A sample of F-18 has an initial decay rate of 1.5⨉10⁵/s. How long will it take for the decay rate to fall to 2.5⨉10³/s? (F-18 has a half-life of 1.83 hours.)

Key Concepts

Radioactive Decay

Radioactive decay is the process by which unstable atomic nuclei lose energy by emitting radiation. This decay occurs at a characteristic rate for each isotope, often described by its decay constant, which is related to the half-life. Understanding this concept is crucial for calculating how the decay rate changes over time.

Half-Life

Half-life is the time required for half of the radioactive nuclei in a sample to decay. For F-18, the half-life is 1.83 hours, meaning that after this time, half of the original amount of F-18 will have decayed. This concept is essential for determining the time it takes for the decay rate to decrease from an initial value to a specified lower value.

Exponential Decay Formula

The exponential decay formula describes how the quantity of a radioactive substance decreases over time. It is expressed as N(t) = N0 * e^(-λt), where N(t) is the quantity at time t, N0 is the initial quantity, λ is the decay constant, and e is the base of the natural logarithm. This formula is fundamental for calculating the time required for the decay rate to reach a specific value.