, Czechoslovakia.

1 Z. Herman, J. D. Kerstetter, T. L. Rose, and R. Wolfgang, J. Chern. Phys. 46,2844 (1967).

2 For a fuller description of the experiment and the mathematical elaboration of the model, see Z. Herman, J. Kerstetter, T. Rose, and R. Wolfgang, Discussions Faraday Soc. 44,123 (1967).

a R. D. Fink and J. S. King, Jr., J. Chern. Phys. 47,1857 (1967) j L. D. Doverspike, R. L. Champion, and T. L. Bailey, ibid. 45, 4385 (1966) j and A. Ding, K. Lacmann, and A. Henglein, Ber. Bunsenges. Physik. Chern. 71, 596 (1967), have independently measured product velocities for the same reactions. However, their work did not extend to the critical very low energy range and furthermore involved a static target (with a three-dimensional distribution of target velocities) rather than a crossed beam. Nevertheless, their data accords with our model, although the magnitude of the apparent effect as found by Fink and Henglein is larger.

4 Intensities on the Newton diagram are given relative to the h;boratory system. Values of Q given here correspond to the posi­tion of maximum intensity in the laboratory system (see Ref. 2, Footnotes 14, 16, and 21).

6 There are actually two such parameters re , corresponding to the closest approach of the reactants, Ar+ -H., and closest approach of products ArH+-H. However, they are related by half the H-H bond distance. • 6 Th~ uncertainty quoted is based on our estimated uncertainty I~ the mtercept of Q at 0 eV. A transformation of the Newton dIagram to the c.m. is diflicult,4 but would result in a larger Q(O eV) and an Ar-D+ distance which would be smaller by ,-....,().3 A (see Ref. 2, Footnote 21).

Mercury 2537-A Emission as a Test for N 2(A 3};,. +) in Active Nitrogen*

D. H. STEDMAN, J. A. MEYER, AND D. W. SETSERt

Chemistry Department, Kansas State University Manhattan, Kansas

(Received 22 January 1968)

The main chemically reactive component of active nitrogen is ground-state N atoms.1 Nevertheless, meta­stable N2 molecules,2 highly vibrationally excited ground-state N2,8 and electronically excited nitrogen atoms4·2a have also been directly observed or invoked to explain some reactions of active nitrogen. Dugan5

has offered striking evidence for a metastable species in active nitrogen, apparently N 2(A 3~u+), whose con­centration was first order in [N]. Recently Thrush6a

reinterpreted the Vegard-Kaplan (A-X) emission data obtained by Noxon6b showing that the emission inten­sity was first order in [N] and in [N2]. We will present data which, combined with these results, show that Hg(3PI~ISO) emission at 2537 A can be used to meas­ure relative [N2(A 3};u+)] in active nitrogen. The excitation of Hg 2537-1 emission by N 2(A) was first demonstrated by Brennen and Kistiakowsky7 and has since been employed in more complicated systems8 as supporting evidence for the presence of N 2 (A 3};" +) . However, the data shown here are the first direct kinetic analysis of the excitation processes.

Nitrogen atoms were generated by a microwave dis­charge through pure N2 or N2/ Ar mixtures in an ordi­nary discharge flow apparatus. Values of [N] were determined by NO titration. Mercury vapor was added to the flow stream with a metered flow of nitrogen or argon which had been saturated with mercury at room temperature. Figure 1 shows that the intensity (1) is first order in [N], and it was also shown to be first order in [Rg] and total pressure, with N2 or Ar carrier gas. I was independent of both time after the discharge and contact!time~ with.the Rg. This shows that the exciting species is being continuously generated in active N 2.

The simplest explanation of the observations is the

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J. CHEM. PHYS., VOL. 48, 1968 LETTERS TO THE EDITOR 4321

following reaction sequence:

N+N+M(N2 or Ar)-"7N2+M (1a)

-"7N2*(A)+M, (1b)

N2*(A) + N-"7N2+ N, (2)

N2*(A) +Hg (ISo)-"7Hg (IPI) +N2, (3)

Hg(3P1)+M-"7Hg(1So, aPo)+M, (4a)

Hg(a PI)-"7Hg(lSO) +hv(2537 A)

(r= 1.1 X 10-7 sec). (4b)

N 2(A 3~,,+) may be generated by direct combination of atoms9 or radiative transfer and collisional quench­ing from the B aITg state. Reaction (2) has been sug­gested previously.5,6a,lo A rate constant6a of 3X 1012

cc mole-l·secl has been estimated, which dominates over all other removal processes for N 2*(A), and cor­relates with Dugan's finding that [N2*(A)]ex:[N]. For 1-10 torr, the emission reaction (4b) dominates over collisional quenching (4a).n Thus the total inten­sity: 1,= (klbk3/k2) [HgJ[N][M]. This clearly fits the experimental first-order dependence for [N], [Hg], and [M]. In order to estimate J" the mercury emission at 2537 A was comparedl2 with the air afterglow emis­sion at 5000 A, for which the quantum efficiency is known,t3 with the same geometric arrangement. Thus I, was measured for various [N], [M], and [Hg]. From known values of klb

9 and k2,6a a value of k3= 1. 7X 1013

CC mole-l'sec-l within a factor of 2-3 was obtained. This leads to a cross section of 1.8 A2 which is certainly of reasonable magnitude.

14

o~ .... 12 ro

~ >10 I-m z .... a ... z >6 a:: ::> (.)

15 4 ~

2

0.0111

FIG. 1. Variation of mercury 2537 A emission intensity (arbi­trary units) with nitrogen atom concentration. Each line repre­sents a different total pressure of nitrogen: 0, 2.5 torr;.6, 4.7 torr; 0, 6.5 torr; 0, 8.7 torr. [HgJ is constant for a g:iven pressure, but no attempt was made to ensure constant [HgJ for the different pressures.

Hg excitation can not be due to N2(B aITg) since numerous investigators have shown that [N2(B IITg) ] ex:

[NJ2, and Dugan detected a metastable with a lifetime greater than a few milliseconds, whereas the radiative lifetimel4 of the B state is 9X 10-6 sec. The addition of NH3, S02, and N20 gives strong quenchingl5 of 2537-A emission; these compounds do not react with N, but all have been suggested2d ,2e to react with N2(A 8~u+).

The work of Dugan5 and Thrush (Noxon)6a has clearly established the presence of N 2(A 3~u+) in active nitrogen. The evidence presented here shows that the Hg 2537-A emission can be used as simple and straightforward method for followingl6 the relative concentration of the metastable nitrogen molecules.

Note added in proof: Recently in this laboratory we have generated the N2(A3~u+) molecule free from other reactive species; the method employs collisions of Nt molecules with argon metastable atoms produced in a flowing hollow cathode discharge. The conclusions herein regarding collisional activation of the Hg(3P1)

state by N2(A) have been verified. Furthermore, the addition of NO and CO to the stream of N 2(A) shows collisional activation of the NO(A211) and CO (a3IT) states, giving, respectively, "'1- and Cameron-band emission spectra.

* This work was supported by grant AP-00391 from the Re­search Grants Branch, National Center for Air Pollution Control Bureau of Disease Prevention and Environmental Control. '

t Alfred P. Sloan Foundation Fellow. I B. Brocklehurst and K. R. Jennings, Progr. Reaction Kinetics

4,3 (1967). 2 (a) S. N. Foner and R. L. Hudson, J. Chern. Phys. 37, 1662

(1962). (b) J. T. Herron, J. Res. Nat!. Bur. Std. A69, 287 (1965). (c) H. B. Dunford, J. Phys. Chern. 67, 258 (1963). (d) R. A. Back and D. R. Salahub, Can. J. Chern. 45, 851 (1967). (e) I. M. Campbell and B. A. Thrush, Chern. Commun. 1967, 932.

3 (a) F. Kaufman and J. R. Kelso, J. Chern. Phys. 41, 903 (1963). (b) J. E. Morgan and H. I. Schiff, Can. J. Chern. 41, 903 (1963). (c) Y. Tanaka, R. F. Innes, A. A.Jursa, and M.J. Naka­mura, J. Chern. Phys. 42,1183 (1965). (d) E. L. Milne, M. Stein­berg, and H. P. Broida, ibid. 42, 2615 (1965).

4 (a) K. M. Evenson and H. E. Radford, Phys. Rev. Letters 15,916 (1965). (b) Y. Tanaka, A. Jursa, and F. LeBlanc, The ft.reshold oj Space (Pergamon Press, Inc., New York, 1957), p.

5 C. H. Dugan, J. Chern. Phys. 47,1512 (1967). 6 (a) B. A. Thrush, J. Chern. Phys. 47, 3691 (1967); (b) J. F.

Noxon, ibid. 36, 926 (1962) . 7 W. R. Brennen and G. B. Kistiakowsky, J. Chern. Phys.44,

2695 (1966). 8 (a) K. H. Becker and K. D. Bayes, J. Phys. Chern. 71, 371

(1967). (b) J. A. Meyer and D. W. Setser, ibid. (to be pub~ lished).

9 I. M. Campbell and B. A. Thrush, Proc. Roy. Soc. (London) 293, 201 (1967). These authors have decided that nearly i of the recombining atoms follow the triplet surfaces.

10 (a) K. L. Wray, J. Chern. Phys. 44, 623 (1966). (b) R. A. Young, Can. J. Chern. 44,1171 (1966).

II R. J. Cvetanovic, Progr. Reaction Kinetics 2, 39 (1964)' the N2 quenching cross sections for Hg(3Pl) is ~O.5 A" and that for Ar is even smaller.

1. B. C. Hudson and B. Curnutte, Jr., Phys. Rev. 152, 56 (1966) .

13 A. Fontijn, C. B. Meyer, and H. I. Schiff, J. Chern. Phys. 40, 64 (1964).

14 M. Jeunehomme and A. B. F. Duncan, J. Chern. Phys.41, 1692 (1964).

15 Linear Stern-Volmer-type quenching plots are obtained when

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4322 LETTERS TO THE EDITOR J. CHEM. PHYS., VOL. 48, 1968

these gases are added to the active nitrogen-Hg flow systems; the detailed explanation of these observations will be published else­where. However, it is worth pointing out that the reduction of the mercury emission is due to the removal of N2(32:u+) in competition with Reaction (2), rather than collisional quenching of Hg (3 PI).

16 It is also quite possible that the COCa "II) state will participate in energy transfer with mercury, and some care must be exercised in trying to differentiate between CO(aan) and N 2(A 32:u+) using the mercury 2537-A. emission in more complex systems.

Notes

Thermodynamic Functions on the Generalized Thomas-Fermi and Thomas-Fermi-Dirac Theories

J. J. GILVARRY*' t Space Sciences Division, Ames Research Center, National Aeronautics and Space Administration,

M o.ffett Field, California (Received 27 September 1967)

The generalized Thomas-Fermi theoryH corresponds to solution of Poisson's equation for the self-consistent potential at a point in a spherically symmetric atom due to electrons with a density fixed by the Fermi distribution function for an absolute temperature T. In the generalized Thomas-Fermi-Dirac theory,'H which includes the effect of exchange, the electron density is determined by a nonlinear integral equation involving the Fermi function at temperature T. For the latter model, Gilvarry7 has shown that the total energy E of the atom is given by

E=!T7/4 jT T-3/4 (OaT). (Pv+Een~ZJL+iEex) dT (1)

for arbitrary temperature, where the integration is carried out at constant volume v and the additive constant of integration is to be ignored.s Here P is the pressure, Een is the potential energy corresponding to the electron-nuclear interaction, Z is the atomic num­ber, JL is the chemical potential per electron, and Eex is the exchange energy. In the Thomas-Fermi case where Eex vanishes, this result for E has the salient advantage of depending only on boundary and initial parameters associated with a solution of the generalized Thomas-Fermi equation.9 •IO Actually, the form with exchange represented by Eq. (1) was derived for the temperature-perturbed model of Umeda and Tomi­shima,6 where the effect of exchange is taken into account approximately by means of an effective tem­perature which minimizes the Helmholtz free energy; that it holds in the exact formulation of the Thomas­Fermi-Dirac theory at arbitrary temperature given by Cowan and Ashkin6 follows since the underlying analogs of the relations of Brachmanl l-l8 which yield Eq. (1) are the same in this rigorous model. The purpose of this Note is to complete the specification of thermo­dynamic functions in a form similar to Eq. (1), by deriving the corresponding expressions for the entropy

S, the heat capacity C. at constant volume, and the Helmholtz function F.

Equation (1) for E yields the entropy S through the relation T(aS/aT).= (aE/aT). by means of inte­grations by parts as

S=!T314 jT T-7/4 (a~). (Pv+E.n+ZJL+iEex)dT (2)

directly.s This result is equivalent to the analog of the Brachman relation for S when the effect of exchange is included, given by Gilvarry7 and by Cowan and Ashkin6

as TS=(5j3)Ekin+2Eee+Een-ZJL+(4j3)Eex, in which Ekin is the kinetic energy and Eee is the potential energy corresponding to the electron-electron inter­action. The corresponding expression for the heat capacity C. is8

C.=!T8/4 JT T-8/4 (OO~). (Pv+Een+ZJL+iEe:rJdT.

(3)

Equation (1) or Eq. (3) yields a direct analog of the Brachman relation for C. when the effect of exchange is included as TC.= (7/4) E+!Tl(ajaT).[(Pv+Een+ ZJL+iEex)jT] in a form corresponding to that of Gilvarry9; the form corresponding to that of Brachmanll

follows immediately with use of the virial theorem 3Pv= 2Ekin+ Eee+ Een+ Eex including the effect of exchange (as given by Gilvarry7 and by Cowan and Ashkin6) .

The Helmholtz function F is given bys

F= _i,T7/4 JT T-ll/4(PV+ Een+ZJL+iEex)dT, (4)

directly from the definition. This expression is entirely equivalent to the form F= -iEkin- Eee+ZJL-tEex of Gilvarry7 and of Cowan and Ashkin,6 which general­izes Brachman's resultll to the case where exchange is included.

These integral representations of thermodynamic functions have a special importance in the Thomas­Fermi case at elevated temperature, because they yield the entirety of thermodynamic functions without the necessity of performing an integration over the volume of the atom.9•10 Further, they must hold (at least in a limiting form) even at temperatures so high (approaching those appropriate for an ideal gas of electrons) that the Fermi-Dirac statistics reduce to the Maxwell-Boltzmann form. In terms of the dimension­less variables cf> and x of the Thomas-Fermi model at zero temperature, one has

Z2e2cf>/-cf>b Een= ----,

JI Xb

and

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