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Sketch the interference pattern that results from the diffraction of electrons passing through two closely spaced slits.
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Ch.7 - Quantum-Mechanical Model of the Atom
Tro4th EditionChemistry: A Molecular ApproachISBN: 9780134112831
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TOC.tableOfContents
- Ch.1 - Matter, Measurement & Problem Solving136
- Ch.2 - Atoms & Elements112
- Ch.3 - Molecules, Compounds & Chemical Equations159
- Ch.4 - Chemical Quantities & Aqueous Reactions140
- Ch.5 - Gases118
- Ch.6 - Thermochemistry106
- Ch.7 - Quantum-Mechanical Model of the Atom62
- Ch.8 - Periodic Properties of the Elements103
- Ch.9 - Chemical Bonding I: The Lewis Model104
- Ch.10 - Chemical Bonding II: Molecular Shapes & Valence Bond Theory89
- Ch.11 - Liquids, Solids & Intermolecular Forces73
- Ch.12 - Solids and Modern Material59
- Ch.13 - Solutions110
- Ch.14 - Chemical Kinetics140
- Ch.15 - Chemical Equilibrium78
- Ch.16 - Acids and Bases155
- Ch.17 - Aqueous Ionic Equilibrium176
- Ch.18 - Free Energy and Thermodynamics108
- Ch.19 - Electrochemistry118
- Ch.20 - Radioactivity and Nuclear Chemistry82
- Ch.21 - Organic Chemistry150
Tro4th EditionChemistry: A Molecular ApproachISBN: 9780134112831Non è quello che usi tu?Cambia libro di testo
Capitolo 7, Problema 50
The smallest atoms can themselves exhibit quantum-mechanical behavior. Calculate the de Broglie wavelength (in pm) of a hydrogen atom traveling at 475 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 (\( 6.626 \times 10^{-34} \) Js), \( m \) is the mass of the particle, and \( v \) is the velocity.
Determine the mass of a hydrogen atom. The mass of a hydrogen atom is approximately \( 1.67 \times 10^{-27} \) kg.
Substitute the given velocity of the hydrogen atom, \( v = 475 \) m/s, into the de Broglie wavelength formula.
Substitute the values for Planck's constant, the mass of the hydrogen atom, and the velocity into the formula: \( \lambda = \frac{6.626 \times 10^{-34}}{1.67 \times 10^{-27} \times 475} \).
Calculate the de Broglie wavelength in meters and then convert it to picometers (1 pm = \( 10^{-12} \) m) for the final answer.
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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. For a moving particle, momentum is calculated as the product of its mass and velocity. This concept illustrates the dual nature of matter, where particles exhibit both wave and particle characteristics.
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Percorso guidato
00:58
De Broglie Wavelength Formula
Planck's Constant
Planck's constant (h) is a fundamental physical constant that relates the energy of a photon to the frequency of its associated electromagnetic wave. Its value is approximately 6.626 x 10^-34 J·s. In the context of the de Broglie wavelength, it serves as a bridge between classical and quantum physics, allowing for the calculation of wavelengths associated with moving particles, such as atoms and electrons.
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00:50Photons and Planck's Constant
Momentum
Momentum is a vector quantity defined as the product of an object's mass and its velocity (p = mv). In the context of quantum mechanics, momentum plays a crucial role in determining the behavior of particles, including their de Broglie wavelength. For a hydrogen atom, knowing its mass and velocity allows us to calculate its momentum, which is essential for finding its associated wavelength and understanding its quantum behavior.
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00:40Angular Momentum Quantum Number
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