can be regarded as being built of one kind of particle called atoms with atomic number 2 has been used in the analysis of ?-ray backscattering (9, 8, 11). Various formulas for the calculation of the effective atomic number have been suggested and correlated with ehperimental data. AIuller (Q), n i t h marked success in his system, used a formula such that
z
[(weight fraction),Z,]
=
(12)
1
Saldick and Allen’s (11) formula fori? [(electron density),Z,]
. i ? =
(13)
i
is a special case of the more general formula ( 6 ) 1
2
[(electron density),Z,”]’
=
(14)
1
nherein 2 = 1. Effective atomic numbers were calculated according to Equations 12 and 13 for all the compounds and mixtures studied herein, and correlation was attempted with the observed backscatter intensities. MullerJs effective atomic number (Equation 12) showed the poorest correlation with marked scatter of the points even after correcting for hydrogen content. The hydrocarbon systems indicated that some correlation existed, but the ternary compound data disputed any general correlation for all compounds. The results of plotting backscatter intensities us. the effective atomic numbers calculated using Equation 13 were much better, but there was still some scattering of the data from a smooth curve. Effective atomic numbers were calculated from Equation 14 with z = 0.93 and found to give a very good correlation n i t h the experimental P-ray backscatter intensities. A graphical representation could be used to obtain an effective atomic number from a backscatter intensity and could subsequently be used to individualize the compound or mixture. However, in view of the success of the mathematical approach this graphical interpretation should principally be of academic interest. The marked discrepancy between the data of Muller and ours in the lack of correlation of the effective atomic numbers can probably be attrib-
uted to the different experimental systems used in each case. The geometry is different as is also the method of detection of the backscattered 0-rays. Muller’s intensity data, obtained with a proportional counter, would be relatively free of ?-ray energy effects; whereas our ionization chamber detector integrates the energy loss of the ?-rays in transversing the active volume of the chamber. Because our data have been limited to the light elements (2 6 9), our effective atomic number calculations have not included values near the inflection points a t 2 = 10, 18, 36, and 54 noted by Muller. The quantitative analysis of binary compounds by either p-ray transmission or backscattering is rapid and accurate. The average time per sample is approximately 10 minutes for backscattering analysis and slightly longer for transmission analysis. The precise density requirements and the necessity of sample temperature being at 30” C. require the longer analysis time for the transmission determinations. Analysis of ternary compounds and mixtures is likewise rapid. The complete analysis of ternary compounds takes less than 30 minutes. If sufficient sample is available for the simultaneous determination of the sample density and backscatter and transmission p-ray intensities, the analysis can be done in less than 20 minutes. This is to be compared with the 3 to 4 hours for a complete analysis by classical microchemical methods. Investigations are continuing on the extension of these B-ray interactions t o higher atomic number materials. ACKNOWLEDGMENT
The authors are indebted to J. R. Scherer for the compilation of the computer program used in the calculation of the elemental backscatter constants. Acknowledgment is also extended t o E. D. Ruby and L. B. Westover for the vapor phase chromatography and mass spectrographic analyses. LITERATURE CITED
(1) Berthold, R., “Proceedings of the
Second United Nations International Conference on the Peaceful Uses of Atomic Energy,” P/983, Vol. 19, p. 288, United Hations, Geneva, 1958.
XII.
Table
Standard Deviations in P-Ray Analyses
Weight Element Fraction Carbon in C-H-0 compounds 0.0018 Oxygen in C;H-O compounds 0.0018 Hydrogen in C-H-0 compounds 0.0003 Hydrogen in nitrogen compounds 0,0002 Hydrogen in fluorine compounds 0,0005 Hydrogen in hydrocarbons (transmissjon) 0.0003 Hydrogen in hydrocarbons (backscatter) 0.0003 Hydrogen in 45 ternary compounds and mixtures 0.0003 (2) Danguy, L., Qiiivy, R., J . phys. radium 17, 320 (1956). (3) Evans, R. D., “The Atomic Nucleus ” Chaps. 19-21, McGraw-Hill, New York, 19.59.
(4) Fodor, J., Varga, C., “Proceedings of the Second United Nations International Conference on,, the Peaceful Uses of Atomic Energy, P/2241, Vol. 19, p. 215, United nations, Geneva, 19.58.
(5) Gray, P. R., Clarey, D. H., Beamer, w.H., ANAL.CHEM. 31, 2065 (1959). (6) Henricksen, T., Baarli, J., Radiation Research 6, 415 (1957). (7) Husain, S. A., Putman, J. L., Proc. Phys. SOC.( L o n d o n ) 70,304 (1957). ( 8 ) Muller, D. C.,ANAL.CHEM.29, 975 (1957). (9) Muller, R. H. Ibid., 29, 969 (1957). (10) Muller, R. k., Phys. Rev. 93, 891 (1954). (11) Saldick, J., Allen, A. O., J. Chem. Ph s. 22, 438 (1954). (12) mith, V. K.,Otvos, J. W., ANAL. CHEM.26,359 (1954). (13) Strominger, D., Hollander, J. &‘I., Seaborg, G. T., Revs. Modern Phys. 30, 585 (1958). RECEIVED for review September 23,. 1959. Accepted December 18, 1959. Division of Anal tical Chemistry, 137th Meeting, ACS, Cikeland, Ohio, April 1960.
4!
Correction Eva1ua t ion of St and ard Model D Keston Polarimetric Attachment for the Beckman DU Spectrophotometer I n this article b y Knud G. Poulsen [ANAL.CHEM.32, 410 (1960)], on page 413, the second line after the Literature Cited section should read Accepted December 17,1959.
VOL. 32, NO. 6, MAY 1960
589
