COMPUTATION PROCEDURES AND EXAMPLES
To determine the activity induced for a given set of irradiation and decay conditions, set the overlay on the appropriate chart so that the S-curve has a positive slope and the top of the centerline coincides with the ordinate of the isotope considered. Read the activity after the chosen irradiation time at the ordinate of the S-curve corresponding to the time t,. Next, move the overlay down vertically until the top of CL is at this activity level. Read the activity after the decay time Finally, t d at the ordinate of the D-curve corresponding to t d . correct for efficiency, sample weight, and flux, using the logarithmic scale on the edge of the overlay as a slide rule. This now yields the count rate of the sample after the chosen irradiation and decay times. Multiplication by the counting factor, if required, is performed by using the C-curve and the time-line t,. The induced or measured activity in a given sample for any set of experimental irradiation conditions can thus be easily calculated, using only the chart and the overlay. The amount of an element that gives rise to a measured activity, or any other unknown in the activity equation, can also be determined. As mentioned before, the saturation and decay curves are also useful in determining optimal irradiation and decay times in cases where additional or competing reactions may obscure the activity of interest. For this purpose, place the overlay so that the saturation curve has a negative slope and compare the saturation and decay factors for competing reactions for different irradiation and decay times by setting the top of the centerline at the corresponding points on the chart. An iterative procedure will generally yield a quick solution that meets the requirements for absolute and relative activities. The following examples illustrate the use of the charts and the overlay. Example 1. Calculate the activities of copper-64 (T,/z = 12.9 hours) and copper-66 (TlI2 = 5.1 minutes) induced in a sample of 0.5 mg of natural copper, irradiated in a flux of 1012 n/cm2 second for 3 minutes followed by a decay time of 10 minutes. What is the additional decay time required to reduce the copper-66 activity to 1 % of the copper-64 activity? First find the copper-66 point on the thermal-neutron activation chart, looking at the time line of 5.1 minutes. The saturated activity is 6.7 X 106. Use the overlay so that the slope of the saturation curve is positive. Set the overlay on the chart so that the top of the centerline is at this point. Read the induced activity at the intersection of the saturation curve and the time line of 3 minutes. It is 2.3 X 106. Next, set the top of the centerline on this level, keeping the center1 ne at the 5.1-minute time line. Read the activity after the decay time at the intersection of the decay curve and the ti.ne line of 10 minutes. It is 5.8 X lo5. Set the top of the vertical scale of the overlay at this level and multiply the activity of the sample by 0.5. The copper-66 activity in disintegrations per second is thus 2.9 X lo5. The copper-64 activity is determined in the same way after locating copper-64 at the half-life line of 12.9 hours = 774 minutes. It is 4.0 X 104 disintegrations per second. To find the additional decay time required to decrease the Asscu to ljl00 AB'^^, first assume that the latter remains constant. Set the overlay so that the centerline coincides
602
ANALYTICAL CHEMISTRY
with the time line of 5.1 minutes and the second highest tickmark is at AWC,= 2.9 X lo6. Read the decay time on the decay curve at the activity level Asrcu = 4.0 X lo4. It is 50 minutes for which the assumption that Asdcu remains constant is justified and no correction is required. Example 2. Compare for different half-lives the activities induced by a reactor pulse of 250 MW X 13 msecond with the saturation activities reached at a constant power level of 100 kW. What are the counting factors corresponding to 3seconds counting time for the same half-lives ? Position the overlay so that the slope of the saturation curve is negative. For convenience, set the asymptotic line of the overlay at the activity level of 2.5 X 10s (corresponding to 2.5 X 10s W = 250 MW) and the centerline at 13, assuming that the time scale is in mseconds. Read the relative activities compared with the activity level of lo5 (corresponding to 105 W = 100 kW) at the intersections of different time lines and the saturation curve. To get the counting factors, set the centerline at 3 X l o 3(corresponding to 3 seconds) and the top of the curve at a decade line. Read the counting factors at the intersections of different time lines and the counting curve. The results can be directly read:
Tli2(seconds)
0.01
0.1
1 . 0 10
22
60
220
Apu1a6(250MW)1500 210 22 2 . 2 1 . 0 0.38 0.10 A d 1 0 0 kW) Counting factor 0.0048 0.048 0.42 0.90 0.95 0.98 1 .O ACKNOWLEDGMENTS
The cooperation and support of S. G . Prussin and R. W. Wallace of Lawrence Radiation Laboratory as well as encouragement by Pekka Jauho of Technical University of Helsinki are gratefully acknowledged. RECEIVED for review August 2, 1967. Accepted December 13, 1967. This work was done under the auspices of the U. S. Atomic Energy Commission.
Correction Quantitative Infrared Multicomponent Determination of Minerals Occurring in Coal In this article by Patricia A. Estep, John J. Kovach, and Clarence Karr, Jr. [ANAL.CHEM.,40, 358 (1968)l the frequency of the analytical absorption band for pyrite should read 41 1 cm-l, instead of 406 cm-', in Tables I and 11, and Figure 2. The correct value of 41 1 cm-l was given in reference (2) by Karr, Estep, and Kovach [Chern. Znd. (London), 9, 356 (196711. Also, the value for marcasite iq Table I should read 412 cm-' instead of 407 cm-'.
