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 MDDC - 734 
 
 NITED STATES ATOMIC ENERGY COMMISSION 
 
 A SLIDE RULE FOR ACTIVATION AND DECAY CALCULATIONS 
 
 by 
 
 A. K. 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 author(s). 
 
 Technical Information Division, Oak Ridge Directed Operations 
 Oak Ridge, Tennessee 
 
H 
 
 Digitized by tine Internet Arcliive 
 
 in 2011 witln funding from 
 
 University of Florida, George A. Smathers Libraries with support from LYRASIS and the Sloan Foundation 
 
 http://www.archive.org/details/slideruleforactiOOusat 
 
A SLIDE RULE FOR ACTIVATION AND DECAY CALCULATIONS 
 
 By A. H. Snell and Thelma Arnette 
 
 The calculation of the strength of radioactive samples after neutron irradiation, followed perhaps 
 by a period of decay, has become so much a matter of routine that it seems that a quick aid 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 of most cross section 
 md flux values. The expression to be evaluated 'a in general the product 
 
 nv a M/A x 6.06 x 10" (l-e-^^') e-^*= 
 
 in which nv is the neutron flux, a the activation cross section, M the mass of the sample in grams, 
 A its atomic weight, A the decay constant of the induced activity, tj the irradiation time and tj the de- 
 cay time subsequent to irradiation. This can be modified and condensed to the form 
 
 nvi:M(l-e-0-693ti ,^..6931^ 
 
 where L is the activation cross section per gram of normal element, and can be read from a table on 
 the back of the slide rule for any of the one hundred and fifty or so .ictivities usually encountered; 
 t'l and t^ are respectively the activation and decay times, now expressed in units of the half -life of the 
 activity concerned. 
 
 The operation of the rule can be understood with reference to Figure 1 — 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 IC. 
 What is the strength of the induced 55-day activity? Using the C-D scales, 30 days is found to be 0.55 
 of a half-life. Reference to the table on the back of the rule (Figure 2)shows that strontium has an 
 activation cross section of 2.8 x 10"^ cm^ per gram. The end of the nv scale on the slide (viz. the 10^ 
 mark) is placed opposite 2.8 x 10"^ on the L 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"^' ) factor). The left-hand 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 disintegrations 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 IC^. What is the 
 strength of the induced 2.3-minute 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 right-hand end of the nv scale, and this 
 means that the answer as given on the -dn/dt scale will have to be multiplied by 10^; the figure 
 " x 10 " is inscribed at the right-hand end of the nv scale to remind the calculator that this is so. 
 Since the 1 — e"^^ factor is imity, (t =°°), the position of 4.4 x itf^ 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 ^^ 
 
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 MDDC - 734 
 
 
 
 
 
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 Figure 1. Slide rule for activation and decay calculations. 
 
MDDC - 734 
 
 13 
 
 Element Half-lite 
 
 Licm= per g 
 
 
 
 
 of element) 
 
 
 H* 
 
 25 y 
 
 5.68 
 
 
 Li 
 
 0.88 s 
 
 <3.2 X 10-* 
 
 
 C" 
 
 25.000 y 
 
 7.3 X 10-= 
 
 
 N 
 
 8s 
 
 < 4 X 10"' 
 
 
 
 
 31 s 
 
 1.7 X 10-« 
 
 
 F 
 
 12 s 
 
 3.0 X lO-' 
 
 
 Na 
 
 14.8 h 
 
 1.0 X 10"' 
 
 
 Mg 
 
 10.2 m 
 
 1.34 X 10-* 
 
 
 Al 
 
 2.4 m 
 
 5.2 X 10-=' 
 
 
 Si 
 
 17.0 m 
 
 1.0 xlO-" 
 
 
 f 
 
 14.3 d 
 
 4.5 X 10-= 
 
 
 S 
 
 87.1 d 
 
 2.1 X 10-* 
 
 
 CI 
 
 37 m 
 
 2.6 X 10-' 
 
 
 A 
 
 110 m 
 
 1.88 X 10-= 
 
 
 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 10-' 
 
 
 Sc 
 
 85 d 
 
 3.0 X 10-' 
 
 
 Ti 
 
 72 d 
 
 9.5 X 10-' 
 
 
 V 
 
 3.9 m 
 
 6.0 X 10-= 
 
 
 Cr 
 
 26.5 d 
 
 5.8 X 10-' 
 
 
 Cr 
 
 1.3 h 
 
 1.6 X 10-" 
 
 
 Mn 
 
 2.50 h 
 
 1.27 X 10-' 
 
 
 Fe 
 
 47 d 
 
 1.1 X 10-= 
 
 
 Co 
 
 10.7 m 
 
 7.5 X 10"' 
 
 
 Co 
 
 5.3 y 
 
 2.3x10-' 
 
 
 Ni 
 
 2.6 h 
 
 2.0 X 10-* 
 
 
 Cu 
 
 12.8 h 
 
 2.1 X 10-= 
 
 
 Cu 
 
 5 m 
 
 5.7 X 10"' 
 
 
 Zn 
 
 250 d 
 
 2.4 X 10-' 
 
 
 Zn 
 
 57 m 
 
 1.9 X 10-' 
 
 
 Zn 
 
 13.8 h 
 
 5.0x10"' 
 
 
 Ga 
 
 20 m 
 
 8.2 X 10-' 
 
 
 Ga 
 
 14.1 h 
 
 1.13 X 10-= 
 
 
 Ge 
 
 40 h 
 
 1.3 X 10-* 
 
 
 Ge 
 
 11 d 
 
 7.9 X lO"" 
 
 
 Ge 
 
 89 m 
 
 1.2 X 10-' 
 
 
 Ge 
 
 12 h 
 
 4.6 X 10-' 
 
 
 Se 
 
 115 d 
 
 1.5 X 10-' 
 
 
 Se 
 
 19 m 
 
 2.0x10-' 
 
 
 Se 
 
 57 m 
 
 1.3 X lO-* 
 
 
 Se 
 
 30 m 
 
 4.3x10"' 
 
 
 As 
 
 26.8 h 
 
 3.7 X 10-= 
 
 
 Br 
 
 18 m 
 
 3.4 X 10-= 
 
 
 Br 
 
 4.4 h 
 
 1.16x10-= 
 
 
 Br 
 
 34 h 
 
 8.4x10"' 
 
 
 Rb 
 
 19,5 d 
 
 3.71 X 10-' 
 
 
 Rb 
 
 17.5 m 
 
 2.6 X 10"^ 
 
 
 Sr 
 
 2.7 h 
 
 9.7 X 10"< 
 
 
 3r 
 
 55 d 
 
 2.8 X 10"' 
 
 
 Y 
 
 60 h 
 
 7.5 X I0-' 
 
 
 Zr 
 
 63 d 
 
 4.8 X 10-' 
 
 
 Zr 
 
 17 h 
 
 6 X 10-' 
 
 
 Zr 
 
 6 m 
 
 1.1 X lO--" 
 
 
 Cb 
 
 6.6 m 
 
 1.4 X lO-" 
 
 
 lo 
 
 67 h 
 
 5.9 X 10-* 
 
 
 .lo 
 
 14.6 m 
 
 1.3 X 10-* 
 
 
 Ru 
 
 42 d 
 
 2.2x10-' 
 
 
 Ru 
 
 37 h 
 
 8.9 X 10-* 
 
 
 Ru 
 
 4 h 
 
 7.3 X 10-* 
 
 
 Rh 
 
 44 s 
 
 8.8 X 10"' 
 
 
 Rh 
 
 4.2 m 
 
 7.5 X 10-= 
 
 
 Pd 
 
 13 h 
 
 1.8 X 10-= 
 
 
 l-d 
 
 26 m 
 
 4.8 X 10-* 
 
 
 Ag 
 
 2.3 m 
 
 1.42 X 10-' 
 
 
 Ag 
 
 22 s 
 
 2.88x10-' 
 
 
 
 
 
 
 # 
 
 From Li 
 
 
 «* 
 
 From N 
 
 Fig 
 
 ure 2. 
 
 Element 
 
 Half -life 
 
 I(cm' |)er g 
 
 
 
 of element) 
 
 Ag 
 
 225 d 
 
 6.2 X 10-' 
 
 Cd 
 
 2.5 d 
 
 l.f < 10-' 
 
 Cd 
 
 46 d 
 
 2.2 X 10-* 
 
 Cd 
 
 3.75 h 
 
 5.4 X 10-* 
 
 Cd 
 
 2 m 
 
 2.7 X 10-* 
 
 In 
 
 48 d 
 
 1.45 X 10-= 
 
 In 
 
 13 s 
 
 2.8 X 10"! 
 
 In 
 
 54 m 
 
 7.9 .\ 10-' 
 
 Sn 
 
 100 d 
 
 6.1 X 10-' 
 
 Sn 
 
 9m 
 
 2.0 X 10-* 
 
 3n 
 
 40 m 
 
 7.2x10-' 
 
 Sn 
 
 26 h 
 
 3.7 X 10-* 
 
 Sn 
 
 400 d 
 
 9.2 X 10-' 
 
 Sn 
 
 10 d 
 
 5x10-' 
 
 Sb 
 
 2.8 d 
 
 1.9 X 10-= 
 
 3b 
 
 60 d 
 
 5.5 X 10-' 
 
 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 
 
 3.8x10-' 
 
 Te 
 
 30 h 
 
 <1.4 X 10-' 
 
 I 
 
 25 m 
 
 3.2 X 10-= 
 
 Cs 
 
 3h 
 
 7.3 X 10-' 
 
 Cs 
 
 1.7 y 
 
 1.17 X 10"' 
 
 Ba 
 
 86 m 
 
 1.8 X 10"' 
 
 La 
 
 40.0 h 
 
 3.7 X 10-= 
 
 fv 
 
 16 h 
 
 4,7 X 10-= 
 
 Sm 
 
 21 m 
 
 4.8 X 10-' 
 
 Sm 
 
 46 h 
 
 1.6 X 10"' 
 
 Eu 
 
 94 h 
 
 2.98 
 
 Eu 
 
 6.6 y 
 
 1.55 
 
 Od 
 
 9.5 h 
 
 8,9x10-' 
 
 Gd 
 
 20 h 
 
 3 X 10-' 
 
 Gd 
 
 8.6 d 
 
 2x10-' 
 
 Tb 
 
 3.9 h 
 
 4.4 X 10-= 
 
 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 
 
 Tm 
 
 105 d 
 
 4.2 X 10"' 
 
 Lu 
 
 6.6 d 
 
 3.4 X 10"' 
 
 Lu 
 
 3.4 h 
 
 6.0x10-= 
 
 Hf 
 
 46 d 
 
 1.2 X 10-= 
 
 Ta 
 
 117 d 
 
 7.5 X 10-= 
 
 Ta 
 
 16.5 m 
 
 1.2x10-* 
 
 W 
 
 77 d 
 
 2.1x10-' 
 
 W 
 
 23 h 
 
 3.6 X 10-= 
 
 Re 
 
 90 h 
 
 1.37x10-' 
 
 Re 
 
 18 h 
 
 1.64 X 10-' 
 
 Os 
 
 32 h 
 
 2.1 X 10"' 
 
 Os 
 
 17 d 
 
 7.0 X 10-' 
 
 Ir 
 
 19 h 
 
 2.7 X 10-' 
 
 Ir 
 
 1.5 m 
 
 6.6 X 10-= 
 
 Ir 
 
 70 d 
 
 1.32 
 
 Pt 
 
 18 h 
 
 9.3 X 10-* 
 
 1-t 
 
 3.3 d 
 
 3,7 xlO-' 
 
 Pt 
 
 31m 
 
 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 10-' 
 
 Tl 
 
 4.23 m 
 
 2.6 X I0-* 
 
 Tl 
 
 3.5 y 
 
 6,5x10-' 
 
 PO 
 
 3.0 h 
 
 7.0x10-' 
 
 Bl 
 
 5.0 d 
 
 4,3 x 10-' 
 
 Th 
 
 23 m 
 
 2.2 X 10-= 
 
 U 
 
 23.5 m 
 
 6.9 X 10-' 
 
 Figure 2. Reference table on back of rule. 
 
4] 
 
 MDDC - 734 
 
 C) A sample of 0.5 curie strength is allowed to decay for 9.62 half -lives. 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 opposite 0.5 on the li scale one can read the answer 
 6.0 X 10"^ 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 half-lives. 
 
 FISSION PRODUCT ACTIVITIES 
 
 The use of the rule can be extended directly to many of the fission products — namely, to the 
 cases in which the growth is uncomplicated by chain relationships. This is done by defining L 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 I scale, and 
 manipulation proceeds as in the case of (n,y) activations. 
 
 DISCUSSION 
 
 It would be more convenient if the linear t-scales 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. 
 
 ■i 
 
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UNIVERSITY OF FLORIDA 
 
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