A Porticn cf the Sun's ener9y ccmes From tte reacticn 4H He t 29e which requires a temperatiore of 16°to 10"K. Use the mass of the helium-4nucleus to determine how much enerqyisreleased
A Porticn cf the Sun's ener9y ccmes From tte reacticn 4H He t 29e which requires a temperatiore of 16°to 10"K. Use the mass of the helium-4nucleus to determine how much enerqyisreleased
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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![### A Portion of the Sun's Energy Production
A portion of the Sun’s energy comes from the reaction:
\[ 4_1^1\text{H} \rightarrow {}_2^4\text{He} + 2e^+ \]
This reaction requires a temperature of \(10^6\) to \(10^7\) Kelvin. The task is to use the mass of the helium-4 nucleus to determine how much energy is released per mole of hydrogen atoms.
#### Data Analysis for Helium-4 Nucleus
| Nucleus | Mass of Nucleus (u) | Mass of Individual Nucleons (u) | Mass Defect (u) | Binding Energy (J) | Binding Energy Per Nucleon (J) |
|---------|---------------------|---------------------------------|-----------------|------------------|-----------------------------|
| \(_2^4\text{He}\) | 4.00150 u | 4.03188 u | 0.03038 u | \(4.53 \times 10^{-12}\) J | \(1.13 \times 10^{-12}\) J |
#### Explanation:
- **Nucleus**: Represents the helium-4 (\(_2^4\text{He}\)) nucleus.
- **Mass of Nucleus (u)**: The actual mass of the helium-4 nucleus is 4.00150 atomic mass units (u).
- **Mass of Individual Nucleons (u)**: The sum of the masses of two protons and two neutrons, totaling 4.03188 u.
- **Mass Defect (u)**: The difference between the mass of individual nucleons and the mass of the nucleus, calculated as 0.03038 u.
- **Binding Energy (J)**: The energy needed to disassemble the nucleus into individual protons and neutrons. For helium-4, it is \(4.53 \times 10^{-12}\) joules.
- **Binding Energy Per Nucleon (J)**: The average energy per nucleon required to remove a nucleon from the nucleus. It is calculated as \(1.13 \times 10^{-12}\) joules.
This data helps illustrate how nuclear fusion in the Sun converts hydrogen atoms into helium, releasing vast amounts of energy that contribute to the Sun's radiance.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6ef85c79-8e8f-4d9a-890a-b67fe0c4488a%2Ffdaa857e-4d20-4ea5-8f5a-209d351d2477%2Fcr1g00m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### A Portion of the Sun's Energy Production
A portion of the Sun’s energy comes from the reaction:
\[ 4_1^1\text{H} \rightarrow {}_2^4\text{He} + 2e^+ \]
This reaction requires a temperature of \(10^6\) to \(10^7\) Kelvin. The task is to use the mass of the helium-4 nucleus to determine how much energy is released per mole of hydrogen atoms.
#### Data Analysis for Helium-4 Nucleus
| Nucleus | Mass of Nucleus (u) | Mass of Individual Nucleons (u) | Mass Defect (u) | Binding Energy (J) | Binding Energy Per Nucleon (J) |
|---------|---------------------|---------------------------------|-----------------|------------------|-----------------------------|
| \(_2^4\text{He}\) | 4.00150 u | 4.03188 u | 0.03038 u | \(4.53 \times 10^{-12}\) J | \(1.13 \times 10^{-12}\) J |
#### Explanation:
- **Nucleus**: Represents the helium-4 (\(_2^4\text{He}\)) nucleus.
- **Mass of Nucleus (u)**: The actual mass of the helium-4 nucleus is 4.00150 atomic mass units (u).
- **Mass of Individual Nucleons (u)**: The sum of the masses of two protons and two neutrons, totaling 4.03188 u.
- **Mass Defect (u)**: The difference between the mass of individual nucleons and the mass of the nucleus, calculated as 0.03038 u.
- **Binding Energy (J)**: The energy needed to disassemble the nucleus into individual protons and neutrons. For helium-4, it is \(4.53 \times 10^{-12}\) joules.
- **Binding Energy Per Nucleon (J)**: The average energy per nucleon required to remove a nucleon from the nucleus. It is calculated as \(1.13 \times 10^{-12}\) joules.
This data helps illustrate how nuclear fusion in the Sun converts hydrogen atoms into helium, releasing vast amounts of energy that contribute to the Sun's radiance.
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