CHEMISTRY · Multi-part · US High School · Chemistry · Atomic Structure & Nuclear · Atomic Structure & Nuclear
Problem
Two radioactive isotopes, X and Y, are under consideration for use as tracers in an underground water–flow study.
• Isotope X has a measured decay constant of 4.1×10−7s−1.
• Isotope Y has a measured half-life of 18days.
Assume both isotopes are initially prepared with the same number of nuclei.
(a) Identify which isotope, X or Y, is the more stable nucleus. Justify your answer qualitatively without performing a numerical calculation.
(b) Describe in words the mathematical relationship between the decay constant and the half-life of a nucleus, and explain how this relationship supports your answer to part (a).
(c) Without calculating precise values, sketch on a set of qualitative axes (activity versus time) the expected decay curves for isotopes X and Y. Clearly indicate which curve corresponds to each isotope and describe two distinguishing features of their shapes.