T Medical Ruthenium-106 is used to treat melanoma in the...

t Medical Ruthenium-106 is used to treat melanoma in the eye. This isotope decays by $\beta^{-}$ emission with a half-life of $373.59$ days. One source of the isotope is reprocessed nuclear reactor fuel. (a) How many protons and neutrons does the ${ }^{106}$ Ru nucleus contain? (b) Could we expect to find significant amounts of 106 Ru in ore mined from the ground? Why or why not? (c) Write the decay equation for ${ }^{106} \mathrm{Ru}$ and identify the daughter nucleus. (d) How many years after ${ }^{106} \mathrm{Ru}$ is implanted in the eye does it take for its decay rate to be reduced by $75 \%$ ? Example $27-5$

t Medical Ruthenium-106 is used to treat melanoma in the eye. This
isotope decays by $\beta^{-}$ emission with a half-life of $373.59$ days. One source of the isotope is reprocessed nuclear reactor fuel. (a) How many protons and neutrons does the ${ }^{106}$ Ru nucleus contain? (b) Could we expect to find significant amounts of 106 Ru in ore mined from the ground? Why or why not?
(c) Write the decay equation for ${ }^{106} \mathrm{Ru}$ and identify the daughter nucleus. (d) How many years after ${ }^{106} \mathrm{Ru}$ is implanted in the eye does it take for its decay rate to be reduced by $75 \%$ ? Example $27-5$

Key Concepts

Nucleon Composition

This concept involves understanding that a nucleus is composed of protons and neutrons. The number of protons is given by the atomic number, while the total number of nucleons (protons plus neutrons) is given by the mass number. Determining these numbers is essential in nuclear physics to understand the structure and identity of an isotope.

Beta-Minus Decay

Beta-minus decay is a form of radioactive decay in which a neutron in the nucleus converts into a proton, emitting an electron (called a beta particle) and an antineutrino. This process increases the atomic number by one while leaving the mass number unchanged, altering the element into its daughter nucleus.

Half-Life

Half-life is the time required for half of the radioactive nuclei in a sample to decay. This parameter is crucial in describing the rate of decay and is used in calculations involving the exponential decay of radioactivity over time, impacting both safety considerations and treatment durations in medical applications.

Radioactive Decay Equations

Decay equations are symbolic representations of the transformation processes in radioactive decay. They show the parent nucleus, the emitted particles (such as beta particles in beta decay), and the resulting daughter nucleus, preserving conservation laws like charge and mass.

Exponential Decay and Decay Rate

Exponential decay describes how the quantity of a radioactive substance decreases over time according to its decay constant, derived from the half-life. This concept is used to calculate the remaining activity of the substance after a given time period, which is critical for determining dosages and exposure levels in medical treatments.

Isotope Production and Natural Abundance

This concept distinguishes between isotopes produced naturally and those synthesized or reprocessed in nuclear reactors. Understanding this helps clarify why certain isotopes, particularly those with short half-lives or those produced as byproducts of nuclear reactors, are not commonly found in nature but must be manufactured for specific applications like medical treatments.

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