A toxic radioactive substance with a density of 9 milligrams per square centimeter is detected in the ventilating ducts of a nuclear processing building that was used 55 years ago. If the​ half- life of the substance is 20 ​years, what was the density of the substance when it was deposited 55 years​ ago?

Accepted Solution

60.5 milligrams per square centimeter First, determine how many half lives have expired by dividing the time by the half-life. So: 55/20 = 2.75 That means that only 2^(-2.75) = 0.148650889 = 14.8650889% of the original substance remains. So just divide the amount remaining by 0.148650889 to get the original amount. 9 / 0.148650889 = 60.5445419 So originally, there was 60.5 milligrams per square centimeter 55 years ago.