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Ch28Hw: Photons, Electrons and Atoms
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Ch28Hw: Photons, Electrons and Atoms
Due: 6:00pm on Thursday, April 24, 2014
To understand how points are awarded, read the
Grading Policy
for this assignment.
Diffraction of an Electron Beam
Learning Goal:
To understand how to find the wavelength and diffraction patterns of electrons.
An electron beam is incident on a single slit of width
. The electron beam was generated using a potential difference of
magnitude
. After passing through the slit, the diffracted electrons are collected on a screen that is a distance
away
from the slit. Assume that
is small enough so that the electrons are nonrelativistic. Ultimately, you will find the width
of the central maximum for the diffraction pattern.
Part A
In any diffraction problem, the wavelength of the waves is important. To find the wavelength of electrons, you can
use the de Broglie relation
, but you first must find the momentum of one of the electrons. The electrons are
accelerated through a potential difference
. Use this information to find the momentum
of the electrons.
Express your answer in terms of the mass of an electron
, the magnitude of the charge on an electron
,
and
.
Hint 1.
Relating kinetic energy to momentum
Recall that the kinetic energy
of a particle with mass
and momentum
is given by the equation
.
Hint 2.
Energy of a charge accelerated by a potential
Recall that the kinetic energy
of a charge
accelerated from rest through a potential difference
is
given by the equation
.
ANSWER:
Correct
Part B
What is the wavelength
of the electron beam? Use the de Broglie relation and the momentum that you found in
Part A.
Express your answer in terms of
,
,
, and
.
ANSWER:
=

5/4/14
Ch28Hw: Photons, Electrons and Atoms
Correct
Part C
The width of the central maximum is defined as the distance between the two minima closest to the center of the
diffraction pattern. Since these are symmetric about the center of the pattern, you need to find only the distance to
one of the minima, and then the width of the central maximum will be twice that distance. Find the angle
between
the center of the diffraction pattern and the first minimum.
The equations for diffraction, which you have seen applied to light, are valid for any wave, including electron waves.
Recall that the angle to a diffraction minimum for singleslit diffraction is given by the equation
,
where
is the width of the slit and
is an integer. Recall that
for the first minima on either side of the
central maximum.
Do not make any approximations at this stage.
Express your answer in terms of
,
,
,
, and
.

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