Strontium-90 has a half-life of 28 years. If a \(1.00\)-mg sample was stored for 112 years, what mass of Sr-90 would remain?

The concept of half-life is crucial when studying radioactive substances. It is the time required for half of the atoms in a radioactive sample to decay. For instance, if you start with 1 mg of a substance, you will have 0.5 mg left after one half-life. This decay process continues, and after a second half-life, you’ll only have 0.25 mg, and so on. In the case of Strontium-90, its half-life is 28 years. Therefore, every 28 years, the amount of Strontium-90 will reduce to half of its previous mass. By understanding the half-life, you can predict how much of a radioactive substance will remain after a certain period.
Knowing this is important in fields such as nuclear medicine, archaeology, and environmental science.

Strontium-90 (Sr-90) is a radioactive isotope that is a byproduct of nuclear reactors and weapon tests. It has a half-life of 28 years, meaning that every 28 years, half of its quantity decays. It emits beta particles during its decay process. Because of its similar chemical properties to calcium, Strontium-90 can be incorporated into bones and teeth, posing significant health risks, including cancer.
Understanding how Sr-90 decays over time helps in managing its presence in the environment and assessing the potential risks to human health. For instance, if you start with 1 mg of Sr-90, after 112 years—which is four half-lives—you will be left with 0.0625 mg.

Radioactive decay is the process by which an unstable atomic nucleus loses energy by radiation. This can occur through various modes, such as alpha decay, beta decay, or gamma decay. Each mode involves the emission of a different type of particle or radiation. Sr-90 undergoes beta decay, where a beta particle (an electron or a positron) is emitted.
The decay process is crucial in nuclear physics and has practical applications in medical treatments, radiometric dating, and nuclear energy. In the exercise example, Sr-90’s decay through beta emission drives the calculation of the remaining mass after a set period. Over 112 years, the Sr-90 mass diminishes in successive steps: first to 0.5 mg, then to 0.25 mg, subsequently to 0.125 mg, and finally to 0.0625 mg.

Radioactive substances contain unstable nuclei that release energy by emitting radiation. These substances can be natural or man-made. Their applications range from medical uses—such as in cancer treatment with radioactive isotopes—to energy production in nuclear reactors. Understanding the properties and behaviors of radioactive substances, like half-life and decay processes, is essential for handling them safely.
The exercise on Sr-90 exemplifies how one calculates the remaining mass of a radioactive substance over time. By knowing its half-life and the elapsed time, you can determine the residual quantity. This helps in assessing safety, effectiveness, and environmental impact. Always remember, handling and managing radioactive substances require strict safety protocols to protect human health and the environment.