Chapter 12 



Tagged Water Masses for Studying the Oceans 



131 



APPENDIX A 



In practice, many factors tend to limit the 

 effectiveness of an under sea gamma detector, 

 but the random fluctuation of a feeble radiation 

 may alone prevent its recognition in the pres- 

 ence of a background of similar magnitude. The 

 lowest detectable concentration, limited only by 

 statistical considerations, may be expressed in 

 terms of the strength of the background, the 

 time permitted for measurement, and the meas- 

 uring efficiency of the instrument. 



Let the sea water be contaminated with a con- 

 centration of radioactivity N curies/ml, and let 

 this activity cause m counts/sec to be indicated 

 by the instrument, and let the average back- 

 ground be b counts/sec. The relative accuracy, 

 n, of a single measurement made during t sec- 

 onds will depend upon signal strength and 

 background strength; if the fluctuations are 

 purely random, the error, 95 per cent of the 

 time will be equal to, or less than. 



mt 



2V 



O-jlf — (Tb 



2yjmt-^ht 



mt 



mt 



and solving for the net signal gives, 



mt — 



2-\-2^\-^nht 



A.l 



A.2 



Now, the counting efficiency of the instru- 

 ment logically should be derived from the ratio 

 of counts recorded to the photons striking the 

 instrument. This ratio would be impossible to 

 evaluate, but it is approximated when the instru- 

 ment is small, and easily penetrated by. 



;;?/ 



3.7xlO"Nz// 



A.3 



that is by the ratio of the net counts recorded to 

 the photons emitted in a volume of liquid, v, 

 equal to that displaced by the detector. Solv- 

 ing this equation for concentration, 



mt 



N= 



iJxlO^'^t^et 



A.4 



curies/ml, and substituting here the value for 

 net count, mt, obtained in equation (2) when 

 the background rate is b, and accuracy is, n, the 

 limiting concentration can be expressed, 



N = 



2 + 2\/l + }i-bt 

 b.lxlQ^^n-vet 



A.5 



curies/ml, wherein b expresses the background 

 rate actually indicated when the instrument is 



surrounded by clean sea water. If no other back- 

 ground exists except that coming from a sur- 

 rounding solution having specific activity B, and 

 if the instrument counts this activity with the 

 same efficiency, e, than the limiting detectable 

 concentration becomes, in curies/ml, 



N= 



2 + 2\/l+Bn-vet 

 ^.1 XlO^'^n-vet 



A.6 



Numerical examples applying to an actual un- 

 dersea instrument 



The sensitive portion of the 1955 model of 

 the Scripps Institution of Oceanography's 

 Geiger instrument has a volume of about 1,000 

 ml. The ratio e, applying to hard gamma rays, 

 was measured directly by submerging the in- 

 strument in a tank containing potassium solu- 

 tion of known concentration, and was found to 

 be approximately 0.03. 



If by "detection" is meant the measurement 

 of the concentration with an error of not more 

 than 50 per cent, then, n=:0.5. 



Formulas (5) and (6) may now be applied 

 to three characteristic background circum- 

 stances: 



Case 1: Here no other background is evi- 

 dent except that caused by a solution having 

 specific activity 6=1.2x10'^ gammas/sec/ml 

 such as comes from the natural potassium in 

 normal sea water. From (6), the limiting de- 

 tectable concentration, 



C,: 



2 + 2V 1+0.009^ 

 iJt 



A.7 



gammas/sec/ml, and when t becomes very 

 large this approaches, 



C^^—^ A.8 



Case 2: In deep water cosmic rays may be 

 neglected, and the S. I. O. probe is likely to 

 indicate a total background of about 15 CPM, 

 or b = 0.25 counts/sec, therefore, the concentra- 

 tion just delectable is. 



2 + 2Vl-f 0.063/ 



C2 — . — ■ 



A.9 



gammas/sec/ml, which approaches as t in- 

 creases to a large value, 



0.067 

 Co= — = A.IO 



Case 3: In shallow water where cosmic rays 

 are unattenuated, the background on the S. I. O. 

 probe amounts to about 60 CPM, or b=1.0 



