8. What mass of plutonium-240 will remain after 32,820 years if the initial sample contained 4.8 g of plutonium-240 and it has a half-life of 6564 years?
8. What mass of plutonium-240 will remain after 32,820 years if the initial sample contained 4.8 g of plutonium-240 and it has a half-life of 6564 years?
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
![**Question 8: Radioactive Decay of Plutonium-240**
What mass of plutonium-240 will remain after 32,820 years if the initial sample contained 4.8 g of plutonium-240 and it has a half-life of 6,564 years?
**Explanation:**
This problem involves the concept of radioactive decay, where a radioactive substance decreases in mass over time. The rate of decay is determined by its half-life, which is the time it takes for half of the substance to decay.
**Key Concepts:**
1. **Initial Mass**: 4.8 grams
2. **Half-Life of Plutonium-240**: 6,564 years
3. **Elapsed Time**: 32,820 years
**Calculations:**
To calculate the remaining mass, use the formula:
\[
m = m_0 \left(\frac{1}{2}\right)^{\frac{t}{T}}
\]
Where:
- \( m \) = remaining mass
- \( m_0 \) = initial mass (4.8 g)
- \( t \) = elapsed time (32,820 years)
- \( T \) = half-life (6,564 years)
**Steps**:
1. **Calculate the number of half-lives**:
\[
\frac{t}{T} = \frac{32,820}{6,564} = 5
\]
2. **Apply the formula**:
\[
m = 4.8 \times \left(\frac{1}{2}\right)^5 = 4.8 \times \frac{1}{32} = 0.15 \text{ grams}
\]
Therefore, after 32,820 years, 0.15 grams of plutonium-240 will remain.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F39adedda-6069-4c18-8ba4-c25003d3e364%2F35b06705-e251-403d-8db5-b640773bd5c9%2Fkfufr3r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 8: Radioactive Decay of Plutonium-240**
What mass of plutonium-240 will remain after 32,820 years if the initial sample contained 4.8 g of plutonium-240 and it has a half-life of 6,564 years?
**Explanation:**
This problem involves the concept of radioactive decay, where a radioactive substance decreases in mass over time. The rate of decay is determined by its half-life, which is the time it takes for half of the substance to decay.
**Key Concepts:**
1. **Initial Mass**: 4.8 grams
2. **Half-Life of Plutonium-240**: 6,564 years
3. **Elapsed Time**: 32,820 years
**Calculations:**
To calculate the remaining mass, use the formula:
\[
m = m_0 \left(\frac{1}{2}\right)^{\frac{t}{T}}
\]
Where:
- \( m \) = remaining mass
- \( m_0 \) = initial mass (4.8 g)
- \( t \) = elapsed time (32,820 years)
- \( T \) = half-life (6,564 years)
**Steps**:
1. **Calculate the number of half-lives**:
\[
\frac{t}{T} = \frac{32,820}{6,564} = 5
\]
2. **Apply the formula**:
\[
m = 4.8 \times \left(\frac{1}{2}\right)^5 = 4.8 \times \frac{1}{32} = 0.15 \text{ grams}
\]
Therefore, after 32,820 years, 0.15 grams of plutonium-240 will remain.
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