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. Na-24 has a half-life of 15 hours. How much of a 20.0 g sample would remai fter decaying for 60 hours?

. Na-24 has a half-life of 15 hours. How much of a 20.0 g sample would remai fter decaying for 60 hours?

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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**Question 1:** Na-24 has a half-life of 15 hours. How much of a 20.0 g sample would remain after decaying for 60 hours? This question involves calculating the remaining quantity of a radioactive isotope, Na-24, over a period of time by using its half-life. The half-life represents the time it takes for half of the sample to decay. **Explanation:** - **Half-life of Na-24:** 15 hours - **Initial mass of sample:** 20.0 g - **Time elapsed:** 60 hours To solve, we determine how many half-life periods occur in the given time: 1. \( \text{Number of half-lives} = \frac{\text{Total time}}{\text{Half-life}} = \frac{60 \text{ hours}}{15 \text{ hours}} = 4 \) Then, calculate the remaining mass: 1. After 1 half-life: \( 20.0 \, \text{g} \div 2 = 10.0 \, \text{g} \) 2. After 2 half-lives: \( 10.0 \, \text{g} \div 2 = 5.0 \, \text{g} \) 3. After 3 half-lives: \( 5.0 \, \text{g} \div 2 = 2.5 \, \text{g} \) 4. After 4 half-lives: \( 2.5 \, \text{g} \div 2 = 1.25 \, \text{g} \) **Final Answer:** 1.25 grams of the Na-24 sample would remain after 60 hours.
Transcribed Image Text:**Question 1:** Na-24 has a half-life of 15 hours. How much of a 20.0 g sample would remain after decaying for 60 hours? This question involves calculating the remaining quantity of a radioactive isotope, Na-24, over a period of time by using its half-life. The half-life represents the time it takes for half of the sample to decay. **Explanation:** - **Half-life of Na-24:** 15 hours - **Initial mass of sample:** 20.0 g - **Time elapsed:** 60 hours To solve, we determine how many half-life periods occur in the given time: 1. \( \text{Number of half-lives} = \frac{\text{Total time}}{\text{Half-life}} = \frac{60 \text{ hours}}{15 \text{ hours}} = 4 \) Then, calculate the remaining mass: 1. After 1 half-life: \( 20.0 \, \text{g} \div 2 = 10.0 \, \text{g} \) 2. After 2 half-lives: \( 10.0 \, \text{g} \div 2 = 5.0 \, \text{g} \) 3. After 3 half-lives: \( 5.0 \, \text{g} \div 2 = 2.5 \, \text{g} \) 4. After 4 half-lives: \( 2.5 \, \text{g} \div 2 = 1.25 \, \text{g} \) **Final Answer:** 1.25 grams of the Na-24 sample would remain after 60 hours.
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