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f.ali'"')'**{. ^*^7. w fr) .\ 1. ii ..! .:.* *:" .., :I :. T,. i' " 1." :I iu s to MDDC 734 UNITED STATES ATOMIC ENERGY CO MMISSION ; A SLIDE RULE FOR ACTIVATION AND DECAY CALCULATIONS by A. H. Snell Thelma Arnette This document consists of 4 pages. Date of Manuscript: April 1, 1946 Date Declassified: February 7, 1947 This document is for official use. Its issuance does not constitute authority for declassification of classified copies of the same or similar content and title and by the same authorss. Technical Information Division, Oak Ridge Directed Operations Oak Ridge, Tennessee Digitized by the Internet Archive in 2011 with funding from University of Florida, Geoige A. Smathers Libraries with support from LYRASIS and the Sloan Foundation htlp: www.archive.org details slider uletoracti0usat NJ. 1. . A SLIDE RULE FOR ACTIVATION AND DECAY CALCULATIONS By A. H. Snell and Thelma Arnetle The calculation of the strength of radioactive samples alter neutron irradiation, followed perhaps by a period of decay, has become so much a matter of routine that it seems that a quick ad to calcula tion might be a time saver to those engaged in this type of work. The accompanying figures show how a slide rule could be constructed which would give answers to these calculations. including in most cases the correct power of 10. to an accuracy commensurate with the precision ol mcl cross section Ind flux values. The expression to be evaluated ': in general the product nv o M A x 6.06 x 10" (1eet'l e\1 in which nv is the neutron flux, a the activation cross section, M the mass of the sample in grams. A its atomic weight, \ the decay constant of the induced activity, t, the irradiation time and t, the de cay time subsequent to irradiation. This can be modified and condensed to the form nv' IM I e0.693t le.693tI where E is the activation cross section per gram of normal element, and can be read from a table on Sthe back of the slide rule for any of the one hundred and fifty or so .ctivities usually encountered; St and t. are respectively the activation and decay times, now expressed in units ot the halilile of the ; activity concerned. SThe operation of the rule can be understood with reference to Figure I A, B, and C, for which the following sample calculations are respectively set up: A) 3.2 grams of strontium are activated for 30 days in an average slow neutron flux of 2.2 x 10". What is the strength of the induced 55day activity Using the CD scales, 30 days is found to be 0.55 of a halflife. Reference to the table on the back of the rule Figure 21shows that strontium has an activation cross section of 2.8 x 105 cm2 per gram. The end of the nv scale on the slide Iviz. the 10" mark) is placed opposite 2.8 x 106 on the S scale. The cursor is then set at 2.2 x 10" on the nv scale, and the slide is moved until 5.5 x 10' on the t scale is under the cursor line. (This takes care of the (1 e't) factor). The lefthand end of the nv scale is then opposite the figure 1.93 x 10' when read from the dn, dt scale; this gives the number of disintegration per second per gram. The nv scale can then be used again to multiply it by 3.2, giving the answer to the problem: 6.1 x 10" disintegrations per second. B) 5.3 grams of silver are activated to saturation in an average flux of 4.4 x 10". What is the strength of the induced 2.3minute activity ? The end of the nv scale is set against the figure E = 1.42 x 10'. In this case we find that we must use the righthand end of the nv scale, and this means that the answer as given on the dn, dt scale will have to be multiplied by 105; the figure x 10"' is inscribed at the righthand end of the nv scale to remind the calculator that this is so. Since the 1ekt factor is unity, (t = o), the position of 4.4 x 103 on the nv scale can then be marked with the cursor, and multiplied directly by 5.3 to give the answer 3.3 x 10" disintegrations per second. MDDC 734 [ V 2 ] MDDC 734 II "   '* K . K *1 I ' S *  A B C Figure 1. Slide rule for activation and decay calculations. . " . "=2"r i. Sld "ul .. ciainaddea aclto I k  MDDC 734 Element Halflife H(em' per g of element) H* 25 y 5.68 Li 0.88 s < 3.2 x 104 C** 25.000 y 7.3 x 102 N 8s <4x109 O 31 s 1.7 x 108 F 12 s 3.0 x 10 Na 14.8 h 1.0 x 102 Mg 10.2 m 1.34 x 10 Al 2.4 m 5.2 x 10' Si 17.0 m 1.0 x 10 P 14.3 d 4.5 x 103 S 87.1 d 2.1 x 10 Cl 37 m 2.6 x 103 A 110 m 1.88 x 102 K 12.4 h 1.04 x 10 Ca 8.5 d < 1.5 x 10' Ca 180 d 2.0 x 10 Ca 2.5 h 5.9 x 105 Sc 85 d 3.0 x 10' Ti 72 d 9.5 x 10s V 3.9 m 6.0 x 10 Cr 26.5 d 5.8 x 103 Cr 1.3 h 1.6 x 106 Mn 2.59 h 1.27 x 10' Fe 47 d 1.1 x 10s Co 10.7 m 7.5 x 10s Co 5.3 y 2.3 x 10' Ni 2.6 h 2.0 x 104 Cu 12.8 h 2.1 x 102 Cu 5 m 5.7 x 10' Zn 250 d 2.4 x 103 Zn 57 m 1.9 x 103 Zn 13.8 h 5.0 x 104 Ga 20 m 8.2 x 10' Ga 14.1 h 1.13 x 102 Ge 40 h 1.3 x 104 Ge 11 d 7.9 x 10 Ge 89 m 1.2 x 10S Ge 12 h 4.6 x 10' Se 115 d 1.5 x 101 Se 19 m 2.0 x 10 Se 57 m 1.3 x 104 Se 30 m 4.3 x 105 As 26.8 h 3.7 x 102 Br 18 m 3.4 x 102 Br 4.4 h 1.16 x 102 Br 34 h 8.4 x 10' Rb 19.5 d 3.71 x 10a Rb 17.5 m 2.6 x 10' Sr 2.7 h 9.7 x 104 Sr 55 d 2.8 x 10s Y 60 h 7.5 x 10' Zr 63 d 4.8 x 104 Zr 17 h 6 x 10' Zr 6 m 1.1 x10 Cb 6.6 m 1.4 x 10 .lo 67 h 5.9 x 104 lo 14.6 m 1.3 x 10 Ru 42 d 2.2 x 10' Ru 37 h 8.9 x 104 Ru 4 h 7.3 x 104 Rh 44 s 8.8 x 101 Rh 4.2 m 7.5 x 102 Pd 13 h 1.8 x 102 vd 26 m 4.8 x 104 Ag 2.3 m 1.42 x 10 Ag 22s 2.88 x 10' *From Li *From N Figure 2. Element Halflife L(cm' per g of element) Ag 225 d 6.2 x 10a Cd 2.5 d 1. < 10' Cd 46 d 2.2 x 10" Cd 3.75 h 5.4 x 104 Cd 2m 2.7 x 10 In 48 d 1.45 x 10' In 13 s 2.8 x 10" In 54 m 7.9 x 10' Sn 100d 6.1 x 10s Sn 9m 2.0 x 10' Sn 40 m 7.2 x 10' Sn 26 h 3.7 x 10 Sn 400 d 9.2 x 105 Sn 10d 5 x 10 Sb 2.8 d 1.9 x 102 3b 60 d 5.5 x 103 Te 9.3 h 7.1 x 10 re 72 m 2.07 x 10 Te 32 d 2.4 x 10" Te 25 m 3.8 x 10 Te 30 h < 1.4 x 10s I 25 m 3.2 x 102 Cs 3 h 7.3 x 10s Cs 1.7 y 1.17 x 10' Ba 86 m 1.8 x 103 La 40.0 h 3.7 x 102 Yr 19 h 4.7 x 102 Sm 21 m 4.8 x 10 Sm 46 h 1.6 x 10' Eu 94 h 2.98 Eu 6.5 y 1.55 .d 9.5 h 8.9 x 10 Gd 20 h 3 x 10s Gd 8.6 d 2 x 10' Tb 3.9 h 4.4 x 102 Tb 72 d 4 x 10' Ho 30 h 2.4 x 10' Dy 1.4 m 1.5 x 10 Dy 2.5 h 2.95 rm 105 d 4.2 x 10 Lu 6.6 d 3.4 x 10 Lu 3.4 h 6.0 x 102 Hf 46 d 1.2 x 102 Ta 117 d 7.5 x 10 Ta 16.5 m 1.2 x 10 W 77 d 2.1x10' W 23 h 3.6 x 102 Re 90 h 1.37 x 10 Re 18 h 1.64 x 10 Os 32 h 2.1 x 10' Os 17 d 7.0 x 103 Ir 19 h 2.7 x 10' Ir 1.5 m 6.5 x 103 Ir 70 d 1.32 Pt 18 h 9.3 x 10 1t 3.3 d 3.7 x 10' Pt 31 m 9.3 x 10' Au 27 d 3.2 x 10' Hg 51.5 d 2.3 x 10' Hg 5.5 m 7.5 x 105 ri 4.23 m 2.6 x 10 TI 3.5 y 6.5 x 10s ko 3.0 h 7.0 x 10 Bi 5.0 d 4.3 x 10s Th 23 m 2.2 x 102 U 23.5 m 6.9 x 103 Reference table on back of rule. MDDC 734 C) A sample of 0.5 curie strength is allowed to decay for 9.62 halflives. What is its strength ? To make decay calculations, the slide is turned over, revealing two linear scales. The upper one is needed for this problem, and by setting its 0 opposite 0.5 on the E scale one can read the answer 6.0 x 104 curies opposite the figure 9.62. For more accurate computation for decay factors of less than 10, the lower t scale is supplied. t is again expressed in halflives. FISSION PRODUCT ACTIVITIES The use of the rule can be extended directly to many of the fission productsnamely, to the cases in which the growth is uncomplicated by chain relationships. This is done by defining 2: as an effective cross section for formation of a particular fission product per gram of normal uranium undergoing slow neutron irradiation. In the use of the rule, the L's are set up on the L scale, and manipulation proceeds as in the case of (ny) activations. DISCUSSION It would be more convenient if the linear tscales were on the same side of the slide as the nv scale. This could be done without crowding if the slide were made proportionately wider. The cross section tables might well be printed on a card which slips into a holder on the back of the rule. Revised cards could then be supplied from time to time. The circular type of slide rule would also be adaptable to these purposes. ?. if !*; !, i UNr ERSiTY OF FLORIDA III 31 lIII 1 1III III IIII IIII I 5 6 3 1262 08910 5265 I 
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