Table of contents

0. Math Review31m
- Math Review
  31m
1. Intro to Physics Units1h 29m
2. 1D Motion / Kinematics3h 56m
3. Vectors2h 43m
4. 2D Kinematics1h 42m
5. Projectile Motion3h 6m
6. Intro to Forces (Dynamics)3h 22m
7. Friction, Inclines, Systems2h 44m
8. Centripetal Forces & Gravitation7h 26m
9. Work & Energy1h 59m
10. Conservation of Energy2h 54m
11. Momentum & Impulse3h 40m
12. Rotational Kinematics2h 59m
13. Rotational Inertia & Energy7h 4m
14. Torque & Rotational Dynamics2h 5m
15. Rotational Equilibrium3h 39m
16. Angular Momentum3h 6m
17. Periodic Motion2h 9m
18. Waves & Sound3h 40m
19. Fluid Mechanics4h 27m
20. Heat and Temperature3h 7m
21. Kinetic Theory of Ideal Gases1h 50m
22. The First Law of Thermodynamics1h 26m
23. The Second Law of Thermodynamics3h 11m
24. Electric Force & Field; Gauss' Law3h 42m
25. Electric Potential1h 51m
26. Capacitors & Dielectrics2h 2m
27. Resistors & DC Circuits3h 8m
28. Magnetic Fields and Forces2h 23m
29. Sources of Magnetic Field2h 30m
30. Induction and Inductance3h 38m
31. Alternating Current2h 37m
32. Electromagnetic Waves2h 14m
33. Geometric Optics2h 57m
34. Wave Optics1h 15m
35. Special Relativity2h 10m

0. Math Review

Math Review

Physics

0. Math Review

Math Review

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Problem 44

Textbook Question

Use the graph of binding energy to estimate the total energy released if three ⁴He nuclei fuse together to form a ¹²C nucleus.

Verified step by step guidance

Identify the binding energy per nucleon for ⁴He and ¹²C from the graph of binding energy. Binding energy per nucleon is typically given in MeV (Mega-electron Volts).

Calculate the total binding energy for three ⁴He nuclei. Since each ⁴He nucleus has 4 nucleons, the total number of nucleons in three ⁴He nuclei is 12. Multiply the binding energy per nucleon of ⁴He by the total number of nucleons (12).

Determine the total binding energy of the ¹²C nucleus. Multiply the binding energy per nucleon of ¹²C by the total number of nucleons in ¹²C (which is 12).

Find the energy released during the fusion process. Subtract the total binding energy of the three ⁴He nuclei from the total binding energy of the ¹²C nucleus. The difference represents the energy released.

Express the energy released in appropriate units (e.g., MeV) and ensure the result is consistent with the conservation of energy principle.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Binding Energy

Binding energy is the energy required to disassemble a nucleus into its constituent protons and neutrons. It is a measure of the stability of a nucleus; the higher the binding energy, the more stable the nucleus. In fusion reactions, the difference in binding energy before and after the reaction indicates the energy released during the process.

Nuclear Fusion

Nuclear fusion is the process where two light atomic nuclei combine to form a heavier nucleus, releasing energy in the process. This occurs under conditions of high temperature and pressure, such as in stars. In the case of helium nuclei fusing to form carbon, the energy released is a result of the increased binding energy of the resulting nucleus compared to the original nuclei.

Energy Release Calculation

To estimate the total energy released in a fusion reaction, one must calculate the difference in binding energy between the reactants and the products. This involves using the binding energy values from a graph or table for the involved nuclei. The energy released can be expressed in MeV (mega-electronvolts) and is a crucial aspect of understanding the efficiency and feasibility of fusion as an energy source.

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