In the 1950 s, radioactive material was spread over the land from aboveground nuclear tests. A woman drinks some contaminated milk and ingests \(0.0500 \mathrm{~g}\) of \({ }^{90} \mathrm{Sr}\), which is taken up by bones and teeth and not eliminated. (a) How much \({ }^{90} \mathrm{Sr}\left(t_{1 / 2}=\right.\) \(29 \mathrm{yr}\) ) is present in her body after \(10 \mathrm{yr} ?\) (b) How long will it take for \(99.9 \%\) of the \({ }^{90} \mathrm{Sr}\) that she ingested to decay?

The half-life is a core concept in nuclear chemistry and refers to the time it takes for half of a given amount of a radioactive substance to decay. This property is crucial because it allows us to predict how a radioactive isotope will behave over time. For example, if a substance has a half-life of 29 years, like \({}^{90}\text{Sr}\), after 29 years, only half of the initial quantity remains. After another 29 years, half of the remaining substance will decay, and so on. The half-life equation is given by:
\( N(t) = N_0 \times \frac{1}{2}^{\frac{t}{t_{1/2}}} \)
Understanding the half-life helps us calculate how much of the substance remains after a certain period. For instance, if someone consumes 0.05 grams of \({}^{90}\text{Sr}\), which has a half-life of 29 years, after 10 years, the amount left can be calculated as:
\( N(10) = 0.0500 \times \frac{1}{2}^{\frac{10}{29}} \)
Which simplifies to about 0.0396 grams.

Radioactive isotopes, also known as radioisotopes, are atoms with an unstable nucleus that lose energy by emitting radiation. This process is known as radioactive decay. Common types of radiation emitted include alpha particles, beta particles, and gamma rays. Radioisotopes are used in a variety of fields including medicine, archaeology, and industry.
In the context of the given exercise, \({}^{90}\text{Sr}\) is a radioactive isotope with a half-life of 29 years. When someone ingests a radioactive isotope, it decays over time. In our example, after 10 years, a portion of the \({}^{90}\text{Sr}\) will have decayed. This decay can be calculated using its half-life.
Different radioisotopes have different half-lives, which can range from fractions of a second to millions of years. This variability allows radioisotopes to be uniquely suited to specific applications. For example:

• Carbon-14 is used in radiocarbon dating to determine the age of archaeological finds.
• Cobalt-60 is used in cancer treatment and sterilization of medical equipment.

Nuclear chemistry is the branch of chemistry that deals with the study of radioactive substances, nuclear processes, and their applications. This field examines how nuclear reactions differ from chemical reactions and involves understanding the behavior of isotopes, both stable and radioactive.
The exercise on \({}^{90}\text{Sr}\) is a typical example of how nuclear chemistry principles apply to real-life scenarios. The equations and concepts used to determine the remaining amount of \({}^{90}\text{Sr}\) or to predict the time taken for a certain amount to decay are part of nuclear chemistry.
Understanding nuclear chemistry is essential for diverse applications, including:

• Nuclear power generation: The controlled fission of radioactive isotopes in reactors provides a significant source of energy.
• Medical diagnostics and treatment: Radioisotopes are used in imaging and cancer treatments.
• Environmental science: Tracking the movement of radioactive materials in the environment helps in managing pollution and contamination.

Nuclear chemistry allows us to harness the power of atomic nuclei for various beneficial uses while also understanding the risks and safety measures needed to handle radioactive materials.