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A hollow aluminum sphere with outer diameter 10.0 cm has a mass of 690 g. What is the sphere's inner diameter?
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Ch 18: A Macroscopic Description of Matter
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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TOC.tableOfContents
- Ch 01: Concepts of Motion35
- Ch 02: Kinematics in One Dimension75
- Ch 03: Vectors and Coordinate Systems58
- Ch 04: Kinematics in Two Dimensions60
- Ch 05: Force and Motion23
- Ch 06: Dynamics I: Motion Along a Line53
- Ch 07: Newton's Third Law27
- Ch 08: Dynamics II: Motion in a Plane52
- Ch 09: Work and Kinetic Energy56
- Ch 10: Interactions and Potential Energy50
- Ch 11: Impulse and Momentum56
- Ch 12: Rotation of a Rigid Body71
- Ch 13: Newton's Theory of Gravity52
- Ch 14: Fluids and Elasticity44
- Ch 15: Oscillations55
- Ch 16: Traveling Waves37
- Ch 17: Superposition39
- Ch 18: A Macroscopic Description of Matter53
- Ch 19: Work, Heat, and the First Law of Thermodynamics60
- Ch 20: The Micro/Macro Connection53
- Ch 21: Heat Engines and Refrigerators34
- Ch 22: Electric Charges and Forces40
- Ch 23: The Electric Field39
- Ch 24: Gauss' Law32
- Ch 25: The Electric Potential63
- Ch 26: Potential and Field57
- Ch 27: Current and Resistance42
- Ch 28: Fundamentals of Circuits39
- Ch 29: The Magnetic Field47
- Ch 30: Electromagnetic Induction60
- Ch 31: Electromagnetic Fields and Waves32
- Ch 32: AC Circuits63
- Ch 33: Wave Optics32
- Ch 34: Ray Optics57
- Ch 35: Optical Instruments30
- Ch 36: Special Relativity38
- Ch 37: The Foundations of Modern Physics25
- Ch 38: Quantization49
- Ch 39: Wave Functions and Uncertainty31
- Ch 40: One-Dimensional Quantum Mechanics35
- Ch 41: Atomic Physics18
- Ch 42: Nuclear Physics27
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Non è quello che usi tu?Cambia libro di testo
Capitolo 18, Problema 7
An element in its solid phase has mass density 1750 kg/m3 and number density 4.39×1028 atoms/m3. What is the element's atomic mass number?
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Step 1: Understand the relationship between mass density, number density, and atomic mass. The mass density (ρ) of a material is related to its number density (n) and atomic mass (mₐ) by the equation: ρ = n × mₐ.
Step 2: Rearrange the formula to solve for the atomic mass (mₐ). Using the equation ρ = n × mₐ, isolate mₐ: mₐ = ρ / n.
Step 3: Substitute the given values into the formula. The mass density (ρ) is 1750 kg/m³, and the number density (n) is 4.39 × 10^28 atoms/m³. Ensure the units are consistent.
Step 4: Convert the atomic mass from kilograms to atomic mass units (u). Recall that 1 atomic mass unit (u) is equal to 1.660539 × 10^-27 kg. Use the conversion factor: mₐ (in u) = mₐ (in kg) / (1.660539 × 10^-27).
Step 5: Interpret the result. The atomic mass number is approximately the atomic mass in atomic mass units (u), rounded to the nearest whole number, as it represents the number of protons and neutrons in the nucleus of the element.
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Mass Density
Mass density is defined as the mass of a substance per unit volume, typically expressed in kilograms per cubic meter (kg/m³). It provides insight into how compact the matter is within a given volume. In this question, the mass density of the solid phase of the element is given as 1750 kg/m³, which is crucial for calculating the atomic mass number.
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04:33
Problems with Mass, Volume, & Density
Number Density
Number density refers to the number of particles (atoms, molecules, etc.) per unit volume, usually expressed in particles per cubic meter (m⁻³). In this case, the number density of the element is provided as 4.39×10²⁸ atoms/m³. This concept is essential for relating the mass density to the atomic mass number, as it helps determine how many atoms are present in a specific volume.
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8:13Intro to Density
Atomic Mass Number
The atomic mass number (A) is the total number of protons and neutrons in an atom's nucleus, which determines the mass of the atom. It is a key factor in calculating the mass of a mole of atoms and is related to both mass density and number density. By using the provided mass density and number density, one can derive the atomic mass number through the relationship between these quantities.
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07:19Moles & Avogadro's Number
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