Question

(c) Compare your answers to (a) and (b), and explain this behavior. 6. The lifetimes of radioactive nuclei are independent and exponentially distributed. The half-life is given by t1/2 = ln2/λ, 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 30 days? (b) How long do you have to wait before 99.99% of a sample of Iodine-131 has decayed? (c) Uranium-238 is radioactive, with a half-life of 4.468×109 years. Suppose you have an 0.1 mg sample of Uranium-238. Let X be the number of nuclei that decay in one second in your sample; calculate E[X]. What is P(X ≤ 1)? 1

Answer 1