The lifetimes of radioactive nuclei are independent and exponentially distributed. The half-life is given by t1/2 = ln 2/, where t1/2 is the time such that the expected fraction of atoms remaining is 1/2. (a) Iodine-131 is radioactive, with a half-life of 8.02 days. What is the probability that a single atom of Iodine-131 is still un-decayed after 20 days? (b) How long do you have to wait before 99.99% of a sample of Iodine-131 has decayed? (c) Now calculate the probability that a single iodine nucleus will decay during a 1-second interval. Suppose we have a sample containing an unknown amount of radioactive iodine. We use a scintillation counter to determine that the mean number of decays per second is 5.0. How many radioactive iodine nuclei are there in the sample?