The accompanying graph illustrates the decay of ⁸⁸₄₂Mo, which decays via positron emission. (c) What fraction of the original sample of ⁸⁸₄₂Mo remains after 12 min? [Section 21.4]

Key Concepts

Radioactive Decay

Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation. This can occur in various forms, including alpha, beta, and positron emissions. The decay of isotopes, such as 88Mo, follows a predictable pattern characterized by a half-life, which is the time required for half of the radioactive sample to decay.

Half-Life

The half-life of a radioactive isotope is the time it takes for half of the original amount of the substance to decay. This concept is crucial for calculating the remaining quantity of a radioactive material after a certain period. For example, if the half-life of 88Mo is known, one can determine how much of the original sample remains after a specified time, such as 12 minutes.

Exponential Decay

Exponential decay describes the process where the quantity of a substance decreases at a rate proportional to its current value. In the context of radioactive decay, this means that the mass of the radioactive isotope decreases rapidly at first and then slows down over time. The graph provided illustrates this behavior, showing a steep decline initially that flattens as time progresses.