Consider a radioactive sample. Determine the ratio of the...

Name: Problem 25, Chapter 44: Physics for Scientists and Engineers with Modern Physics
Uploaded: 2020-08-02T04:29:47-08:00
Duration: 2 min 50 s
Channel: Ren Jie Tuieng
Description: Consider a radioactive sample. Determine the ratio of the number of nuclei decaying during the first half of its half- life to the number of nuclei decaying during the scondhalf of its half-life.

Consider a radioactive sample. Determine the ratio of the number of nuclei decaying during the first half of its half- life to the number of nuclei decaying during the scondhalf of its half-life.

Key Concepts

Radioactive Decay

Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation. This decay transforms the nucleus into a different state or a different element altogether. It is inherently stochastic at the level of individual atoms but exhibits predictable behavior when considering large numbers of atoms.

Exponential Decay Law

The exponential decay law describes how the quantity of a radioactive substance decreases over time by a constant fraction during equal time intervals. This law is expressed mathematically through an exponential function where the remaining amount at any time is a fixed proportion of the initial amount, emphasizing the probabilistic nature of decay processes.

Half-Life

The half-life is the period required for half of the radioactive nuclei in a sample to decay. It is a fundamental metric used to characterize the rate of a radioactive reaction and links directly to the exponential decay law. Understanding half-life allows for predictions of how much of the substance remains after a given time and helps in analyzing decay over subintervals.

Integration Over Time Intervals

To determine the number of decay events occurring in a specific time interval, one often integrates the decay rate over that interval. This method is essential when comparing decays across different segments of time, such as comparing a first time subinterval to a second one, as it provides an accurate account of the changes in the number of undecayed nuclei.

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