A 53.8-mg sample of sodium perchlorate contains radioactive chlorine-36 (whose atomic mass is 36.0 amu). If 29.6% of the chlorine atoms in the sample are chlorine-36 and the remainder are naturally occurring nonradioactive chlorine atoms, how many disintegrations per second are produced by this sample? The half-life of chlorine-36 is 3.0 * 10⁵ yr.

Radioactive decay is the process by which unstable atomic nuclei lose energy by emitting radiation. This decay occurs at a predictable rate characterized by the half-life, which is the time required for half of the radioactive atoms in a sample to decay. Understanding this concept is crucial for calculating the activity of a radioactive sample, as it directly relates to the number of disintegrations per second.

The half-life of a radioactive isotope is the time it takes for half of the radioactive atoms in a sample to decay. For chlorine-36, the half-life is 3.0 × 10^5 years, meaning that after this period, only half of the original amount of chlorine-36 will remain. This concept is essential for determining the remaining quantity of a radioactive substance over time and calculating its activity.

The activity of a radioactive sample, measured in disintegrations per second (Becquerels), indicates the rate at which decay events occur. It can be calculated using the formula A = λN, where A is the activity, λ is the decay constant, and N is the number of radioactive atoms present. Understanding how to calculate activity is vital for determining the safety and implications of handling radioactive materials.