A slide rule for activation and decay calculations

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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


































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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" (1-e-et'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 -e-0.693t 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 hali-lile 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 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 21shows that strontium has an
activation cross section of 2.8 x 10-5 cm2 per gram. The end of the nv scale on the slide Iviz. the 10"
mark) is placed opposite 2.8 x 10-6 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 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 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 2.3-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 105; 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-kt 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 [






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Figure 1. Slide rule for activation and decay calculations.
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MDDC 734


Element Half-life H(em' per g
of element)
H* 25 y 5.68
Li 0.88 s < 3.2 x 10-4
C** 25.000 y 7.3 x 10-2
N 8s <4x10-9
O 31 s 1.7 x 10-8
F 12 s 3.0 x 10-
Na 14.8 h 1.0 x 10-2
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 10-3
S 87.1 d 2.1 x 10-
Cl 37 m 2.6 x 10-3
A 110 m 1.88 x 10-2
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 10-5
Sc 85 d 3.0 x 10-'
Ti 72 d 9.5 x 10-s
V 3.9 m 6.0 x 10-
Cr 26.5 d 5.8 x 10-3
Cr 1.3 h 1.6 x 10-6
Mn 2.59 h 1.27 x 10-'
Fe 47 d 1.1 x 10-s
Co 10.7 m 7.5 x 10-s
Co 5.3 y 2.3 x 10-'
Ni 2.6 h 2.0 x 10-4
Cu 12.8 h 2.1 x 10-2
Cu 5 m 5.7 x 10-'
Zn 250 d 2.4 x 10-3
Zn 57 m 1.9 x 10-3
Zn 13.8 h 5.0 x 10-4
Ga 20 m 8.2 x 10-'
Ga 14.1 h 1.13 x 10-2
Ge 40 h 1.3 x 10-4
Ge 11 d 7.9 x 10-
Ge 89 m 1.2 x 10-S
Ge 12 h 4.6 x 10-'
Se 115 d 1.5 x 10-1
Se 19 m 2.0 x 10-
Se 57 m 1.3 x 10-4
Se 30 m 4.3 x 10-5
As 26.8 h 3.7 x 10-2
Br 18 m 3.4 x 10-2
Br 4.4 h 1.16 x 10-2
Br 34 h 8.4 x 10-'
Rb 19.5 d 3.71 x 10-a
Rb 17.5 m 2.6 x 10'
Sr 2.7 h 9.7 x 10-4
Sr 55 d 2.8 x 10-s
Y 60 h 7.5 x 10-'
Zr 63 d 4.8 x 10-4
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 10-4
-lo 14.6 m 1.3 x 10-
Ru 42 d 2.2 x 10-'
Ru 37 h 8.9 x 10-4
Ru 4 h 7.3 x 10-4
Rh 44 s 8.8 x 10-1
Rh 4.2 m 7.5 x 10-2
Pd 13 h 1.8 x 10-2
vd 26 m 4.8 x 10-4
Ag 2.3 m 1.42 x 10-
Ag 22s 2.88 x 10-'

*From Li
*From N Figure 2.


Element Half-life L(cm' per g
of element)
Ag 225 d 6.2 x 10-a
Cd 2.5 d 1. < 10'
Cd 46 d 2.2 x 10"
Cd 3.75 h 5.4 x 10-4
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 10-s
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 10-5
Sn 10d 5 x 10-
Sb 2.8 d 1.9 x 10-2
3b 60 d 5.5 x 10-3
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 10-s
I 25 m 3.2 x 10-2
Cs 3 h 7.3 x 10-s
Cs 1.7 y 1.17 x 10'
Ba 86 m 1.8 x 103
La 40.0 h 3.7 x 10-2
Yr 19 h 4.7 x 10-2
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 10-s
Gd 8.6 d 2 x 10-'
Tb 3.9 h 4.4 x 10-2
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 10-2
Hf 46 d 1.2 x 10-2
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 10-2
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 10-3
Ir 19 h 2.7 x 10-'
Ir 1.5 m 6.5 x 10-3
Ir 70 d 1.32
Pt 18 h 9.3 x 10-
1-t 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 10-5
ri 4.23 m 2.6 x 10-
TI 3.5 y 6.5 x 10-s
ko 3.0 h 7.0 x 10-
Bi 5.0 d 4.3 x 10-s
Th 23 m 2.2 x 10-2
U 23.5 m 6.9 x 10-3


Reference table on back of rule.











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 0 opposite 0.5 on the E scale one can read the answer
6.0 x 10-4 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 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 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.























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