The half-life of iodine- \(-131\) is 8.02 days. What percentage of an iodine-131 sample will remain after 40.2 days?

Understanding radioactive decay is crucial when studying nuclear chemistry and handling radioactive materials. Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation, such as alpha particles, beta particles, or gamma rays. Each radioactive isotope has a characteristic decay that occurs at a fixed rate, known as its 'half-life'.

The half-life represents the time required for half of the radioactive atoms in a sample to decay. For instance, if you start with 100% of a radioactive isotope, after one half-life, only 50% remains, after two half-lives, 25% remains, and so on. This predictable pattern allows scientists and engineers to calculate the amount of a radioactive substance that will remain after any given period. For students tackling such problems, knowing the half-life enables them to determine the future composition of the sample.

Exponential decay is the mathematical model that describes the process of reducing an amount by a consistent percentage rate over a period of time. This concept is not only applied in nuclear chemistry but also spans across disciplines like finance, biology, and physics.

The general formula for exponential decay is expressed as \( N = N_0 \times (1/2)^{t/t_{1/2}} \), where:\

• \(N\) is the final amount remaining after time \(t\)
• \(N_0\) is the initial amount
• \(t\) is the elapsed time
• \(t_{1/2}\) is the half-life of the substance

Understanding this formula is vital for students to solve problems related to half-life calculations. By substituting the known values into the equation, it allows for the computation of how much substance will remain after a specific duration. The process displays an exponential nature because the quantity decreases at a rate proportional to its current value, leading to a rapid decline initially that slows down over time.

Nuclear chemistry is a field of chemistry focusing on the chemical processes associated with nuclear reactions and radioactive substances. It involves studying the behavior and characteristics of atomic nuclei, the changes they undergo during reactions, and their applications.

Central to nuclear chemistry are reactions such as fusion, fission, and radioactive decay. Applications are diverse, ranging from medical treatments using radioisotopes to the generation of electrical power through nuclear reactors and understanding the mechanisms of nuclear weapons. A deep comprehension of nuclear chemistry is essential for responsible handling and disposal of nuclear materials, as well as for safety in nuclear medicine.

In the context of half-life calculations, nuclear chemistry provides the framework to predict radioactive isotopes' behavior and to ensure their safe use in various industries. For students exploring this field, mastering half-life calculations is a fundamental skill that aids in understanding how radioactive materials change over time.