5. If 800-ug of arsenic-76 are present in an artifact, how much arsenic-76 will be present after 132.5 hours? [SHOW WORK] The half-life of arsenic-76 is 26.5 hours.
5. If 800-ug of arsenic-76 are present in an artifact, how much arsenic-76 will be present after 132.5 hours? [SHOW WORK] The half-life of arsenic-76 is 26.5 hours.
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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![**Question:**
If 800 micrograms (ug) of arsenic-76 are present in an artifact, how much arsenic-76 will be present after 132.5 hours? The half-life of arsenic-76 is 26.5 hours. \[SHOW WORK\]
**Explanation:**
To answer this question, we'll use the concept of radioactive decay and half-life. The half-life is the time required for half of the radioactive substance to decay.
Here are the steps to solve the problem:
1. **Determine the number of half-lives:**
The number of half-lives (\(n\)) that have passed can be calculated using the formula:
\[
n = \frac{\text{total time}}{\text{half-life}}
\]
Given:
- Total time (\(t\)) = 132.5 hours
- Half-life (\(t_{1/2}\)) = 26.5 hours
\[
n = \frac{132.5}{26.5} \approx 5
\]
2. **Calculate the remaining amount of arsenic-76:**
After each half-life, the amount of radioactive substance decreases by half. So, the remaining amount can be calculated using the formula:
\[
\text{Remaining amount} = \text{initial amount} \times \left( \frac{1}{2} \right)^n
\]
Given:
- Initial amount = 800 micrograms
- Number of half-lives (\(n\)) = 5
\[
\text{Remaining amount} = 800 \times \left( \frac{1}{2} \right)^5
\]
\[
\text{Remaining amount} = 800 \times \frac{1}{32} = 25 \text{ micrograms}
\]
Therefore, 25 micrograms of arsenic-76 will be present after 132.5 hours.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5623d6a3-334a-4b1a-9cf6-41cb3cd5d075%2Fce8e52ba-ef72-4dff-90e7-3907eb9a9cf5%2Fv74tp5l_processed.png&w=3840&q=75)
Transcribed Image Text:**Question:**
If 800 micrograms (ug) of arsenic-76 are present in an artifact, how much arsenic-76 will be present after 132.5 hours? The half-life of arsenic-76 is 26.5 hours. \[SHOW WORK\]
**Explanation:**
To answer this question, we'll use the concept of radioactive decay and half-life. The half-life is the time required for half of the radioactive substance to decay.
Here are the steps to solve the problem:
1. **Determine the number of half-lives:**
The number of half-lives (\(n\)) that have passed can be calculated using the formula:
\[
n = \frac{\text{total time}}{\text{half-life}}
\]
Given:
- Total time (\(t\)) = 132.5 hours
- Half-life (\(t_{1/2}\)) = 26.5 hours
\[
n = \frac{132.5}{26.5} \approx 5
\]
2. **Calculate the remaining amount of arsenic-76:**
After each half-life, the amount of radioactive substance decreases by half. So, the remaining amount can be calculated using the formula:
\[
\text{Remaining amount} = \text{initial amount} \times \left( \frac{1}{2} \right)^n
\]
Given:
- Initial amount = 800 micrograms
- Number of half-lives (\(n\)) = 5
\[
\text{Remaining amount} = 800 \times \left( \frac{1}{2} \right)^5
\]
\[
\text{Remaining amount} = 800 \times \frac{1}{32} = 25 \text{ micrograms}
\]
Therefore, 25 micrograms of arsenic-76 will be present after 132.5 hours.
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