OpenStax College Physics for AP® Courses, Chapter 32, Problem 2 (Test Prep for AP® Courses)

This is College Physics Answers with Shaun Dychko. A 90 kilogram person is exposed to 15 millirems of alpha particles and we are meant to calculate the dosage in rads and then also the amount of energy absorbed by the person. So we will write down the stuff that we know: mass is 90 kilograms, dose equivalent is 50 millirems which we convert into sieverts by multiplying 50 times 10 to the minus 3 rems by 1 sievert for every 100 rems and then the RBE—relative biological effectiveness—is 16 so dose equivalent in rems is dose absorbed multiplied by relative biological effectiveness so we can divide both sides by RBE to calculate the dose absorbed. So the dose absorbed then is the dose equivalent divided by RBE so that's 50 times 10 to the minus 5 sieverts divided by 16, which is 3.125 times 10 to the minus 5 grays but the question asks for our answer in rads so we multiply by 100 rads for every gray and that's 3.13 times 10 to the minus 3 rads. And then we want to know the energy absorbed. So the dose absorbed is energy absorbed divided by mass. So we can multiply both sides by m then to solve for energy absorbed. So we multiply 90 kilograms by the dose absorbed in grays— 3.125 times 10 to the minus 5 grays— and that gives an energy absorbed of 2.81 millijoules.