What formula is used to estimate the activity of a radioactive sample?

The formula used to estimate the activity of a radioactive sample is expressed as A = A_0 exp(-λt). This equation characterizes the exponential decay of a radioactive substance over time, where A represents the remaining activity at time t, A_0 is the initial activity, λ is the decay constant specific to the radioactive isotope, and t is the elapsed time since the start of the decay process.

This relationship emphasizes the nature of radioactive decay, which is a continuous and probabilistic process. Each radioactive nucleus has a certain probability of decaying over a specific time period, characterized by the decay constant. As time progresses, the number of undecayed nuclei decreases exponentially, leading to a corresponding decrease in activity.

Understanding this formula is crucial in nuclear power engineering, as it allows engineers and scientists to predict the behavior of radioactive materials over time. Whether assessing the decay of spent fuel, monitoring radiation levels, or ensuring safety measures, this formula is foundational for calculations involving radioactivity and decay.

Additionally, while other choices involve concepts related to radioactivity and decay, they do not describe the straightforward exponential decay process captured by the correct formula, thus supporting the significance of the chosen equation in estimating radioactive activity.