Understanding Nuclei Half-Life in Physics

Given that nucleus a has a half-life t and nucleus b has a half-life 2t, what fraction of the nuclei of type a remains after three half-lives?

Given that nucleus a has a half-life t, after one half-life (t), half of the nuclei will remain. After two half-lives (2t), one-fourth (1/2 * 1/2 = 1/4) of the nuclei will remain. After three half-lives (3t), one-eighth (1/2 * 1/2 * 1/2 = 1/8) of the nuclei will remain. Therefore, after three half-lives, this means 1/8 or 12.5% of the nuclei of type a will remain.

Understanding Nuclei Half-Life in Physics

Half-Life Concept: In the field of physics, the concept of half-life refers to the time required for half of the nuclei in a sample to undergo radioactive decay. This concept is used to understand how the number of radioactive nuclei decreases over time.

Calculating Nuclei Remaining:

For nucleus a with a half-life of t, the fraction of nuclei remaining after each half-life can be calculated. After three half-lives, one-eighth of the nuclei of type a will remain. This means that 1/8 or 12.5% of the nuclei will still be present.

On the other hand, nucleus b with a half-life of 2t follows a similar pattern. After three half-lives, one-eighth of the nuclei of type b will remain as well. The passage of three half-lives indicates a significant reduction in the number of nuclei present in the samples.

This information provides insights into the stability and decay of radioactive nuclei, allowing scientists to make predictions about the remaining nuclei based on their respective half-lives. Understanding these concepts is crucial in various fields such as nuclear physics, archaeology, and medical diagnostic imaging.