Chapter 1.1, Problem 7E

In Exercises 6—10, we consider the phenomenon of radioactive decay which, from experimentation, we know behaves according to the law:
The rate at which a quantity of a radioactive isotope decays is proportional to the amount of the isotope present. The proportionality constant depends only on which radioactive isotope is used.

7. The half-life of a radioactive isotope is the amount of time it takes for a quantity of radioactive material to decay to one-half of its original amount.
(a) The half-life of Carbon 14 (C-14) is 5230 years. Determine the decay-rate pa-rameter $\lambda$ for C-14.
(b) The half-life of Iodine 131 (I-131) is 8 days. Determine the decay-rate param-eter for I-131.
(c) What are the units of the decay-rate parameters in parts (a) and (b)?
(d) To determine the half-life of an isotope, we could start with atoms of the isotope and measure the amount of time it takes 500 of them to decay, or we could start with 10,000 atoms of the isotope and measure the amount of time it takes 5000 of them to decay. Will we get the same answer? Why?