Fundamentals of Physics Extended
10th Edition
ISBN: 9781118230725
Author: David Halliday, Robert Resnick, Jearl Walker
Publisher: Wiley, John & Sons, Incorporated
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Chapter 38, Problem 40P
To determine
To find:
Maximum kinetic energy of electrons knocked out of a thin copper foil
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In the Compton scattering, the photon of energy 8.7 MeV is scattered from a
free electron of mass 9.1 × 10 31
the electron (in MeV), if the scattering angle is 164°?
kg, What is the kinetic energy acquired by
Answer:
A photon with wavelength X scatters off an electron at rest, at an angle with the incident direction.
The Compton wavelength of the electron Ac = 0.0024 nm.
a)
For λ = 0.0006 nm and 0 = 53 degrees, find the wavelength X' of the scattered photon in
nanometres.
b)
Obtain a formula for the energy of the electron Ee after collision, in terms of the universal constants
h, c and the variables X, X' and Ac. The answer must be expressed in terms of these variables
only. (Please enter an algebraic expression using latex format; do not input any numerical values)
c)
Using the energy conservation condition, find the value of the electron energy Ee after scattering in
units of keV.
d)
Write an algebraic expression for the electron's momentum pe in
terms of its energy Ee, its mass me and the speed of light c.
e)
What is the de Broglie wavelength of the scattered electron ? Express your answer in terms of Ee,
me, and X and c.
f)
Find the value of the de Broglie wavelength of the scattered electron…
In the Compton scattering, the photon of energy 8.4 MeV is scattered from a
free electron of mass 9.1 x 10
-31
kg, What is the recoil angle of the electron,
if the scattering angle is 52°?
Answer:
Chapter 38 Solutions
Fundamentals of Physics Extended
Ch. 38 - Prob. 1QCh. 38 - Prob. 2QCh. 38 - Prob. 3QCh. 38 - Prob. 4QCh. 38 - Prob. 5QCh. 38 - Prob. 6QCh. 38 - Prob. 7QCh. 38 - Prob. 8QCh. 38 - Prob. 9QCh. 38 - Prob. 10Q
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- Consider the Compton effect. We direct a beam of 2.21 MeV photons toward some material. Many of the photons collide with electrons in the material, ejecting the electrons from the material. The collisions also cause the photons to be scattered in a variety of directions, each scattered photon having less energy than it had initially. (a) Find the wavelength of the photons in the initial beam. (b). Consider a particular collision where the scattered photon comes out at an angle of 75.1 degrees with respect to its initial direction. Find the wavelength of this scattered photon. (c) Find its energy. (d) Find the kinetic energy of the electron this photon collided with.arrow_forwardShow that the maximum kinetic energy of the recoil electron in Compton scattering is given by 2hf mc² K. E.max (electron) = hf · 2hf 1+ mc² At what angles and does this occur? If we detect a scattered electron at angle = 0° of 100 keV, what energy photon was scattered?arrow_forwardAn electron with an initial total energy of E=3.757 eV (in a region with zero potential) is incident on a potential step (extending from x=0 to infinity) to V=1.952 eV. What is the electron's de Broglie wavelength in nm once it crosses the potential step?arrow_forward
- Neutrons in thermal equilibrium with matter have an average kinetic energy of (3/2)kT, where k is the Boltzmann constant and T, which may be taken to be 300 K, is the temperature of the environment of the neutrons. (a) What is the average kinetic energy of such a neutron? (b) What is the corresponding de Broglie wavelength?arrow_forwardX rays of wavelength 0.0123 nm are directed in the positive direction of an x axis onto a target containing loosely bound electrons. For Compton scattering from one of those electrons, at an angle of 156°, what are (a) the Compton shift, (b) the corresponding change in photon energy, (c) the kinetic energy of the recoiling electron, and (d) the angle between the positive direction of the x axis and the electron's direction of motion? The electron Compton wavelength is 2.43 x 10-12 m.arrow_forwardElectrons with a speed of 2.6 x 106 m/s pass through a double-slit apparatus. Interference fringes are detected with a fringe spacing of 5.8 mm. What will the fringe spacing be if the electrons are replaced by neutrons with the same speed? What speed must neutrons have to produce interference fringes with a fringe spacing of 5.8 mm?arrow_forward
- Question in the Attachmentsarrow_forwardX rays of wavelength 0.0100 nm are directed in the positive direction of an x axis onto a target containing loosely bound electrons. For Compton scattering from one of those electrons, at an angle of 180°, what are (a) the Compton shift, (b) the corresponding change in photon energy, (c) the kinetic energy of the recoiling electron, and (d) the angle between the positive direction of the x axis and the electron’s direction of motion?arrow_forwardIn an experiment done by scattering 5.5-MeV a particles from a thin gold foil, students find that 10,000 a particles are scattered at an angle greater than 50⁰. (a) How many of these particles will be scattered greater than 110°? particles (b) How many will be scattered between 58° and 76°? particlesarrow_forward
- What are (a) the Compton shift Δλ, (b) the fractional Compton shift Δλ/λ, and (c) the change ΔEphoton in photon energy for light of wavelength λ = 590 nm scattering from a free, initially stationary electron if the scattering is at 90° to the direction of the incident beam? What are (d) Δλ, (e) Δλ/λ, and (f) ΔEphoton for 90° scattering for photon energy 50.0 keV (x-ray range)?arrow_forwardWhat is the de Broglie wavelength of(a) a bullet of mass 0.040 kg travelling at the speed of 1.0 km/s,(b) a ball of mass 0.060 kg moving at a speed of 1.0 m/s, and(c) a dust particle of mass 1.0 × 10-9 kg drifting with a speed of 2.2 m/s?arrow_forwardShow that the maximum kinetic energy E, called the Compton edge, that a recoiling electron can carry away from a Compton scattering event is given by hf E (1+ mc /2hf) where f is the frequency of the incident photon and m is the electron mass.arrow_forward
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