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

1. Intro to Physics Units

Introduction to Units

Physics

1. Intro to Physics Units

Introduction to Units

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Problem 32c

Textbook Question

"(II) Use Table 1–3 to estimate the total number of protons or neutrons in the human body"

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Identify the average mass of a human body. For estimation purposes, assume the average human body mass is approximately 70 kg.

Determine the fraction of the human body that is composed of water. The human body is roughly 70% water by mass, so calculate the mass of water: $ m_{\text{water}} = 0.7 \times 70 \ \text{kg} $.

Break down water (H₂O) into its atomic components. Each water molecule consists of 2 hydrogen atoms and 1 oxygen atom. Use the atomic masses: hydrogen has approximately 1 proton per atom, and oxygen has approximately 8 protons and 8 neutrons per atom.

Estimate the number of water molecules in the body. Use the molar mass of water (18 g/mol) and Avogadro's number $ N_A = 6.022 \times 10^{23} \ \text{molecules/mol} $ to calculate the number of molecules: $ N_{\text{molecules}} = \frac{m_{\text{water}}}{18 \times 10^{-3}} \times N_A $.

Multiply the number of molecules by the number of protons and neutrons per molecule. Each water molecule has 10 protons (2 from hydrogen and 8 from oxygen) and 8 neutrons (from oxygen). Add contributions from other elements in the body (e.g., carbon, nitrogen) for a more refined estimate if needed.

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Key Concepts

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

Atomic Structure

Atomic structure refers to the composition of an atom, which consists of protons, neutrons, and electrons. Protons and neutrons are located in the nucleus, while electrons orbit around it. Understanding atomic structure is essential for estimating the number of protons and neutrons in a given mass of matter, such as the human body.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It allows for the conversion between the mass of a substance and the number of atoms or molecules it contains. In the context of estimating protons and neutrons in the human body, knowing the average molar mass of biological elements helps in calculating the total number of these particles.

Composition of the Human Body

The human body is primarily composed of elements such as oxygen, carbon, hydrogen, nitrogen, calcium, and phosphorus. Each of these elements has a specific number of protons and neutrons, which contribute to the overall atomic makeup of the body. Understanding the elemental composition is crucial for accurately estimating the total number of protons and neutrons present in a human body.

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