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...
icon
Related questions
Question
100%
Please help me how to solve this question. Thank you very much.
### 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.
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.
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Knowledge Booster
Chemical Equilibrium
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, chemistry and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Chemistry
Chemistry
Chemistry
ISBN:
9781305957404
Author:
Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:
Cengage Learning
Chemistry
Chemistry
Chemistry
ISBN:
9781259911156
Author:
Raymond Chang Dr., Jason Overby Professor
Publisher:
McGraw-Hill Education
Principles of Instrumental Analysis
Principles of Instrumental Analysis
Chemistry
ISBN:
9781305577213
Author:
Douglas A. Skoog, F. James Holler, Stanley R. Crouch
Publisher:
Cengage Learning
Organic Chemistry
Organic Chemistry
Chemistry
ISBN:
9780078021558
Author:
Janice Gorzynski Smith Dr.
Publisher:
McGraw-Hill Education
Chemistry: Principles and Reactions
Chemistry: Principles and Reactions
Chemistry
ISBN:
9781305079373
Author:
William L. Masterton, Cecile N. Hurley
Publisher:
Cengage Learning
Elementary Principles of Chemical Processes, Bind…
Elementary Principles of Chemical Processes, Bind…
Chemistry
ISBN:
9781118431221
Author:
Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher:
WILEY