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 (5.00±0.01) × 104 m/s. The mass of a proton is 1.673×10−27 kg.
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Ch.6 - Electronic Structure of Atoms
Brown15th EditionChemistry: The Central ScienceISBN: 9780137542970
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TOC.tableOfContents
- Ch.1 - Introduction: Matter, Energy, and Measurement146
- Ch.2 - Atoms, Molecules, and Ions200
- Ch.3 - Chemical Reactions and Reaction Stoichiometry176
- Ch.4 - Reactions in Aqueous Solution155
- Ch.5 - Thermochemistry126
- Ch.6 - Electronic Structure of Atoms131
- Ch.7 - Periodic Properties of the Elements126
- Ch.8 - Basic Concepts of Chemical Bonding123
- Ch.9 - Molecular Geometry and Bonding Theories143
- Ch.10 - Gases147
- Ch.11 - Liquids and Intermolecular Forces91
- Ch.12 - Solids and Modern Materials122
- Ch.13 - Properties of Solutions126
- Ch.14 - Chemical Kinetics174
- Ch.15 - Chemical Equilibrium101
- Ch.16 - Acid-Base Equilibria139
- Ch.17 - Additional Aspects of Aqueous Equilibria146
- Ch.18 - Chemistry of the Environment72
- Ch.19 - Chemical Thermodynamics129
- Ch.20 - Electrochemistry142
- Ch.21 - Nuclear Chemistry101
- Ch.22 - Chemistry of the Nonmetals68
- Ch.23 - Transition Metals and Coordination Chemistry66
- Ch.24 - The Chemistry of Life: Organic and Biological Chemistry10
Brown15th EditionChemistry: The Central ScienceISBN: 9780137542970Non 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 1.25 Å. The mass of a neutron is 1.675×10−27 kg.
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Identify the relationship between velocity, wavelength, and mass using the de Broglie equation: \( \lambda = \frac{h}{mv} \), where \( \lambda \) is the wavelength, \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \) Js), \( m \) is the mass, and \( v \) is the velocity.
Rearrange the de Broglie equation to solve for velocity \( v \): \( v = \frac{h}{m\lambda} \).
Substitute the given values into the equation: \( h = 6.626 \times 10^{-34} \) Js, \( m = 1.675 \times 10^{-27} \) kg, and \( \lambda = 1.25 \times 10^{-10} \) m (since 1 Å = 1 \(\times\) 10^{-10} m).
Calculate the velocity \( v \) by performing the division: \( v = \frac{6.626 \times 10^{-34}}{1.675 \times 10^{-27} \times 1.25 \times 10^{-10}} \).
Ensure the units are consistent and simplify the expression to find the velocity of the neutron.
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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 a neutron, the momentum can be expressed as p = mv, where m is the mass and v is the velocity. This relationship is crucial for understanding how particles like neutrons exhibit wave-like properties.
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00:58
De Broglie Wavelength Formula
Planck's Constant
Planck's constant (h) is a fundamental physical constant that plays a central role in quantum mechanics. It has a value of approximately 6.626 × 10^-34 Js and is used to describe the quantization of energy levels in atoms and the wave-particle duality of matter. In the context of neutron diffraction, it is essential for calculating the wavelength of neutrons based on their momentum, thereby linking classical and quantum physics.
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00:50Photons and Planck's Constant
Kinetic Energy and Velocity
The kinetic energy of a particle is the energy it possesses due to its motion, expressed as KE = 0.5mv², where m is the mass and v is the velocity. In neutron diffraction, the velocity of the neutron is directly related to its kinetic energy and is essential for determining the appropriate conditions for achieving a specific wavelength. Understanding this relationship allows for the calculation of the velocity needed to produce a desired wavelength in neutron scattering experiments.
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02:27Kinetic Energy Formulas
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