How does radioactive decay follow first-order kinetics?

Radioactive decay follows first-order kinetics due to the random nature of decay and the constant probability of decay per unit time.

In first-order kinetics, the rate of decay is proportional to the number of radioactive nuclei present. This means that the larger the number of radioactive nuclei, the faster the decay rate. However, the probability of decay per unit time remains constant, regardless of the number of nuclei present. This is because the decay of each nucleus is a random event, independent of the decay of other nuclei.

The constant probability of decay per unit time is known as the decay constant, denoted by λ. The rate of decay can be expressed as the product of the number of radioactive nuclei present and the decay constant, i.e. dN/dt = -λN, where N is the number of radioactive nuclei and t is time.

The half-life of a radioactive substance is the time taken for half of the radioactive nuclei to decay. It is a characteristic property of the substance and is related to the decay constant by the equation t1/2 = ln2/λ. The half-life is independent of the initial number of nuclei and is a useful parameter for determining the age of rocks and fossils.

In summary, radioactive decay follows first-order kinetics due to the random nature of decay and the constant probability of decay per unit time. This allows for the determination of the decay constant and half-life of a radioactive substance, which are important parameters in various fields such as nuclear physics, geology, and medicine.