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The electronic partition functions of atoms and ions between 1500°K and 7000°K
SpectrochimicaActa, 1968,Vol. 23B, pp. 521 to 525. Pergamon Preee. Printed in Northern Ireland
The electronic partition functions of atoms and ions between 1!5OO”K and 7000°K L. DE GALAN*, R. SMITHand J. D. WINEFORDNER Department of Chemistry, University of Florida, Gainesville, Florida 32601 (Received 18 April 1968) Abstract-Electronic partition functions of the atoms and fist ions of 73 elements have been The results are presented in the form calculated over the temperature range of 1500-7000%. of a fifth order polynomial expression which has been fitted to the data by a method of least squares.
atomic spectrometry, the electronic partition function is a factor in the expressions relating the intensity of emitted or absorbed radiation to the pertinent concentration of atoms and ions in such light sources as flames, arcs, plasma jets, and stars. Even at the relatively low temperatures of some of these sources, the variation of electronic partition function with temperature cannot be neglected for many elements. The common approximation of equating the electronic partition function with the statistical weight of the ground state holds true only for a few elements. DRAWINand FELENBOK[l] have calculated partition functions up to very high temperatures, but their data are less useful at the lower temperatures prevailing in flames. CLAAS[2] has calculated partition functions for a number of elements at five temperatures between 5000°K and 7000°K and BOUMANS[3] has calculated the partition functions of fifty-six elements at 5000°K and 6000°K. Calculations of electronic partition functions for atoms at typical flame temperatures have not been reported. For elements with a split ground state, and also for a number of transition metals, the electronic partition function varies appreciably, even over the range of flame temperatures. In this manuscript, the electronic partition functions of atoms and ions of seventyfive elements between 1500°K and 7000’K are compiled. The electronic partition function B( 2’) is given by the expression: IN
B(T) = t g, exp a=0
( --E,/kT)
where B(T) is the electronic partition function, k is the Boltzmann constant, g, and are the statistical weight and energy respectively of the electronic level a. The
E,
* Present Address: Technische Hogeschool Delft, Delft, The Netherlands. [I] H. W. DRAWIN and P. FELENBOK, Data for Plasmas in Local ThermodynamicEquilibrium. Gauthiers-Villars (1965). [2] W. J. CLAAS,Proc. Koninkl. Ned. Akad. 52, 528 (1949); W. J. CLMS, Rechn. A&r. Obs. Utrecht 12, 49 (1951). [3] P. W. J. M. BOUMANS, Proc. IXth Coil. Spectr. Int., Lyon, p. 84 (1961). 521
522
L.
DE
GALAN, R.
SMITH
and J. D.
~INIWORDNEB
statistical weight is calculated from the expression: g, =
2J, + 1
(2)
where J, is the inner quantum number of the energy level, 8, and was obtained from the tables of MOORE[4], together with the corresponding values for $7,. The calculations included all levels (E,) of energy lower than E, = 15,000 cm-l for temperatures between 1500’K and 3OOO”K, and energy levels up to E, = 30,000 cm-l were considered for temperatures between 3000°K and 7000’K. The contribution of higher levels to the partition function is smaller than 0.001 and can be neglected. Values of B(T) were calculated at intervals of 2OO’K using equation (1). To facilitate presentation of these results, polynomial expressions of one through the f&h order were fitted using a least squares Chebyshev procedure. The values of B(T) were then re-calculated, using the polynomial coefficients, and compared with the original values of B(T), in order to determine the accuracy of the curve fitting process. The coefficients of the lowest order polynomial are listed, which gave B(T) to within -~=0.02or to -&l%, (w~chever is the most accurate~. In practi~~ly all cases, the accuraoy of fit is nearer kO.01. With the least accurate fit, only about 6% of the values of B(T) had errors of as much as AO.02, whereas about 30% of the values were within +O.Ol. The remainder of the Bf 2’) values resulted in an exact fit to two decimal places. In Table 1, values are presented for the pol~omial Treble 1. Valuea of polynomial ooeffioients for atoms and ions (first ionization states) of 73 elements* B
0
b
AI AII A01 AC II &I Ag II
1.0900 E 4.8088 E 2.8150 E 1.6601 E 2.0158 E 1.0000 E
AI1 Al II As1 AB II AllI AUII
6.2855 E 0 1.0000 E 0 4.2641 E 0 -2.5384 E-l 2.2056 E 0 1.0546 E 0
0 0 0 0 0 0
4.6646 E-l 1.6044 E 0 -1.0677 E 0 -1.1712 E-2
-7.8367 E-2 -33.2661 E-l 6.2893 E-1 1.8708 E-3
d
8
4.7063 E-3 7.0008 E-2 -6.1366 E-2
- 3.6227 E-3 2.0866 E-3
E-2
3.0199 E-3
7.6632 E-2 -3.3383 E-l 7.6490 E-2 2.8438 E-3
-2.3876 E-3 3.0408 E-2 -3.8320 E-3 1.6586 E-3
-2.7064 E-l -9.6758 E-l 1.3176 E-2
2.9301 E-2 5.3003 E-l -6.3713 E-3
2.1826 E-2 -7.1694 E-2 9.6637 E-4
-1.4227 E-3 3.4164 E-3
- 6.8468 E-4
2.7833 E-1 -2.7507 E-I 2.2840 E 0 -2.3937 E-l -4.0809 E-2
-4.7628
6.9351 E 0 1.0000 E 0 1.2868 E 0 2.6399 E 0 8.9130 E-l 2.0000 E 0
Bi I BiII BrI Br II CI c II
3.8804 E 1.0628 E 3.7536 E 4.4654 E 8.6986 E 6.6648 E
0 0 0 0 0 0
6.2809 E-2 -4.4352 E-2 I.8396 E-1 4.6610 E-l 2.0486 E-2 1.8968 E-l
-4.2232 E-2 6.9467 E-3 4.1647 E-3 7.2400 E-3 1.7629 E-2 -3.3341 E-2
1.1727 E-2 7.8728 E-4 -1.0971 E-3 - 1.4165 E-3 -3.9081 E-4 2.0597 E-3
CSI CeII CdI
1.0007 E 0 2.1126 E 0 1.0000 E 0
2.0540 E-2 -1.0186 E-l
--1.8616 E-2 2.0713 E-2
4.4420 E-3 6.4364 E-4
Atomic
-1.1608
E-3
1.0438 E-2
BX BII B8I Ba XI Be1 Be II
[4] C. E. MOORE, III (1958).
f
Energy Leveb,
Circular 467, Nat. BUG &da I (1949);
II
(1952);
The electronic partition functions of atom and ions between 1600°K and 7OOO’K
623
Table 1 (cont.) b
a
e
d
f
Cd II Cl I Cl II co I co II CrI cr II cs I cs II
2.0000 E 3.8461 E 6.0876 E 7.0250 E 6.4162 E 8.1008 E 6.7868 E 1.9398 E 1.0000 E
0 0 0 0 0 0 0 0 0
9.6051 E-l 1.7463 E 0 6.9330 E 0 4.6806 E 0 - 1.4239 E 0 4.2061 E-l 1.0627 E-l
-2.2642 E-l -4.1309 E-l -4.3327 E-l 2.6184 E-l 6.4376 E-l -2.6244 E-1 -6.2648 E-2
2.6316 E-2 6.0727 E-2 1.6702 E-2 -6.7064 E.2 -4.8687 E-2 6.1803 E-2 1.2145 E-2
- 1.2008 E-3 -2.3308 E-3 1.0166 E-3 3.8188 E-3 3.0023 E-3 -3.1244 E-3 1.0147 E-4
GUI cu 11 FI F II Fe1 Fe II
2.1906 E 0 9.6326 E-l 4.6832 E 0 6.4670 E 0 1.0668 E 1 7.6314 E 0
- 1.9380 E-l 5.4446 E-2 7.7683 E-l 1.2968 E-O 7.3013 E 0 1.4304 E 1
6.1491 E-2 -2.0179 E-2 -2.0884 E-l -3.2666 E-l -2.2102 E 0 -2.6286 B 0
-1.4419 E-3 2.4160 E-3 2.6771 E-2 3.9536 E-2 4.6301 E-l 2.7466 E-l
- 1.3036 E-3 - 1.8070 E-3 -4.0732 E-2 -1.0992 E-2
GSI GMII &I Ge II HI H II
1.7931 E 0 1.0000 E 0 6.7739 E-l 1.1769 E 0 2.0000 E 0 undefhable
1.9338 E 0
-4.6430
E-l
6.4876 E-2
-2.6054
E-3
3.0921 E 0 1.2694 E 0
-6.0416 E-l -1.6666 E-l
6.8363 E-2 8.4231 E-3
-3.1065
E-3
He1 HeH HI1 HfII
1.0000 E 2.0000 E 4.1768 E 3.7701 E 1.0000 E 2.0000 E
0 0 0 0 0 0
II III In1 In II Ir 1 Ir II
3.9366 E 6.1623 E 1.0731 E 1.0000 E 1.1070 E
0 0 0 0 1
KI KII RrI KrII La1 Le II
1.9909 E 1.0000 E 1.0000 E 3.9&6 E 2.0646 E -1.0728 E
0 0 0 0 0 0
HgI Hg II
Li I Li II MgI Mg II MnI Mn II MoI
2.0810 E 0 1.0000 E 0 9.9101 E-l 2.Or)OOE 0 6.7492 E 0 6.9764 E 0 6.3987 E 0
MO II NI NII NE%1 Ne II
6.6000 E 3.9914 E 7.3929 E 2.0078 E 1.0000 E
NbI NbII NeI Ne II NiI NiII 01 011 OS1 OS II
4.0700 E-l -4.9310 E-l
2.3645 E-2 -2.1833 E-l 1.1097 E 0 -2.4120
E 0
2.3169 E-2
-1.1428 E-2 2.9467 E 0 1.0191 E 1 -6.8926
E-2
6.7862 E-l 7.6941 E-l
6.6893 E-3 8.6690 E-2 -1.3211 E-l 1.9388 E 0 -1.7423
-7.2887 -8.3412
E-2 E-2
1.6017 E-3
3.6848 E-3 3.7846 E-3
-4.6646 E-3 6.3919 E-3 -3.4389
E-l
E-2
4.0938 E-3
3.3880 E-2 3.9142 E-1 -1.3894 E 0
-2.6683 E-3 - 1.4788 E-2 1.3912 E-l
3.3511 E-2
- 1.3376 E-3
1.6460 E-3 -4.9009 E-3
1.4081 E-2
1.3474 E-2
-6.4669
E-3
9.7446 E-4
3.6614 E-l 9.6612 E-2 8.9208 E-l
- 1.7998 E-l -9.0924 E-2 -4.6701 E-l
3.1846 E-2 2.7782 E-2 9.31518E-2
9.9149 E-4 -1.4948 E-3 -3.1992 E-3
0 0 0 0 0
7.0382 E-l 1.7491 E-2 8.8636 E-1 2.3147 E-3
-4.1916 E-1 -1.0148 E-2 -2.3679 E-l -6.3878 E-3
9.0921 E-2 1.7138 E-3 3.0766 E-2 1.6002 E-3
-3.7829
-2.7816 E 1.0219 E 1.0000 E 4.2068 E 8.9964 E 6.7188 E
0 0 0 0 0 0
2.4216 E 1 1.0405 E 1
-7.1137 E 0 - 1.2338 E 0
1.4186 E 0 2.2748 E-l
-1.2606 E-I - 1.2293 E-2
6.4814 E-l 9.8924 E 0 9.6002 E-l
-1.0458 E-1 -1.8785 E 0 - 1.3666 E-l
6.1122 E-3 1.9243 E-l 4.4294 E-2
-7.4831 -2.8600
7.6413 E 4.0232 E 8.6643 E 9.7086 E
0 0 0 0
7.4904 E-l -1.7262 E-2 -3.2616 E-l -3.8140 E-l
-2.0133 E-l 2.7661 E-3 6.8181 E-l 6.6292 E-l
2.6166 E-2
- 1.2266 E-3
-4.4262 -6.4984
E-2 E-2
E-3
- 1.4624 E-3
E-3 E-3
1.9976 E-3 2.8792 E-3
4.4289 E-3
L.
524 Table
DE GALAN,
R.
Smrr~
and
J.
D.
WINEZORDNER
1 (co&) a
b
0
d
6.7306 E-2 -6.6371 E-l
- 1.0381 E-3 7.1913 E-2
e
f
PI P II
4.2251 E 0 4.4161 E 0
-2.2476 E-l 2.2494 E 0
PbI Pb II PdI Pd II
1.2430 E 2.0663 E 1.4811 E 5.7306 E
0 0 0 0
-2.7649 E-l -6.6909 E-2 -6.7500 E-l 1.1960 E-l
8.8724 E-2 1.1277 E.2 2.6930 E-l 1.2969 E-l
PO1 PO II P11 Pt II RaI RaII RbI Rb II
6.0023 E 0
- 1.4898 E-2
6.8170 E-3
3.9411 E-4
6.2171 E 0 6.6712 E 0 7.9239 E-l 2.1669 E 0 1.9869 E 0 1.0000 E 0
8.6683 E 0 -1.0363 E 0 3.2001 E-l -1.6014 E-l 3.8600 E-2
-2.8182 E 0 6.7234 E-l -1.7242 E-l 3.3166 E-2 -2.8329 E-2
6.6124 E-l -6.1219 E-2 3.6107 E-2
ReI Re II Rhl Rh II RnI Rn II
6.6671 E 6.6699 E 6.9164 E 7.2902 E 1.0000 E 4.0000 E
0 0 0 0 0 0
7.2721 E-l 6.9999 E-l 3.8468 E 0 1.7476 E 0
-4.2096 E-l -2.8632 E-l 4.3126 E-2 -3.8267 E-2
9.0760 E-2 6.0724 E-2 -8.7907 E-3 2.0140 E-3
- 3.9331 E-3 - 1.8644 E-3 6.9689 E-4 2.1218 E-4
RuI Ru II SI s II Sb I Sb II
7.2113 E 0 7.2138 E 0 6.3026 E 0 4.0754 E 0 4.3114 E 0 9.1346 E-l
7.0168 E 0 4.2834 E 0 1.2760 E 0 -6.2664 E-2 -3.6681 E-l -1.6093 E-l
-1.6028 E 0 -6.0479 E-l -3.1216 E-l 9.3699 E-3 1.1172 E-l 2.7036 E-l
4.3173 E-l 1.1008 E-l 4.2862 E-2 1.2001 E-3 -4.4909 E-3 -3.7073 E-2
-4.4164 -6.6846 -2.1798
SC I so II Se1 Se II Si I Si II SnI Sn II Sri sr II TaI Te II
7.6269 E 0 1.1624 E 1 4.3632 E 0 4.1786 E 0 6.7868 E 0 3.9839 E 0 -1.9638 E-l 2.0009 E 0 8.7127 E-l 1.9366 E 0 3.0679 E 0 1.6834 E 0
1.9781 E 0 1.1329 E 0 8.8160 E-l -1.6392 E-l 8.6319 E-l 1.0330 E 0 1.4076 E 0 -2.0414 E-l 2.0148 E-l 9.6844 E-2 8.1776 E-l 2.0103 E 0
-8.3426 E-l 4.9827 E-l -6.3171 E-2 3.2063 E-2 -1.1622 E-l -2.6689 E-l -7.6162 E-2 2.0687 E-l -1.0746 E-l -6.0332 E-2 3.4936 E-l 6.6443 E-l
1.6172 E-l -7.3723 E-2 2.5242 E-3
-7.9096 E-3 3.6934 E-3
1.3109 E-2 3.0743 E-2 1.6788 E-3 -3.2011 E-2 2.1424 E-2 1.0363 E-2 7.4861 E-3 -3.1036 E-2
-6.2013 -1.4190
To I To II TeI Te II Ti I Ti II
4.4388 E 8.1096 E 5.1239 E 4.2666 E 1.4643 E 9.2912 E
3.0648 E-l -2.9630 E 0 -2.9839 E-l -2.6894 E-l 2.0096 E 0 2.3978 E 1
1.6626 E 0 2.3690 E 0 1.9304 E-l 6.9390 E-2 -3.6619 E-l -7.3970 E 0
-4.0779 E-l -5.0200 E-l -2.2031 E-2 -2.4271 E-3 1.4760 E-l 1.4602 E 0
TlI Tl II VI v II WI w II
2.1277 E 0 1.0000 E 0 6.3211 E 0 1.0337 E 1 3.9611 E-l 1.0660 E 0
X01 xe II YI YII ZnI Zn II ZrI Zr II
1.0000 E 4.0468 E 4.8488 E -1.2762 E 1.0000 E 2.0000 E
0 0 0 0 1 0
0 0 0 0 0 0
6.3459 E 0 4.0623 E 0
-1.6764 E-l
6.3187 E-2
-4.2066
E-3
-1.6213 -2.3613
E-2 E-2
-3.6166
E-3
1.3441 E-3
-6.4166 E-2 2.6878 E-3 - 1.8939 E-3
2.1168 E.3
6.1101 E-3
E-2 E-3 E-3
1.7278 E-3
-4.4389 E-5 1.7249 E-3
E-4 E-3
1.6436 E-3 -1.0231 E-3 -4.8626 E-4 3.0739 E-4 8.9666 E-4 4.8401 E-2 4.9666 E-2 8.9622 E-4 -7.1902 E-3 -1.4208 E-l
-2.1638 E-3 - 1.9087 E-3
5.4322 E-3
-3.6946 E-3
1.6446 E 1 1.0244 E 1 -2.6067 E-l 1.0396 E 0
-3.6791 E 0 - 1.6380 E 0 1.4433 E 0 3.3030 E-l
6.2047 E-l 2.3600 E-l -3.4373 E-l -8.4971 E-3
-2.2682 E-2 -1.0888 E-2 4.1924 E-2 6.6794 E-4
-6.0967 E-2 3.0826 E 0 6.2962 E 0
1.4823 E-2 -1.0879 E 0 -1.0736 E 0
-6.2726 E-4 1.9721 E-l 1.2900 E-l
9.6671 E-3 -6.8804 E-3
4.5026 E 0 8.4092 E 0
- 1.6307 E-2 1.6201 E-2
3.2396 E-2 -9.9477 E-3
6.6393 E-3
- 1.8402 E-3
-5.7919
E-4
* Exponential notation is used, eg., 7.2138 E 0 and -6.0479 E-l correspond to 7.2138 and -6.0479 x 10-l. Blank spaces indiaate that the coeffioient is essentially zero, and the data may be represented by a polpomial of lower order than five.
The electronic partition functions of atoms and ions between 15OO’K and 7000’K
coefficients for the fifth-order B(T)
=a
+b
(5)
polynomial, fc
(*)’ 103
525
equation given below: +d
( 103 T)3
+e
( 103 T)4
+f
( 103 T)5
(3)
This communication is incomplete insofar as values of B(T) were not calculated for astatine, francium, the lanthanides, the actinides, and the first ion spectra of indium and polonium. Energy level data for these species are not available in the tables given by MOORE [4]. The authors would be pleased to supply a tabular listing of calculated partition functions for the 73 elements in the Table. of the authors (R. S.) thanks the National Science Foundation Science Development Grant of the University of Florida for financial support in the form of a postdoctorate research fellowship. This work was supported in part by AFOSR (SRC)-OAR, U.S.A.F. Grant No. AF-AFOSR-103348. AcknowZedgments-One
The electronic partition functions of atoms and ions between 1!5OO”K and 7000°K L. DE GALAN*, R. SMITHand J. D. WINEFORDNER Department of Chemistry, University of Florida, Gainesville, Florida 32601 (Received 18 April 1968) Abstract-Electronic partition functions of the atoms and fist ions of 73 elements have been The results are presented in the form calculated over the temperature range of 1500-7000%. of a fifth order polynomial expression which has been fitted to the data by a method of least squares.
atomic spectrometry, the electronic partition function is a factor in the expressions relating the intensity of emitted or absorbed radiation to the pertinent concentration of atoms and ions in such light sources as flames, arcs, plasma jets, and stars. Even at the relatively low temperatures of some of these sources, the variation of electronic partition function with temperature cannot be neglected for many elements. The common approximation of equating the electronic partition function with the statistical weight of the ground state holds true only for a few elements. DRAWINand FELENBOK[l] have calculated partition functions up to very high temperatures, but their data are less useful at the lower temperatures prevailing in flames. CLAAS[2] has calculated partition functions for a number of elements at five temperatures between 5000°K and 7000°K and BOUMANS[3] has calculated the partition functions of fifty-six elements at 5000°K and 6000°K. Calculations of electronic partition functions for atoms at typical flame temperatures have not been reported. For elements with a split ground state, and also for a number of transition metals, the electronic partition function varies appreciably, even over the range of flame temperatures. In this manuscript, the electronic partition functions of atoms and ions of seventyfive elements between 1500°K and 7000’K are compiled. The electronic partition function B( 2’) is given by the expression: IN
B(T) = t g, exp a=0
( --E,/kT)
where B(T) is the electronic partition function, k is the Boltzmann constant, g, and are the statistical weight and energy respectively of the electronic level a. The
E,
* Present Address: Technische Hogeschool Delft, Delft, The Netherlands. [I] H. W. DRAWIN and P. FELENBOK, Data for Plasmas in Local ThermodynamicEquilibrium. Gauthiers-Villars (1965). [2] W. J. CLAAS,Proc. Koninkl. Ned. Akad. 52, 528 (1949); W. J. CLMS, Rechn. A&r. Obs. Utrecht 12, 49 (1951). [3] P. W. J. M. BOUMANS, Proc. IXth Coil. Spectr. Int., Lyon, p. 84 (1961). 521
522
L.
DE
GALAN, R.
SMITH
and J. D.
~INIWORDNEB
statistical weight is calculated from the expression: g, =
2J, + 1
(2)
where J, is the inner quantum number of the energy level, 8, and was obtained from the tables of MOORE[4], together with the corresponding values for $7,. The calculations included all levels (E,) of energy lower than E, = 15,000 cm-l for temperatures between 1500’K and 3OOO”K, and energy levels up to E, = 30,000 cm-l were considered for temperatures between 3000°K and 7000’K. The contribution of higher levels to the partition function is smaller than 0.001 and can be neglected. Values of B(T) were calculated at intervals of 2OO’K using equation (1). To facilitate presentation of these results, polynomial expressions of one through the f&h order were fitted using a least squares Chebyshev procedure. The values of B(T) were then re-calculated, using the polynomial coefficients, and compared with the original values of B(T), in order to determine the accuracy of the curve fitting process. The coefficients of the lowest order polynomial are listed, which gave B(T) to within -~=0.02or to -&l%, (w~chever is the most accurate~. In practi~~ly all cases, the accuraoy of fit is nearer kO.01. With the least accurate fit, only about 6% of the values of B(T) had errors of as much as AO.02, whereas about 30% of the values were within +O.Ol. The remainder of the Bf 2’) values resulted in an exact fit to two decimal places. In Table 1, values are presented for the pol~omial Treble 1. Valuea of polynomial ooeffioients for atoms and ions (first ionization states) of 73 elements* B
0
b
AI AII A01 AC II &I Ag II
1.0900 E 4.8088 E 2.8150 E 1.6601 E 2.0158 E 1.0000 E
AI1 Al II As1 AB II AllI AUII
6.2855 E 0 1.0000 E 0 4.2641 E 0 -2.5384 E-l 2.2056 E 0 1.0546 E 0
0 0 0 0 0 0
4.6646 E-l 1.6044 E 0 -1.0677 E 0 -1.1712 E-2
-7.8367 E-2 -33.2661 E-l 6.2893 E-1 1.8708 E-3
d
8
4.7063 E-3 7.0008 E-2 -6.1366 E-2
- 3.6227 E-3 2.0866 E-3
E-2
3.0199 E-3
7.6632 E-2 -3.3383 E-l 7.6490 E-2 2.8438 E-3
-2.3876 E-3 3.0408 E-2 -3.8320 E-3 1.6586 E-3
-2.7064 E-l -9.6758 E-l 1.3176 E-2
2.9301 E-2 5.3003 E-l -6.3713 E-3
2.1826 E-2 -7.1694 E-2 9.6637 E-4
-1.4227 E-3 3.4164 E-3
- 6.8468 E-4
2.7833 E-1 -2.7507 E-I 2.2840 E 0 -2.3937 E-l -4.0809 E-2
-4.7628
6.9351 E 0 1.0000 E 0 1.2868 E 0 2.6399 E 0 8.9130 E-l 2.0000 E 0
Bi I BiII BrI Br II CI c II
3.8804 E 1.0628 E 3.7536 E 4.4654 E 8.6986 E 6.6648 E
0 0 0 0 0 0
6.2809 E-2 -4.4352 E-2 I.8396 E-1 4.6610 E-l 2.0486 E-2 1.8968 E-l
-4.2232 E-2 6.9467 E-3 4.1647 E-3 7.2400 E-3 1.7629 E-2 -3.3341 E-2
1.1727 E-2 7.8728 E-4 -1.0971 E-3 - 1.4165 E-3 -3.9081 E-4 2.0597 E-3
CSI CeII CdI
1.0007 E 0 2.1126 E 0 1.0000 E 0
2.0540 E-2 -1.0186 E-l
--1.8616 E-2 2.0713 E-2
4.4420 E-3 6.4364 E-4
Atomic
-1.1608
E-3
1.0438 E-2
BX BII B8I Ba XI Be1 Be II
[4] C. E. MOORE, III (1958).
f
Energy Leveb,
Circular 467, Nat. BUG &da I (1949);
II
(1952);
The electronic partition functions of atom and ions between 1600°K and 7OOO’K
623
Table 1 (cont.) b
a
e
d
f
Cd II Cl I Cl II co I co II CrI cr II cs I cs II
2.0000 E 3.8461 E 6.0876 E 7.0250 E 6.4162 E 8.1008 E 6.7868 E 1.9398 E 1.0000 E
0 0 0 0 0 0 0 0 0
9.6051 E-l 1.7463 E 0 6.9330 E 0 4.6806 E 0 - 1.4239 E 0 4.2061 E-l 1.0627 E-l
-2.2642 E-l -4.1309 E-l -4.3327 E-l 2.6184 E-l 6.4376 E-l -2.6244 E-1 -6.2648 E-2
2.6316 E-2 6.0727 E-2 1.6702 E-2 -6.7064 E.2 -4.8687 E-2 6.1803 E-2 1.2145 E-2
- 1.2008 E-3 -2.3308 E-3 1.0166 E-3 3.8188 E-3 3.0023 E-3 -3.1244 E-3 1.0147 E-4
GUI cu 11 FI F II Fe1 Fe II
2.1906 E 0 9.6326 E-l 4.6832 E 0 6.4670 E 0 1.0668 E 1 7.6314 E 0
- 1.9380 E-l 5.4446 E-2 7.7683 E-l 1.2968 E-O 7.3013 E 0 1.4304 E 1
6.1491 E-2 -2.0179 E-2 -2.0884 E-l -3.2666 E-l -2.2102 E 0 -2.6286 B 0
-1.4419 E-3 2.4160 E-3 2.6771 E-2 3.9536 E-2 4.6301 E-l 2.7466 E-l
- 1.3036 E-3 - 1.8070 E-3 -4.0732 E-2 -1.0992 E-2
GSI GMII &I Ge II HI H II
1.7931 E 0 1.0000 E 0 6.7739 E-l 1.1769 E 0 2.0000 E 0 undefhable
1.9338 E 0
-4.6430
E-l
6.4876 E-2
-2.6054
E-3
3.0921 E 0 1.2694 E 0
-6.0416 E-l -1.6666 E-l
6.8363 E-2 8.4231 E-3
-3.1065
E-3
He1 HeH HI1 HfII
1.0000 E 2.0000 E 4.1768 E 3.7701 E 1.0000 E 2.0000 E
0 0 0 0 0 0
II III In1 In II Ir 1 Ir II
3.9366 E 6.1623 E 1.0731 E 1.0000 E 1.1070 E
0 0 0 0 1
KI KII RrI KrII La1 Le II
1.9909 E 1.0000 E 1.0000 E 3.9&6 E 2.0646 E -1.0728 E
0 0 0 0 0 0
HgI Hg II
Li I Li II MgI Mg II MnI Mn II MoI
2.0810 E 0 1.0000 E 0 9.9101 E-l 2.Or)OOE 0 6.7492 E 0 6.9764 E 0 6.3987 E 0
MO II NI NII NE%1 Ne II
6.6000 E 3.9914 E 7.3929 E 2.0078 E 1.0000 E
NbI NbII NeI Ne II NiI NiII 01 011 OS1 OS II
4.0700 E-l -4.9310 E-l
2.3645 E-2 -2.1833 E-l 1.1097 E 0 -2.4120
E 0
2.3169 E-2
-1.1428 E-2 2.9467 E 0 1.0191 E 1 -6.8926
E-2
6.7862 E-l 7.6941 E-l
6.6893 E-3 8.6690 E-2 -1.3211 E-l 1.9388 E 0 -1.7423
-7.2887 -8.3412
E-2 E-2
1.6017 E-3
3.6848 E-3 3.7846 E-3
-4.6646 E-3 6.3919 E-3 -3.4389
E-l
E-2
4.0938 E-3
3.3880 E-2 3.9142 E-1 -1.3894 E 0
-2.6683 E-3 - 1.4788 E-2 1.3912 E-l
3.3511 E-2
- 1.3376 E-3
1.6460 E-3 -4.9009 E-3
1.4081 E-2
1.3474 E-2
-6.4669
E-3
9.7446 E-4
3.6614 E-l 9.6612 E-2 8.9208 E-l
- 1.7998 E-l -9.0924 E-2 -4.6701 E-l
3.1846 E-2 2.7782 E-2 9.31518E-2
9.9149 E-4 -1.4948 E-3 -3.1992 E-3
0 0 0 0 0
7.0382 E-l 1.7491 E-2 8.8636 E-1 2.3147 E-3
-4.1916 E-1 -1.0148 E-2 -2.3679 E-l -6.3878 E-3
9.0921 E-2 1.7138 E-3 3.0766 E-2 1.6002 E-3
-3.7829
-2.7816 E 1.0219 E 1.0000 E 4.2068 E 8.9964 E 6.7188 E
0 0 0 0 0 0
2.4216 E 1 1.0405 E 1
-7.1137 E 0 - 1.2338 E 0
1.4186 E 0 2.2748 E-l
-1.2606 E-I - 1.2293 E-2
6.4814 E-l 9.8924 E 0 9.6002 E-l
-1.0458 E-1 -1.8785 E 0 - 1.3666 E-l
6.1122 E-3 1.9243 E-l 4.4294 E-2
-7.4831 -2.8600
7.6413 E 4.0232 E 8.6643 E 9.7086 E
0 0 0 0
7.4904 E-l -1.7262 E-2 -3.2616 E-l -3.8140 E-l
-2.0133 E-l 2.7661 E-3 6.8181 E-l 6.6292 E-l
2.6166 E-2
- 1.2266 E-3
-4.4262 -6.4984
E-2 E-2
E-3
- 1.4624 E-3
E-3 E-3
1.9976 E-3 2.8792 E-3
4.4289 E-3
L.
524 Table
DE GALAN,
R.
Smrr~
and
J.
D.
WINEZORDNER
1 (co&) a
b
0
d
6.7306 E-2 -6.6371 E-l
- 1.0381 E-3 7.1913 E-2
e
f
PI P II
4.2251 E 0 4.4161 E 0
-2.2476 E-l 2.2494 E 0
PbI Pb II PdI Pd II
1.2430 E 2.0663 E 1.4811 E 5.7306 E
0 0 0 0
-2.7649 E-l -6.6909 E-2 -6.7500 E-l 1.1960 E-l
8.8724 E-2 1.1277 E.2 2.6930 E-l 1.2969 E-l
PO1 PO II P11 Pt II RaI RaII RbI Rb II
6.0023 E 0
- 1.4898 E-2
6.8170 E-3
3.9411 E-4
6.2171 E 0 6.6712 E 0 7.9239 E-l 2.1669 E 0 1.9869 E 0 1.0000 E 0
8.6683 E 0 -1.0363 E 0 3.2001 E-l -1.6014 E-l 3.8600 E-2
-2.8182 E 0 6.7234 E-l -1.7242 E-l 3.3166 E-2 -2.8329 E-2
6.6124 E-l -6.1219 E-2 3.6107 E-2
ReI Re II Rhl Rh II RnI Rn II
6.6671 E 6.6699 E 6.9164 E 7.2902 E 1.0000 E 4.0000 E
0 0 0 0 0 0
7.2721 E-l 6.9999 E-l 3.8468 E 0 1.7476 E 0
-4.2096 E-l -2.8632 E-l 4.3126 E-2 -3.8267 E-2
9.0760 E-2 6.0724 E-2 -8.7907 E-3 2.0140 E-3
- 3.9331 E-3 - 1.8644 E-3 6.9689 E-4 2.1218 E-4
RuI Ru II SI s II Sb I Sb II
7.2113 E 0 7.2138 E 0 6.3026 E 0 4.0754 E 0 4.3114 E 0 9.1346 E-l
7.0168 E 0 4.2834 E 0 1.2760 E 0 -6.2664 E-2 -3.6681 E-l -1.6093 E-l
-1.6028 E 0 -6.0479 E-l -3.1216 E-l 9.3699 E-3 1.1172 E-l 2.7036 E-l
4.3173 E-l 1.1008 E-l 4.2862 E-2 1.2001 E-3 -4.4909 E-3 -3.7073 E-2
-4.4164 -6.6846 -2.1798
SC I so II Se1 Se II Si I Si II SnI Sn II Sri sr II TaI Te II
7.6269 E 0 1.1624 E 1 4.3632 E 0 4.1786 E 0 6.7868 E 0 3.9839 E 0 -1.9638 E-l 2.0009 E 0 8.7127 E-l 1.9366 E 0 3.0679 E 0 1.6834 E 0
1.9781 E 0 1.1329 E 0 8.8160 E-l -1.6392 E-l 8.6319 E-l 1.0330 E 0 1.4076 E 0 -2.0414 E-l 2.0148 E-l 9.6844 E-2 8.1776 E-l 2.0103 E 0
-8.3426 E-l 4.9827 E-l -6.3171 E-2 3.2063 E-2 -1.1622 E-l -2.6689 E-l -7.6162 E-2 2.0687 E-l -1.0746 E-l -6.0332 E-2 3.4936 E-l 6.6443 E-l
1.6172 E-l -7.3723 E-2 2.5242 E-3
-7.9096 E-3 3.6934 E-3
1.3109 E-2 3.0743 E-2 1.6788 E-3 -3.2011 E-2 2.1424 E-2 1.0363 E-2 7.4861 E-3 -3.1036 E-2
-6.2013 -1.4190
To I To II TeI Te II Ti I Ti II
4.4388 E 8.1096 E 5.1239 E 4.2666 E 1.4643 E 9.2912 E
3.0648 E-l -2.9630 E 0 -2.9839 E-l -2.6894 E-l 2.0096 E 0 2.3978 E 1
1.6626 E 0 2.3690 E 0 1.9304 E-l 6.9390 E-2 -3.6619 E-l -7.3970 E 0
-4.0779 E-l -5.0200 E-l -2.2031 E-2 -2.4271 E-3 1.4760 E-l 1.4602 E 0
TlI Tl II VI v II WI w II
2.1277 E 0 1.0000 E 0 6.3211 E 0 1.0337 E 1 3.9611 E-l 1.0660 E 0
X01 xe II YI YII ZnI Zn II ZrI Zr II
1.0000 E 4.0468 E 4.8488 E -1.2762 E 1.0000 E 2.0000 E
0 0 0 0 1 0
0 0 0 0 0 0
6.3459 E 0 4.0623 E 0
-1.6764 E-l
6.3187 E-2
-4.2066
E-3
-1.6213 -2.3613
E-2 E-2
-3.6166
E-3
1.3441 E-3
-6.4166 E-2 2.6878 E-3 - 1.8939 E-3
2.1168 E.3
6.1101 E-3
E-2 E-3 E-3
1.7278 E-3
-4.4389 E-5 1.7249 E-3
E-4 E-3
1.6436 E-3 -1.0231 E-3 -4.8626 E-4 3.0739 E-4 8.9666 E-4 4.8401 E-2 4.9666 E-2 8.9622 E-4 -7.1902 E-3 -1.4208 E-l
-2.1638 E-3 - 1.9087 E-3
5.4322 E-3
-3.6946 E-3
1.6446 E 1 1.0244 E 1 -2.6067 E-l 1.0396 E 0
-3.6791 E 0 - 1.6380 E 0 1.4433 E 0 3.3030 E-l
6.2047 E-l 2.3600 E-l -3.4373 E-l -8.4971 E-3
-2.2682 E-2 -1.0888 E-2 4.1924 E-2 6.6794 E-4
-6.0967 E-2 3.0826 E 0 6.2962 E 0
1.4823 E-2 -1.0879 E 0 -1.0736 E 0
-6.2726 E-4 1.9721 E-l 1.2900 E-l
9.6671 E-3 -6.8804 E-3
4.5026 E 0 8.4092 E 0
- 1.6307 E-2 1.6201 E-2
3.2396 E-2 -9.9477 E-3
6.6393 E-3
- 1.8402 E-3
-5.7919
E-4
* Exponential notation is used, eg., 7.2138 E 0 and -6.0479 E-l correspond to 7.2138 and -6.0479 x 10-l. Blank spaces indiaate that the coeffioient is essentially zero, and the data may be represented by a polpomial of lower order than five.
The electronic partition functions of atoms and ions between 15OO’K and 7000’K
coefficients for the fifth-order B(T)
=a
+b
(5)
polynomial, fc
(*)’ 103
525
equation given below: +d
( 103 T)3
+e
( 103 T)4
+f
( 103 T)5
(3)
This communication is incomplete insofar as values of B(T) were not calculated for astatine, francium, the lanthanides, the actinides, and the first ion spectra of indium and polonium. Energy level data for these species are not available in the tables given by MOORE [4]. The authors would be pleased to supply a tabular listing of calculated partition functions for the 73 elements in the Table. of the authors (R. S.) thanks the National Science Foundation Science Development Grant of the University of Florida for financial support in the form of a postdoctorate research fellowship. This work was supported in part by AFOSR (SRC)-OAR, U.S.A.F. Grant No. AF-AFOSR-103348. AcknowZedgments-One