Radioactive decay: The half-life of a radioactive substance is the time H that it takes for half of the substance to change form through radioactive decay. This number does not depend on the amount...

Radioactive decay: The half-life of a radioactive substance is the time H that it takes for half of the substance to change form through radioactive decay. This number does not depend on the amount with which you start. For example, carbon 14 is known to have a half-life of H = 5770 years. Thus if you begin with 1 gram of carbon 14, then 5770 years later you will have 1 2 gram of carbon 14. And if you begin with 30 grams of carbon 14, then after 5770 years there will be 15 grams left. In general, radioactive substances decay according to the formula

where H is the half-life, t is the elapsed time, A0 is the amount you start with (the amount when t = 0), and A is the amount left at time t. a. Uranium 228 has a half-life H of 9.3 minutes. Thus the decay function for this isotope of uranium is

where t is measured in minutes. Suppose we start with 8 grams of uranium 228. i. How much uranium 228 is left after 2 minutes? ii. How long will you have to wait until there are only 3 grams left? b. Uranium 235 is the isotope of uranium that can be used to make nuclear bombs. It has a halflife of 713 million years. Suppose we start with 5 grams of uranium 235. i. How much uranium 235 is left after 200 million years? ii. How long will you have to wait until there are only 3 grams left?