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
![**Problem:**
If a sample of strontium-89 weighs 1.065 g, what was its mass 153 days ago? The half-life of strontium-89 is 51 days.
**Solution Explanation:**
To solve this problem, we need to calculate the original mass of the strontium-89 sample 153 days ago, taking into account its radioactive decay over time. The concept of half-life, which is the time it takes for half of the radioactive substance to decay, will be used.
**Steps:**
1. **Determine the number of half-lives:**
- The half-life of strontium-89 is 51 days.
- The time period given is 153 days.
- Calculate the number of half-lives elapsed:
\[
\text{Number of half-lives} = \frac{153 \text{ days}}{51 \text{ days/half-life}} = 3 \text{ half-lives}
\]
2. **Use the half-life formula:**
- The formula for calculating remaining mass after a certain number of half-lives is:
\[
\text{Remaining mass} = \text{Initial mass} \times \left( \frac{1}{2} \right)^{\text{Number of half-lives}}
\]
- We know the remaining mass (1.065 g) and need to find the initial mass. Set up the equation:
\[
1.065 = \text{Initial mass} \times \left( \frac{1}{2} \right)^3
\]
3. **Solve for the Initial mass:**
- Simplify the equation:
\[
1.065 = \text{Initial mass} \times \frac{1}{8}
\]
\[
\text{Initial mass} = 1.065 \times 8
\]
\[
\text{Initial mass} = 8.52 \text{ g}
\]
Therefore, the original mass of the strontium-89 sample 153 days ago was 8.52 grams.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F39adedda-6069-4c18-8ba4-c25003d3e364%2Fdaa4020a-1d2f-468d-973f-8c8111d44023%2Fopqgcqn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem:**
If a sample of strontium-89 weighs 1.065 g, what was its mass 153 days ago? The half-life of strontium-89 is 51 days.
**Solution Explanation:**
To solve this problem, we need to calculate the original mass of the strontium-89 sample 153 days ago, taking into account its radioactive decay over time. The concept of half-life, which is the time it takes for half of the radioactive substance to decay, will be used.
**Steps:**
1. **Determine the number of half-lives:**
- The half-life of strontium-89 is 51 days.
- The time period given is 153 days.
- Calculate the number of half-lives elapsed:
\[
\text{Number of half-lives} = \frac{153 \text{ days}}{51 \text{ days/half-life}} = 3 \text{ half-lives}
\]
2. **Use the half-life formula:**
- The formula for calculating remaining mass after a certain number of half-lives is:
\[
\text{Remaining mass} = \text{Initial mass} \times \left( \frac{1}{2} \right)^{\text{Number of half-lives}}
\]
- We know the remaining mass (1.065 g) and need to find the initial mass. Set up the equation:
\[
1.065 = \text{Initial mass} \times \left( \frac{1}{2} \right)^3
\]
3. **Solve for the Initial mass:**
- Simplify the equation:
\[
1.065 = \text{Initial mass} \times \frac{1}{8}
\]
\[
\text{Initial mass} = 1.065 \times 8
\]
\[
\text{Initial mass} = 8.52 \text{ g}
\]
Therefore, the original mass of the strontium-89 sample 153 days ago was 8.52 grams.
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