This problem has always bugged me, and the only answers I've been given were on the lines of "meh". What I don't understand is that if we are given 1 gram of a radioactive substance with a half life of n years, why is it that after n years, the substance is reduced to 0.5 grams of radioactive material; but after another n years, the substance has now reduced 0.25g. Does the substance know how much radioactive material is in its vicinity? What is actually happening at the atomic level in terms of the amount of radioactive atoms that become inactive? I doubt it has anything to do with probabilities of whether a certain atom will decay or not. So what is actually going on here?