I
LIANG-TSENG FAN Department of Chemical Engineering, Kansas State University, Manhattan, Kan.
Nomogram for Correcting Measured Radioactivity to Datum Time A nomogram of exponential decay equation, one of the most frequently
WHEN
A radioisotope decays fairly rapidly during the time required to carry out a n investigation, it is necessary to convert the measured activity of the isotope to datum time ( t = 0) by using the decay law of the radioactivity, Z = ( 3 ) . This nomogram, specifically constructed for iron-55 isotope, is used to save considerable time and labor especially when the number of these calculations are required ( 7 , 2 ) . T h e use of the nomogram for iron-55 ( 4 ) is illustrated for the case where Z is 900 counts per 5 minutes and t is 400 days. 13 is 1165 counts per 5 minutes. Application of this nomogram is not restricted by the level of activity of the isotope measured. T h e values used for I a n a Zo, which are the present and the original activity, respectively, may be expressed in any system of unit as long as the units are the same for both I and Zo-e.g., 1 count per second, 100 counts per 5 minutes, and 1 microcurie, etc. Another application of this nomogram is to estimate any fraction ( l l n ) of the life of the isotope by connecting unity or its equivalent on the I scale with the value of n or its equivalent on the lo scale and extending the straight line to the t scale. T h e value obtained o n the t scale gives the 1/1.5th life of Fe-55 is 630 days. To extend the application range of the nomogram, correction lines for other values of X are provided in a form of network. Hence, 1/1.5th life of a n isotope with X = 0.0005 is 810 days from the nomogram as well as from computation. I n general, the comparison between nomogram and actual calculation is good, running about 1% deviation. If we consider the t (for iron-55)scale as a reference scale and use any consistent units for each t-scale and Xscale, as seconds for t-scales and l,/second for A-scale or years for t-scales and l/year for bscale, the nomogram may be extended to any other isotopes decaying much faster or much slower than Fe-55 and should be generally useful in radioisotope application such as chemical industry.
710
employed
equations at present,
I t may also be adapted for computation of the rates of the first order chemical reactions, distribution of free path of gas molecules, and absorption of light because they also obey the exponential decay law.
literature Cited (1) Baker, W. W., Simons, H. P., “Simpli-
fied Procedure for Nomograph Construc-
I
Decay
Io
is
illustrated
tion,” pp. 1-16, West Virginia University, Morgantown, 1952* (2) Davis, D. S., “Nomography and Empirical Eauations.” DD. 137-67. Reinhold. New Ybrk, 1955. (3) Friedlander, G., Kennedy, J. W., “Nuclear and Radiochemistry,” p. 127, Wiley, New York, 1955. (4) Ibid., p. 149. RECEIVED for review September 25, 1958 ACCEPTED February 13, 1959 constant,
A,-!-. d OY
t
0 0 L
a
VI
0
E
VI
O
-
r
.-> .-
U
.-0
0 O
K
This nomogram is used for correcting the measured radioactivity to datum time. Any consistent unit may be used for I and 10
INDUSTRIAL AND ENGINEERING CHEMISTRY
