Inverse Square Law :Inverse Square Law By: Nicole Pedrera Manuel Diaz Amy Garciga Yolanda Rodriguez Alain Castellanos Sean Carthy


What is Inverse Square Law? :What is Inverse Square Law? The radiation exposure from a radioactive point source is governed by a mathematical relationship called the inverse square law. This states that the radiation exposure or intensity (i) at a distance (d) from a radioactive source is proportional to the inverse square of the distance.


Formulas :Formulas I1= (D2)² OR I1(D1)² = I2(D2)² I2= (D1)² I1= Original intensity I2= New intensity D1= Original distance D2 =New distance


How to solve for intensity :How to solve for intensity I1 = (D2)² I2 = (D1)² Square distance Cross multiply Isolate & solve for I


Example :Example A radioactive source produces 160mrem/hr at 1 meter. What is the exposure rate at 3 meters? 160mrem/hr = (3m)²  160mrem/hr = (9m) ? (1m)² ? (1m) 160mrem/hr / 9m = Answer :18mrem/hr @ 3 meters


How to solve for intensity :How to solve for intensity I1 (D1)² = I1 (D1)² First square your distances Then multiply your I1 by (D1)² Then divide by (D2)² = I2


Example :Example A radioactive source produces 160mrem/hr at 1 meter. What is the exposure rate at 3 meters? I1 (D1)² = I1 (D1)² 160mrem/hr (1m)² = ? (3m)² 160mrem/hr (1m) = ? (9m) 160mrem/hr = ? 9m = Answer : 18mrem/hr @ 3 meters


How to solve for distance :How to solve for distance I1 = (D2)² I2 = (D1)² Square distance Cross multiply Isolate & solve for D


Slide 9:A technologist is standing 6 inches from a radioactive source, which results in an exposure rate of 10mrem/hr. What distance must the technician move to decrease the exposure to a back round level of 0.05mre/hr? 10mrem/hr = __(?)²___  10mrem/hr = __(?)²__ 0.05mrem/hr (6 inches)² 0.05mrem/hr 36inches 360mrem/hr = 7200^½ = Answer 85 inches 0.05mrem/hr **Note : In order to remove the exponent from “?”, you must square root (^½) the solution.


How to solve for distance :How to solve for distance I1 (D1)² = I2 (D2)² First square your distances Then multiply your I1 by (D1)² Then divide by (I2)= D2


Slide 11:A technologist is standing 6 inches from a radioactive source, which results in an exposure rate of 10mrem/hr. What distance must the technician move to decrease the exposure to a back round level of 0.05mre/hr? 10mrem/hr (6in)² = 0.05mrem/hr (?in)² 10mrem/hr (36in) = 0.05mrem/hr (?in)² 360mrem/hr / 0.05mrem/hr = 7200^½ = Answer : 84 inches **Note : In order to remove the exponent from “?”, you must square root (^½) the solution.


References :References Christian, Paul E., Donald R. Bernier, and James K. Langan, eds. Nuclear Medicine and PET: Technology and Techniques. 5th ed. St. Louis, Missouri: Mosby, Inc., 2004. 1-574.