A nuclear accident produces equal numbers of two fission products, (half-life 28.8…

CHEMISTRY · Multi-part · US High School · Chemistry · Atomic Structure & Nuclear · Atomic Structure & Nuclear

Problem

A nuclear accident produces equal numbers of two fission products,

^{90}\text{Sr}

(half-life 28.8\,y) and

^{137}\text{Cs}

(half-life 30.2\,y). Both nuclides pose long-term radiological hazards. Assume no additional production or removal of either nuclide after the initial release. (a) Calculate the fraction of the original

^{90}\text{Sr}

nuclei remaining after 100\,y. (b) Calculate the fraction of the original

^{137}\text{Cs}

nuclei remaining after 100\,y and determine the ratio

\bigl(^{137}\text{Cs}\,\text{remaining}\bigr)\,/\bigl(^{90}\text{Sr}\,\text{remaining}\bigr)

at that time. (c) Determine the time at which the quantity of

^{90}\text{Sr}

has decreased to 25\% of its initial value while more than 40\% of the

^{137}\text{Cs}

remains. Show your reasoning clearly. (d) Explain how the difference in half-lives calculated above influences strategies for the long-term storage and monitoring of nuclear waste containing these two isotopes.

Related theory

Chemical Kinetics

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