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A sample of a radioactive metal starts with a mass of 400 grams. When a chemist examines it later, it has gone through 4 half-lives. How much metal remains? *

A sample of a radioactive metal starts with a mass of 400 grams. When a chemist examines it later, it has gone through 4 half-lives. How much metal remains? *

Chemistry
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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**Half-Life Calculation of a Radioactive Sample** Consider a sample of a radioactive metal that initially has a mass of 400 grams. After being examined by a chemist, it is determined that the sample has gone through 4 half-lives. The question posed is: How much metal remains? **Solution:** A half-life is the time required for half of the radioactive nuclei in a sample to decay. With each half-life, the remaining mass of the sample is halved. - **Initial mass:** 400 grams - **After 1 half-life:** 400 grams ÷ 2 = 200 grams - **After 2 half-lives:** 200 grams ÷ 2 = 100 grams - **After 3 half-lives:** 100 grams ÷ 2 = 50 grams - **After 4 half-lives:** 50 grams ÷ 2 = 25 grams Therefore, after 4 half-lives, 25 grams of the radioactive metal remains.
Transcribed Image Text:**Half-Life Calculation of a Radioactive Sample** Consider a sample of a radioactive metal that initially has a mass of 400 grams. After being examined by a chemist, it is determined that the sample has gone through 4 half-lives. The question posed is: How much metal remains? **Solution:** A half-life is the time required for half of the radioactive nuclei in a sample to decay. With each half-life, the remaining mass of the sample is halved. - **Initial mass:** 400 grams - **After 1 half-life:** 400 grams ÷ 2 = 200 grams - **After 2 half-lives:** 200 grams ÷ 2 = 100 grams - **After 3 half-lives:** 100 grams ÷ 2 = 50 grams - **After 4 half-lives:** 50 grams ÷ 2 = 25 grams Therefore, after 4 half-lives, 25 grams of the radioactive metal remains.
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25 g of metal remains after 4 half-lives.

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