Domanda del libro di testo
Calculate the de Broglie wavelength of a 143-g baseball traveling at 85 mph. Is the wave nature of matter significant for a baseball?
Ch.8 - The Quantum-Mechanical Model of the Atom
Tro6th EditionChemistry: A Molecular ApproachISBN: 9780137832217
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TOC.tableOfContents
- Ch.1 - Matter, Measurement & Problem Solving118
- Ch.2 - Atoms & Elements106
- Ch.3 - Molecules and Compounds131
- Ch.4 - Chemical Reactions and Chemical Quantities56
- Ch.5 - Introduction to Solutions and Aqueous Solutions82
- Ch.6 - Gases114
- Ch.7 - Thermochemistry96
- Ch.8 - The Quantum-Mechanical Model of the Atom60
- Ch.9 - Periodic Properties of the Elements90
- Ch.10 - Chemical Bonding I: The Lewis Model89
- Ch.11 - Chemical Bonding II: Molecular Shapes, VSEPR & MO Theory85
- Ch.12 - Liquids, Solids & Intermolecular Forces51
- Ch.13 - Solids & Modern Materials47
- Ch.14 - Solutions90
- Ch.15 - Chemical Kinetics115
- Ch.16 - Chemical Equilibrium68
- Ch.17 - Acids and Bases136
- Ch.18 - Aqueous Ionic Equilibrium153
- Ch.19 - Free Energy & Thermodynamics93
- Ch.20 - Electrochemistry106
- Ch.21 - Radioactivity & Nuclear Chemistry74
- Ch.22 - Organic Chemistry140
Tro6th EditionChemistry: A Molecular ApproachISBN: 9780137832217Non è quello che usi tu?Cambia libro di testo
Capitolo 8, Problema 53
What is the de Broglie wavelength of an electron traveling at 1.35 x 10^5 m/s?
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Identify the formula for the de Broglie wavelength: \( \lambda = \frac{h}{mv} \), where \( \lambda \) is the wavelength, \( h \) is Planck's constant (6.626 x 10^{-34} \(\text{ m}\)^2 \(\text{ kg/s}\)), \( m \) is the mass of the electron (9.109 x 10^{-31} \(\text{ kg}\)), and \( v \) is the velocity of the electron.
Substitute the given velocity \( v = 1.35 \times 10^5 \text{ m/s} \) into the formula.
Substitute the known values for Planck's constant \( h = 6.626 \times 10^{-34} \text{ m}^2 \text{ kg/s} \) and the mass of the electron \( m = 9.109 \times 10^{-31} \text{ kg} \) into the formula.
Calculate the de Broglie wavelength by performing the division \( \lambda = \frac{6.626 \times 10^{-34}}{9.109 \times 10^{-31} \times 1.35 \times 10^5} \).
Simplify the expression to find the de Broglie wavelength \( \lambda \).
Concetti chiave
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de Broglie Wavelength
The de Broglie wavelength is a fundamental concept in quantum mechanics that describes the wave-like behavior of particles. It is given by the formula λ = h/p, where λ is the wavelength, h is Planck's constant, and p is the momentum of the particle. This concept illustrates that all matter exhibits both particle and wave characteristics, which is essential for understanding phenomena at the quantum level.
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Percorso guidato
00:58
De Broglie Wavelength Formula
Momentum
Momentum is a physical quantity defined as the product of an object's mass and its velocity (p = mv). In the context of the de Broglie wavelength, momentum is crucial because it directly influences the wavelength of a particle. For an electron, which has a small mass, even a relatively high speed can result in a significant momentum, thereby affecting its wave properties.
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00:40Angular Momentum Quantum Number
Planck's Constant
Planck's constant (h) is a fundamental constant in quantum mechanics, valued at approximately 6.626 x 10^-34 Js. It relates the energy of a photon to its frequency and plays a critical role in the de Broglie wavelength equation. Understanding Planck's constant is essential for calculating the wave properties of particles, as it bridges the gap between classical and quantum physics.
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Percorso guidato
00:50Photons and Planck's Constant
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