The distance between atoms in a crystal of NaCl is 0.28 nm. The crystal is being studied in a n

Name: Problem 8, Chapter 28: College Physics
Uploaded: 2020-05-24T07:08:28-08:00
Channel: Kathleen Tatem
Description: The distance between atoms in a crystal of NaCl is 0.28 nm. The crystal is being studied in a neutron diffraction experiment. At what speed must the neutrons be moving so that their de Broglie wavelength is 0.28 nm ?

Step 1: Write down the de Broglie wavelength formula. The de Broglie wavelength (Î») of a partic

Question

The distance between atoms in a crystal of $\mathrm{NaCl}$ is $0.28 \mathrm{~nm}$. The crystal is being studied in a neutron diffraction experiment. At what speed must the neutrons be moving so that their de Broglie wavelength is $0.28 \mathrm{~nm}$ ?

   The distance between atoms in a crystal of $\mathrm{NaCl}$ is $0.28 \mathrm{~nm}$. The crystal is being studied in a neutron diffraction experiment. At what speed must the neutrons be moving so that their de Broglie wavelength is $0.28 \mathrm{~nm}$ ?

College Physics

lan Giambattista,… 2nd Edition

Chapter 28, Problem 8

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Solved by Expert Kathleen Tatem

05/24/2020

Step 1

The de Broglie wavelength (λ) of a particle is given by the formula: λ = h / p where h is the Planck's constant (6.626 x 10^-34 Js) and p is the momentum of the particle. Show more…

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The distance between atoms in a crystal of $\mathrm{NaCl}$ is $0.28 \mathrm{~nm}$. The crystal is being studied in a neutron diffraction experiment. At what speed must the neutrons be moving so that their de Broglie wavelength is $0.28 \mathrm{~nm}$ ?

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Key Concepts

De Broglie Wavelength

The de Broglie wavelength is a key concept in quantum mechanics that assigns a wavelength to any particle based on its momentum (? = h/p). It reveals the wave-like properties of matter and is essential in analyzing diffraction phenomena.

Momentum and Its Relation to Velocity

Momentum, defined as the product of mass and velocity, is central to linking classical mechanics with quantum behavior. In the de Broglie relation, knowing the momentum (via particle mass and speed) allows one to calculate the associated wavelength, which is particularly relevant in diffraction experiments.

Planck's Constant

Planck's constant (h) is a fundamental constant in quantum mechanics that directly connects energy and frequency, and in the context of de Broglie's hypothesis, it scales the relationship between a particle's momentum and its associated wavelength. It serves as the bridge between wave and particle descriptions.

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