Domanda del libro di testo
Sketch the interference pattern that results from the diffraction of electrons passing through two closely spaced slits.
525
views
Ch.8 - The Quantum-Mechanical Model of the Atom
Tro5th EditionChemistry: A Molecular ApproachISBN: 9780134874371
Non è quello che usi tu?Cambia libro di testoScegli un libro di testo diverso
TOC.tableOfContents
- Ch.1 - Matter, Measurement & Problem Solving117
- Ch.2 - Atoms & Elements106
- Ch.3 - Molecules and Compounds128
- Ch.4 - Chemical Reactions and Chemical Quantities56
- Ch.5 - Introduction to Solutions and Aqueous Solutions84
- Ch.6 - Gases112
- Ch.7 - Thermochemistry96
- Ch.8 - The Quantum-Mechanical Model of the Atom60
- Ch.9 - Periodic Properties of the Elements86
- Ch.10 - Chemical Bonding I: The Lewis Model91
- Ch.11 - Chemical Bonding II: Molecular Shapes, VSEPR & MO Theory85
- Ch.12 - Liquids, Solids & Intermolecular Forces51
- Ch.13 - Solids & Modern Materials48
- Ch.14 - Solutions93
- Ch.15 - Chemical Kinetics114
- Ch.16 - Chemical Equilibrium68
- Ch.17 - Acids and Bases137
- Ch.18 - Aqueous Ionic Equilibrium154
- Ch.19 - Free Energy & Thermodynamics91
- Ch.20 - Electrochemistry105
- Ch.21 - Radioactivity & Nuclear Chemistry74
- Ch.22 - Organic Chemistry141
Tro5th EditionChemistry: A Molecular ApproachISBN: 9780134874371Non è quello che usi tu?Cambia libro di testo
Capitolo 8, 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.
Guida verificata passo dopo passo1
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.
Risposta video verificata per un problema simile:
Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
6mConcetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
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.
Video consigliato:
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.
Video consigliato:
Percorso guidato
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.
Video consigliato:
Percorso guidato
00:40Angular Momentum Quantum Number
Pratica correlata
Domanda del libro di testo
A proton in a linear accelerator has a de Broglie wavelength of 122 pm. What is the speed of the proton?
4557
views
2
rank
Domanda del libro di testo
The resolution limit of a microscope is roughly equal to the wavelength of light used in producing the image. Electron microscopes use an electron beam (in place of photons) to produce much higher resolution images, about 0.20 nm in modern instruments. Assuming that the resolution of an electron microscope is equal to the de Broglie wavelength of the electrons used, to what speed must the electrons be accelerated to obtain a resolution of 0.20 nm?
2106
views
Domanda del libro di testo
Calculate the de Broglie wavelength of a 143-g baseball traveling at 95 mph. Why is the wave nature of matter not important for a baseball?
2283
views