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Ionization in the Plasma of a Copper Arc Charles H JOURNAL OF RESEARCH of the National Bureau of Standards—A. Physics and Chemistry Vol. 66A, No. 2, March-April 1962 Ionization in the Plasma of a Copper Arc Charles H. Corliss (December 8, 1961) From the relative intensities of arc and spark lines observed in a d-c arc in air between copper electrodes, the degree of ionization of eleven elements added to the copper has been determined. With the aid of Sana's ionization equation, the electron density in the arc was calculated to be 2.4X 1014 cm"3. Partition functions for atoms and ions of 29 elements are newly calculated or estimated and a table of first ionization potentials and partition functions of atoms and ions for seventy elements is presented. The degree of ionization of seventy elements separately added to the arc is calculated. The electron density in the arc is confirmed by three independent spectroscopic and electrical determinations. The data developed in this paper will enable the calculation of relative transition probabilities from the intensities in the NBS Tables of Spectral-Line Intensities. 1. Introduction source, it is possible to calculate the relative particle density of atoms and ions for that element, if the It is possible to determine the relative transition absolute transition probabilities or absolute ^/-values probabilities for the lines of a particular spectrum for those lines are available. Designating quantities emitted by a hot gas, from measurements of the associated with a neutral atom and its spectrum by relative intensities of those lines, provided that the the superscript ° we can write the Einstein-Boltzmann excitation in the radiating gas can be described by equation for the intensity of a line of that spectrum Boltzmann's law. It is necessary to know only the in the form temperature of the gas. If the relative transition probabilities for lines of both the first and second =1V hv°g°A°e~kT- spectra of an element are to be determined on the u (1) same scale, the degree of ionization in the radiating gas must be found. In this equation iV° is the particle density of neutral In this paper we shall investigate the ionization in atoms, u° is the partition function for the atom which the positive column or plasma of a 10 amp d-c arc in expresses the distribution of neutral atoms over their air between copper electrodes. This is the arc possible energy states, hv° is the energy of a single which served as the light source for obtaining the photon, g° is the statistical weight of the upper state, intensity values reported in the NBS Tables of 1 A° is Einstein's transition probability for the particu- Spectral-Line Intensities [I] . lar line, E° is the energy of the upper state, k is In that work, an element under investigation was Boltzmann's constant and T is the temperature of the mixed with pure copper powder in the atomic ratio copper arc. If we write a similar equation, desig- of 1 to 1,000. The mixtures were pressed into solid nating quantities associated with an ion and its spec- cylindrical pellets }{ in. in diameter, }{ in. in length, trum by the superscript4", and take the ratio of the and weighing about \){ g. The pellets were mounted two equations, we obtain as electrodes in water-cooled clamps and a direct current of 10 amp passed between them from a g°A° 220-v line with a resistive ballast. A 3-mm gap (2) between the electrodes was imaged entirely within N+ u° the aperture of a stigmatic grating spectrograph by For convenience we make appropriate substitutions a lens at the slit. In this arrangement light from of X instead of v and gf instead of gA and solve for all parts of the arc stream contributed to the spectral- N+/N° line intensities. Although the temperature and + s ^E+-E° N _(IX )+u+ (gf) h electron density in the arc stream are functions of 3 kT . (3) the axial and radial positions, we deal here only iV°~(/X )° u ( with mean values which are inherently weighted according to the intensity distribution in the arc. For computation we take common logarithms and The excitation in this light source has been shown in insert a numerical value for Boltzmann's constant. a previous paper [2] to follow Boltzmann's law. N+ 2. Relative Intensities of Arc and Spark Lines 0 When the intensity ratio of lines from neutral • (E+-E )- (4) atoms and ions of an element is known in such a light JL i Figures in brackets indicate the literature references at the end of this paper. In (4), E is in kilokaysers and Tis in °K. 169 Of the 70 elements in the NBS Tables of Spectral- TABLE 1. Experimental determination of ionization for eleven Line Intensities, there are, at present, only 11 for elements in the copper arc which all the quantities on the right side of eq (4) are known. The data used in obtaining the numerical Atom or Wave- Inten- Refer- Percent solutions are given in table 1. The 11 atoms and ion length sity u 9f ence E Log£ ioniza- ions are listed in order of atomic number in column tion 1. The wavelengths and intensities for the first A kK Be0 term of the right member of eq (4) are taken from the 3321 160 1.0 3.06 52. 082 -1.236 5.5 Tables of Spectral-Line Intensities and given in Be+ 3130 800 2.0 1.50 31.932 Mg° 3838 940 1.0 6.0 47.957 -0.852 12 columns 2 and 3. In most cases, the total intensity Mg+ 2795 1,600 2.0 1.80 35.72 for a multiplet is used; and only the first 4 figures HI Ca° 1.46 4226. 73 1,100 1.2 [8] 23. 652 .957 90 of the wavelength of the leading line in the multiplet Ca+ 3933 6,400 2.2 2.20 [9] 25.3 are listed. When /-values were available for more Sc° 5671 598 12.1 11. [7] 29.16 .761 85 than one multiplet, an attempt was made to select Sc+ 3613 6,606 23.2 6.9 [7] 27.65 Ti° 7.4 multiplets of moderately high intensity for each 4305 1,636 30.4 [7] 29.98 -. 056 47 spectrum. In cases where a single line is used, the Ti+ 3759 532 55.9 5. [7] 31.36 V° 4111 decimals are given also. For the second term we 2,760 48.8 7.3 26.59 .284 66 list in column 4 the partition functions calculated by V+ 3093 1,936 43.0 11.2 ft 35.06 Zn° 4810 1.0 280 1.0 53. 672 -2.931 0.12 Claas and given in tables 27 and 29 of his paper [3]. Zn+ 2061 15. 5 2.0 1.8 [IS 48.62 In column 5 are found the sums of the absolute gf- Sr° 4607.33 650 1.8 1.3 21. 698 1.564 97 values for the lines. With two exceptions, only Sr+ 4077 7,800 2.2 1.87 ft 24.19 theoretical gf-values or experimental relative values Cd° 3261.06 32 0.0022 1.0 30. 656 -0.608 20 adjusted to a theoretical absolute scale are employed. Cd+ 2265 170 2.0 1.8 & 45.01 Ba° 5535. 48 650 1.92 This is done because of the scarcity of experimental 2.5 18.060 97 absolute values, especially for second spectra. The Ba+ 4554 8,500 4.3 2.0 ft 21.65 1.569 Pb° 2401.95 36 1.6 0.064 49. 440 value for Cd i, however, is a measurement in absorp- -0.260 35 tion by King and Stockbarger [4]. The value used Pb+ 2203. 53 9 2.1 .604 59. 448 for Pb II is Stephenson's measurement [5] for the corresponding transition in isoelectronic Tl i. Refer- ences to the origin of the absolute (//-values are given determination of the degree of ionization of the in column 6. remaining 59. For these latter elements, the equa- The energy levels of the upper states given in tion of ionization first developed by Sana [11] will column 7 are taken from the Tables of Spectral-Line be used. This is an equation describing the equilib- Intensities and are given in units of kilokaysers 1 rium existing, in a hot gas, between the relative (1 kK=1000 cm" ). For multiplets, weighted mean concentration of atoms and ions of any particular values are given. These values are used in the last atomic species and the concentration of free electrons, term of eq (4) along with the temperature of the as a function of the temperature of the gas ana the copper arc determined in a previous paper [2]. This ionization potential of the atom under study. For temperature (5,100 °K) was determined by com- our purpose it is convenient to write it in the form paring 31 sets of experimental relative transition probabilities with the corresponding spectral-line intensities measured in the copper arc and reported in the Tables of Spectral-Line Intensities. The log N° e~ (5) ratio N+/N° calculated from the data in the table by means of eq (4) is given in column 8 and the percent ionization of the element in column 9 is simply where Ne is the electron density, m is the mass of the electron, and V is the ionization potential of 100JV+ _100N+/N° the atom.
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