Learning Goal: To understand de Broglie waves and the calculation of wave properties. In 1924, Louis de Broglie postulated that particles such as electrons and protons might exhibit wavelike properties. His thinking was guided by the notion that light has both wave and particle characteristics, so he postulated that particles such as electrons and protons would obey the same wavelength-momentum relation as that obeyed by light:=h/p, where X is the wavelength, p the momentum, and h Planck's constant. A = 1.06×10-34 m Submit Correct Previous Answers As a comparison, an atomic nucleus has a diameter of around 10-14 m. Clearly, the wavelength of a moving baseball is too small for you to hope to see diffraction or interference effects during a baseball game. ▾ Part C Consider a beam of electrons in a vacuum, passing through a very narrow slit of width 2.00 μm. The electrons then head toward an array of detectors a distance 0.9540 m away. These detectors indicate a diffraction pattern, with a broad maximum of electron intensity (i.e., the number of electrons received in a certain area over a certain period of time) with minima of electron intensity on either side, spaced 0.490 cm from the center of the pattern. What is the wavelength of one of the electrons in this beam? Recall that the location of the first intensity minima in a single slit diffraction pattern for light is y = LA/a, where I is the distance to the screen (detector) and a is the width of the slit. The derivation of this formula was based entirely upon the wave nature of light, so by de Broglie's hypothesis it will also apply to the case of electron waves.
Learning Goal: To understand de Broglie waves and the calculation of wave properties. In 1924, Louis de Broglie postulated that particles such as electrons and protons might exhibit wavelike properties. His thinking was guided by the notion that light has both wave and particle characteristics, so he postulated that particles such as electrons and protons would obey the same wavelength-momentum relation as that obeyed by light:=h/p, where X is the wavelength, p the momentum, and h Planck's constant. A = 1.06×10-34 m Submit Correct Previous Answers As a comparison, an atomic nucleus has a diameter of around 10-14 m. Clearly, the wavelength of a moving baseball is too small for you to hope to see diffraction or interference effects during a baseball game. ▾ Part C Consider a beam of electrons in a vacuum, passing through a very narrow slit of width 2.00 μm. The electrons then head toward an array of detectors a distance 0.9540 m away. These detectors indicate a diffraction pattern, with a broad maximum of electron intensity (i.e., the number of electrons received in a certain area over a certain period of time) with minima of electron intensity on either side, spaced 0.490 cm from the center of the pattern. What is the wavelength of one of the electrons in this beam? Recall that the location of the first intensity minima in a single slit diffraction pattern for light is y = LA/a, where I is the distance to the screen (detector) and a is the width of the slit. The derivation of this formula was based entirely upon the wave nature of light, so by de Broglie's hypothesis it will also apply to the case of electron waves.
Modern Physics
3rd Edition
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Chapter3: The Quantum Theroy Of Light
Section: Chapter Questions
Problem 1P
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Question
Transcribed Image Text:Learning Goal:
To understand de Broglie waves and the calculation
of wave properties.
In 1924, Louis de Broglie postulated that particles
such as electrons and protons might exhibit
wavelike properties. His thinking was guided by the
notion that light has both wave and particle
characteristics, so he postulated that particles such
as electrons and protons would obey the same
wavelength-momentum relation as that obeyed by
light: \ =h/p, where X is the wavelength, p the
momentum, and h Planck's constant.
X = 1.06×10-34
Submit
Correct
m
Previous Answers
-14
As a comparison, an atomic nucleus has a diameter of around 10 m. Clearly, the wavelength of a
moving baseball is too small for you to hope to see diffraction or interference effects during a baseball
game.
Part C
Consider a beam of electrons in a vacuum, passing through a very narrow slit of width 2.00 μm. The electrons then
head toward an array of detectors a distance 0.9540 m away. These detectors indicate a diffraction pattern, with a
broad maximum of electron intensity (i.e., the number of electrons received in a certain area over a certain period of
time) with minima of electron intensity on either side, spaced 0.490 cm from the center of the pattern. What is the
wavelength of one of the electrons in this beam? Recall that the location of the first intensity minima in a single slit
diffraction pattern for light is y = Lλ/a, where L is the distance to the screen (detector) and a is the width of the
slit. The derivation of this formula was based entirely upon the wave nature of light, so by de Broglie's hypothesis it
will also apply to the case of electron waves.
Express your answer in meters to three significant figures.
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Previous Answers Request Answer
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