A research laboratory monitors the therapeutic radioisotope iodine-131 ( ) used for…
CHEMISTRY · Multi-part · US High School · Chemistry · Atomic Structure & Nuclear · Atomic Structure & Nuclear
Problem
A research laboratory monitors the therapeutic radioisotope iodine-131 (131I) used for thyroid treatments. Immediately after production, the activity of the sample is measured to be 4.80 mCi. The laboratory records the activity at regular time intervals and obtains the following data:
Time after production (days): 0, 2, 4, 6, 8
Measured activity (mCi): 4.80, 3.54, 2.61, 1.92, 1.41
Assume no material is lost except by nuclear decay.
(a) Describe the mathematical transformation you would apply to the activity–time data to test whether the decay of 131I follows first-order kinetics. Explain why this transformation is appropriate.
(b) After making the transformation described in part (a), the data yield a straight line. Interpret the slope of this line in terms of a physical parameter that characterizes the decay process.
(c) Without performing any numerical calculation, explain qualitatively why the half-life of a first-order process remains constant throughout the decay.
(d) Suppose a second researcher proposes that the decay might instead be second order. Cite one specific mathematical or graphical feature of the data that contradicts that proposal.