MATHEMATICAL AIDS IN THE UNDERSTANDING OF THE BIOLOGICAL HAZARDS OF RESIDUAL RADIATION By Lt. Col. James T. Brennan, MC Walter Reed Army Medical Center Tn attempting to cope with radiation hazard problems, many a biologist has, like the writer, found that a meager working knowledge of mathematics places a frustrating upper limit on one’s insight into many important situations. The mathematical treatmont of the idealized contaminated plane surface is an example of this difficulty, A reference which is commonly cited in this connection is “Effects of Atomic Weapons,” page 432 ff. The treatment given therein is by and for mathematicians, and as such is beyond most biologists and nearly all physicians. In 1951 C.S. Maupin [1] developed \ \ an expénded version of the analysis which appears useful in that it might significantly / inercase the number of biologists who can ar -7 follow the derivation, This expanded version has not heretofore been published and is shown below (see fig. 1). Consider a point P at a height 2 above a uniformly contaminated circular disk of radius a. Let the concentration of radioactivity be such that there are k photons, each of m (Mev) energy emitted (equally in all directions) per em? of surface. Then the number of Mev emitted from the infinitesimal area rdrdé@ is kmrdrdé. The number of Mev reaching point P per unit time from this small area will be dene “VFhidrag det where » is the total narrow beam absorption coefficient in air for photons of energy m. From this point on, no attempt is made to follow the fate of scattered photons. Ultimately this causes the estimate of dose at point P to be / ‘ee me cee Friawre 1. low (30 percent low when 4=6 meters, 10 percent low when h==1 meter). But to return to the analysis, the energy flow reaching P from the entire disk will be __km 7 ft reneee Soe oe Integrating with respect to 8, 25, rh Conversion to dose in roentgens at point P may be made at any time by means of simple assumptions such as that one roentgen is delivered by a flux of 10° photons/em?, 127