Textbook Question
A glass rod that has been charged to +12 nC touches a metal sphere. Afterward, the rod’s charge is +8.0 nC. How many charged particles were transferred?
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Ch 22: Electric Charges and Forces
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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Table of contents
- 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: 9780137344796Not the one you use?Change textbook
Chapter 22, Problem 6
What mass of aluminum has a total nuclear charge of C? Aluminum has atomic number .
Verified step by step guidance1
Determine the number of protons in one aluminum atom. The atomic number of aluminum is 13, which means each aluminum atom has 13 protons. Since the nuclear charge is due to protons, each proton has a charge of approximately 1.6 × 10⁻¹⁹ C.
Calculate the total charge of one aluminum atom. Multiply the number of protons (13) by the charge of a single proton (1.6 × 10⁻¹⁹ C). This gives the nuclear charge of one aluminum atom.
Determine the number of aluminum atoms required to produce a total nuclear charge of 1.0 C. Divide the total charge (1.0 C) by the nuclear charge of one aluminum atom (calculated in the previous step).
Find the mass of one aluminum atom. Use the molar mass of aluminum (approximately 27 g/mol) and Avogadro's number (6.022 × 10²³ atoms/mol) to calculate the mass of a single aluminum atom.
Calculate the total mass of aluminum. Multiply the number of aluminum atoms (calculated in step 3) by the mass of one aluminum atom (calculated in step 4). This gives the total mass of aluminum required to have a nuclear charge of 1.0 C.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Nuclear Charge
Nuclear charge refers to the total charge of the nucleus of an atom, which is determined by the number of protons it contains. Each proton carries a charge of +1 elementary charge (approximately 1.6 x 10^-19 C). For aluminum, with an atomic number of 13, the nuclear charge is +13 C, as it has 13 protons.
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Atomic Mass and Molar Mass
Atomic mass is the mass of a single atom, typically measured in atomic mass units (amu), while molar mass is the mass of one mole of a substance, expressed in grams per mole (g/mol). For aluminum, the molar mass is approximately 27 g/mol, which is essential for converting between mass and the number of atoms or moles in calculations.
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Charge and Mass Relationship
The relationship between charge and mass in this context involves calculating the mass of aluminum that corresponds to a specific total nuclear charge. Given that each aluminum atom contributes a charge of +1 C per proton, the total charge can be used to determine the number of aluminum atoms, which can then be converted to mass using the molar mass.
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Related Practice
Textbook Question
Figure 22.8 showed how an electroscope becomes negatively charged. The leaves will also repel each other if you touch the electroscope with a positively charged glass rod. Use a series of charge diagrams to explain what happens and why the leaves repel each other.
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Textbook Question
A linear accelerator uses alternating electric fields to accelerate electrons to close to the speed of light. A small number of the electrons collide with a target, but a large majority pass through the target and impact a beam dump at the end of the accelerator. In one experiment the beam dump measured charge accumulating at a rate of −2.0 nC/s. How many electrons traveled down the accelerator during the 2.0 h run?
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Textbook Question
A plastic rod that has been charged to −15 nC touches a metal sphere. Afterward, the rod's charge is −10 nC. How many charged particles were transferred?
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Textbook Question
What is the total charge of all the electrons in L of liquid water?
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Textbook Question
Two small plastic spheres each have a mass of 2.0 g and a charge of −50.0 nC. They are placed 2.0 cm apart (center to center). What is the magnitude of the electric force on each sphere?