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5. 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.

5. 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.

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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**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.
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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