Chapter 12, Problem 17ICA

The total quantity (mass) of a radioactive substance decreases (decays) with time as

$m=m_0{e}^{\frac{t}{r}}$

^Where

t = time [days]

r = time constant

m₀ = initial mass (at t=0)

m = mass at time t [mg]

A few milligrams each of three different isotopes of uranium were assayed for isotopic composition over a period of several days to determine the decay rate of each. The data were graphed and a mathematical model derived to describe the decay of each isotope.

1. a. What are the units of T if time is measured in days?
2. b. What is the initial amount of each isotope at t = 0?
3. c. When will 1 milligram of the original isotope remain in each sample?
4. d. Four isotopes of uranium are shown in the following table with their half-lives. Which isotope most likely matches each of the three samples? Note that one isotope does not have a match on the graph.

Isotope	Half-life [days]
230U	20.8
231U	4.2
237U	6.75
240U	0.59