Domanda del libro di testo
Use the de Broglie relationship to determine the wavelengths of the following objects: (a) an 85-kg person skiing at 50 km/hr (b) a 10.0-g bullet fired at 250 m/s
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Ch.6 - Electronic Structure of Atoms
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232
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TOC.tableOfContents
- Ch.1 - Introduction: Matter, Energy, and Measurement177
- Ch.2 - Atoms, Molecules, and Ions231
- Ch.3 - Chemical Reactions and Reaction Stoichiometry216
- Ch.4 - Reactions in Aqueous Solution189
- Ch.5 - Thermochemistry175
- Ch.6 - Electronic Structure of Atoms168
- Ch.7 - Periodic Properties of the Elements150
- Ch.8 - Basic Concepts of Chemical Bonding177
- Ch.9 - Molecular Geometry and Bonding Theories200
- Ch.10 - Gases179
- Ch.11 - Liquids and Intermolecular Forces113
- Ch.12 - Solids and Modern Materials154
- Ch.13 - Properties of Solutions157
- Ch.14 - Chemical Kinetics199
- Ch.15 - Chemical Equilibrium128
- Ch.16 - Acid-Base Equilibria164
- Ch.17 - Additional Aspects of Aqueous Equilibria163
- Ch.18 - Chemistry of the Environment105
- Ch.19 - Chemical Thermodynamics164
- Ch.20 - Electrochemistry171
- Ch.21 - Nuclear Chemistry122
- Ch.22 - Chemistry of the Nonmetals82
- Ch.23 - Transition Metals and Coordination Chemistry79
- Ch.24 - The Chemistry of Life: Organic and Biological Chemistry16
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232Non è quello che usi tu?Cambia libro di testo
Capitolo 6, Problema 49
Neutron diffraction is an important technique for determining the structures of molecules. Calculate the velocity of a neutron needed to achieve a wavelength of 125 pm. (Refer to the inside cover for the mass of the neutron.)
Guida verificata passo dopo passo1
First, recall the de Broglie wavelength equation, which relates the wavelength (\( \lambda \)) of a particle to its momentum (\( p \)): \( \lambda = \frac{h}{p} \), where \( h \) is the Planck constant.
Next, express the momentum (\( p \)) in terms of mass (\( m \)) and velocity (\( v \)) of the neutron: \( p = m \cdot v \).
Substitute the expression for momentum into the de Broglie equation to relate wavelength, mass, and velocity: \( \lambda = \frac{h}{m \cdot v} \).
Rearrange the equation to solve for velocity (\( v \)): \( v = \frac{h}{m \cdot \lambda} \).
Finally, use the given wavelength (125 pm) and the mass of a neutron (refer to the inside cover of your textbook or a reliable source) to calculate the velocity.
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De Broglie Wavelength
The De Broglie wavelength is a fundamental concept in quantum mechanics that relates the wavelength of a particle to its momentum. 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 neutrons, this relationship is crucial for understanding how their wave-like properties can be utilized in diffraction experiments.
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00:58
De Broglie Wavelength Formula
Momentum of a Particle
Momentum is a vector quantity defined as the product of an object's mass and its velocity (p = mv). In the context of neutron diffraction, the momentum of the neutron is essential for calculating its wavelength. Understanding how to manipulate this relationship allows for the determination of the velocity required to achieve a specific wavelength.
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05:19Subatomic Particles
Neutron Properties
Neutrons are subatomic particles found in the nucleus of an atom, possessing a mass approximately equal to that of a proton but no electric charge. Their unique properties, including their ability to penetrate materials without causing ionization, make them particularly useful in diffraction techniques for studying molecular structures. Knowing the mass of the neutron is vital for calculations involving its velocity and wavelength.
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01:38Neutron-to-Proton Plot
Pratica correlata
Domanda del libro di testo
Using Heisenberg's uncertainty principle, calculate the uncertainty in the position of (b) a proton moving at a speed of 15.00 { 0.012 * 104 m/s. (The mass of a proton is given in the table of fundamental constants in the inside cover of the text.)
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Domanda del libro di testo
Using Heisenberg's uncertainty principle, calculate the uncertainty in the position of (a) a 1.50-mg mosquito moving at a speed of 1.40 m/s if the speed is known to within {0.01 m/s;
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Domanda del libro di testo
Calculate the uncertainty in the position of (a) an electron moving at a speed of 13.00 ± 0.012 × 105 m/s (b) a neutron moving at this same speed. (The masses of an electron and a neutron are given in the table of fundamental constants in the inside cover of the text.)
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Domanda del libro di testo
Among the elementary subatomic particles of physics is the muon, which decays within a few microseconds after formation. The muon has a rest mass 206.8 times that of an electron. Calculate the de Broglie wavelength associated with a muon traveling at 8.85 * 105 cm/s.
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Domanda del libro di testo
Use the de Broglie relationship to determine the wavelengths of the following objects: (c) a lithium atom moving at 2.5 × 105 m/s (d) an ozone (O3) molecule in the upper atmosphere moving at 550 m/s.
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