Question

In a comparison of two radioisotopes, isotope $A$ requires 18.0 hours for its decay rate to fall to $\frac{1}{16}$ its initial value, while isotope B has a half-life that is 2.5 times that of A. How long does it take for the decay rate of isotope $B$ to decrease to $\frac{1}{32}$ of its initial value?

Name: Problem 20, Chapter 25: General Chemistry: Principles and Modern Applications
Uploaded: 2020-07-27T20:55:38-08:00
Channel: Bin Chen
Description: In a comparison of two radioisotopes, isotope A requires 18.0 hours for its decay rate to fall to (1)/(16) its initial value, while isotope B has a half-life that is 2.5 times that of A. How long does it take for the decay rate of isotope B to decrease to (1)/(32) of its initial value?

   In a comparison of two radioisotopes, isotope $A$ requires 18.0 hours for its decay rate to fall to $\frac{1}{16}$ its initial value, while isotope B has a half-life that is 2.5 times that of A. How long does it take for the decay rate of isotope $B$ to decrease to $\frac{1}{32}$ of its initial value?

General Chemistry: Principles and Modern Applications

Ralph H. Petrucci,… 10th Edition

Chapter 25, Problem 20

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Solved by Expert Bin Chen

07/27/2020

Step 1

We know that it takes 18.0 hours for its decay rate to fall to $\frac{1}{16}$ its initial value. This means that after 18.0 hours, the decay rate is $\frac{1}{16}$ of its initial value. Since half-life is the time it takes for the decay rate to fall to half its Show more…

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In a comparison of two radioisotopes, isotope $A$ requires 18.0 hours for its decay rate to fall to $\frac{1}{16}$ its initial value, while isotope B has a half-life that is 2.5 times that of A. How long does it take for the decay rate of isotope $B$ to decrease to $\frac{1}{32}$ of its initial value?

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Key Concepts

Exponential Decay

Exponential decay refers to the process in which a quantity decreases at a rate proportional to its current value. This principle is used to model radioactive decay, where the number of undecayed nuclei decreases over time according to an exponential function.

Half-Life

The half-life of a radioactive substance is the time it takes for the substance's activity (or number of radioactive nuclei) to reduce to half its initial value. It provides a convenient measure of the rate of decay and is central to calculations involving exponential decay.

Radioactive Decay Process

The radioactive decay process describes the disintegration of unstable atomic nuclei, which emit radiation as they transform into more stable configurations. This process is governed by the exponential decay law, where the remaining amount of the substance at any time is determined by its half-life.

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