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Chapter 18: Problem 66

Calculate the time required for three- fourths of a sample of cesium-138 to decay given that its half-life is 32.2 \(\mathrm{min} .\)

Short Answer

Expert verified
The total time required for three-fourths of a sample of cesium-138 to decay is 64.4 minutes.

Step by step solution

01

Recognize The Problem

First, one needs to recognize that the task is to calculate the decay time for three-fourths of the cesium-138 sample. Since cesium-138 has a half-life of 32.2 minutes, this means when this time passes, half of the original sample will have decayed.
02

Calculating First Half-Life

The first half-life allows half of the sample to decay. Starting with a full sample, after 1 half-life of 32.2 minutes, half the sample would remain.
03

Calculating Second Half-Life

For the second half-life, half of the remaining sample will decay. So, after another half-life of 32.2 minutes (totaling 64.4 minutes now), half of the remaining half will have decayed, leaving one-fourth of the original sample.
04

Adding Up The Time

By adding up the time, it takes two half-lives (or 64.4 minutes) for three-fourths of the sample to decay, leaving one-fourth of the original sample.

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