Physics for Scientists and Engineers with Modern Physics, Technology Update
9th Edition
ISBN: 9781305401969
Author: SERWAY, Raymond A.; Jewett, John W.
Publisher: Cengage Learning
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Chapter 40, Problem 3OQ
To determine
The true statement regarding Compton scattering of electron by an electron at rest.
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In a Compton scattering experiment, an x-ray photon scatters through an angle of 15.0° from a free electron that is initially at rest. The electron recoils with a speed of 2,200 km/s.
(a) Calculate the wavelength of the incident photon.
nm
(b) Calculate the angle through which the electron scatters.
O
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…
A) Calculate the de Broglie wavelength of a neutron (mn = 1.67493×10-27 kg) moving at one six hundredth of the speed of light (c/600).
(Enter at least 4 significant figures.)
B) Calculate the velocity of an electron (me = 9.10939×10-31 kg) having a de Broglie wavelength of 230.1 pm.
Chapter 40 Solutions
Physics for Scientists and Engineers with Modern Physics, Technology Update
Ch. 40.1 - Prob. 40.1QQCh. 40.2 - Prob. 40.2QQCh. 40.2 - Prob. 40.3QQCh. 40.2 - Prob. 40.4QQCh. 40.3 - Prob. 40.5QQCh. 40.5 - Prob. 40.6QQCh. 40.6 - Prob. 40.7QQCh. 40 - Prob. 1OQCh. 40 - Prob. 2OQCh. 40 - Prob. 3OQ
Ch. 40 - Prob. 4OQCh. 40 - Prob. 5OQCh. 40 - Prob. 6OQCh. 40 - Prob. 7OQCh. 40 - Prob. 8OQCh. 40 - Prob. 9OQCh. 40 - Prob. 10OQCh. 40 - Prob. 11OQCh. 40 - Prob. 12OQCh. 40 - Prob. 13OQCh. 40 - Prob. 14OQCh. 40 - Prob. 1CQCh. 40 - Prob. 2CQCh. 40 - Prob. 3CQCh. 40 - Prob. 4CQCh. 40 - Prob. 5CQCh. 40 - Prob. 6CQCh. 40 - Prob. 7CQCh. 40 - Prob. 8CQCh. 40 - Prob. 9CQCh. 40 - Prob. 10CQCh. 40 - Prob. 11CQCh. 40 - Prob. 12CQCh. 40 - Prob. 13CQCh. 40 - Prob. 14CQCh. 40 - Prob. 15CQCh. 40 - Prob. 16CQCh. 40 - Prob. 17CQCh. 40 - The temperature of an electric heating element is...Ch. 40 - Prob. 2PCh. 40 - Prob. 3PCh. 40 - Prob. 4PCh. 40 - Prob. 5PCh. 40 - Prob. 6PCh. 40 - Prob. 7PCh. 40 - Prob. 8PCh. 40 - Prob. 9PCh. 40 - Prob. 10PCh. 40 - Prob. 11PCh. 40 - Prob. 12PCh. 40 - Prob. 14PCh. 40 - Prob. 15PCh. 40 - Prob. 16PCh. 40 - Prob. 17PCh. 40 - Prob. 18PCh. 40 - Prob. 19PCh. 40 - Prob. 20PCh. 40 - Prob. 21PCh. 40 - Prob. 22PCh. 40 - Prob. 23PCh. 40 - Prob. 25PCh. 40 - Prob. 26PCh. 40 - Prob. 27PCh. 40 - Prob. 28PCh. 40 - Prob. 29PCh. 40 - Prob. 30PCh. 40 - Prob. 31PCh. 40 - Prob. 32PCh. 40 - Prob. 33PCh. 40 - Prob. 34PCh. 40 - Prob. 36PCh. 40 - Prob. 37PCh. 40 - Prob. 38PCh. 40 - Prob. 39PCh. 40 - Prob. 40PCh. 40 - Prob. 41PCh. 40 - Prob. 42PCh. 40 - Prob. 43PCh. 40 - Prob. 45PCh. 40 - Prob. 46PCh. 40 - Prob. 47PCh. 40 - Prob. 48PCh. 40 - Prob. 49PCh. 40 - Prob. 50PCh. 40 - Prob. 51PCh. 40 - Prob. 52PCh. 40 - Prob. 53PCh. 40 - Prob. 54PCh. 40 - Prob. 55PCh. 40 - Prob. 56PCh. 40 - Prob. 57PCh. 40 - Prob. 58PCh. 40 - Prob. 59PCh. 40 - Prob. 60APCh. 40 - Prob. 61APCh. 40 - Prob. 62APCh. 40 - Prob. 63APCh. 40 - Prob. 64APCh. 40 - Prob. 65APCh. 40 - Prob. 66APCh. 40 - Prob. 67APCh. 40 - Prob. 68APCh. 40 - Prob. 69APCh. 40 - Prob. 70APCh. 40 - Prob. 71APCh. 40 - Prob. 72CPCh. 40 - Prob. 73CPCh. 40 - Prob. 74CPCh. 40 - Prob. 75CPCh. 40 - Prob. 76CP
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- Compton scattering can also occur if a photon collides with a proton (mass 1.673 * 10-27 kg) at rest. If you do an experiment of this kind using gamma-ray photons with wavelength 2.50 * 10-12 m = 2.50 pm, for what scattering angle is the wavelength of the scattered gamma rays longer than the wavelength of the incident gamma rays by (a) 0.0100% and (b) 0.0800%?arrow_forwardIn a Compton scattering experiment, an x-ray photon scatters through an angle of 17.8° from a free electron that is initially at rest. The electron recoils with a speed of 2,200 km/s. (a) Calculate the wavelength of the incident photon.answer in nm(b) Calculate the angle through which the electron scatters.answer in degrees°arrow_forwardIn a Compton scattering experiment, an x-ray photon scatters through an angle of 12.2° from a free electron that is initially at rest. The electron recoils with a speed of 1,480 km/s. (a) Calculate the wavelength of the incident photon. 0.144 Your response differs from the correct answer by more than 10%. Double check your calculations. nm (b) Calculate the angle through which the electron scatters.arrow_forward
- The Compton Effect is a fundamental phenomenon in physics that describes the change in wavelength of electromagnetic radiation (such as light) when it interacts with charged particles, such as electrons. When photons (particles of light) collide with electrons, some of their energy is transferred to the electrons, resulting in a change in the direction and wavelength of the scattered photons. Statement: Knowing that Planck's constant is h = 6.6x10^-34 m2 kg/s, the mass of the electron is 9.11x10^-31 kg, and the speed of light is 3.0x10^8 m/ s; Calculate for an x-ray photon, with a wavelength equal to 5.0 nm (5.0x10^-9 m), which undergoes a scattering of 30º, what would be its new wavelength. Question options: a) 5.00502nm b) 5.11111nm c) 4.032nm d) 4.90000nm e) 5.00032nmarrow_forwardAn electron has a kinetic energy of 4.1 × 10–¹³ J. 46. What is the electron's speed? (a) 0.960c (b) 0.968c (c) 0.972c (d) 0.980c (e) 0.986c 47. What is the de Broglie wavelength of the electron described? (a) 4.09 × 10-13 m (b) 4.94 × 10-13m (c) 5.42 × 10-13 m (d) 6.25 × 10-13 m (e) 7.81 x 10-13marrow_forwardYou want to use a microscope to study the structure of a mitochondrion about 1.00 um in size. To be able to observe small details within the mitochondrion, you want to use a wavelength of 0.0500 nm. If your microscope uses light of this wavelength, what is the momentum p of a photon? p = kg-m/s If your microscope uses light of this wavelength, what is the energy E of a photon? E = If instead your microscope uses electrons of this de Broglie wavelength, what is the momentum p. of an electron? Pe = kg-m/s If instead your microscope uses electrons of this de Broglie wavelength, what is the velocity v of an electron? v = m/s If instead your microscope uses electrons of this de Broglie wavelength, what is the kinetic energy K of an electron? K = What advantage do your calculations suggest electrons have compared to photons? O An electron's charge allows it to attach to observed particles, whereas a photon's electric neutrality prevents it from moving close enough to the observed particles…arrow_forward
- Compton scattering can also occur if a photon collides with a proton (mass 1.673 x 10-27 kg) at rest. If you do an experiment of this kind using gamma-ray photons with wavelength 2.50 x 10-12 m = 2.50 pm, for what scattering angle is the wavelength of the scattered gamma rays longer than the wavelength of the incident gamma rays by (a) 0.0100% and (b) 0.0800%?arrow_forwardProblem 4: A photon originally traveling along the x axis, with wavelength λ = 0.100 nm is incident on an electron (m = 9.109 x 10-31 kg) that is initially at rest. The x-component of the momentum of the electron after the collision is 5.0 x 10-24 kg m/s and the y-component of the momentum of the electron after the collision is -6.0 x 10-24 kg m/s. If the photon scatters at an angle + from its original direction, what is wavelength of the photon after the collision. h= 6.626 x 10:34 J·s and c = 3.0 x 108 m/s.arrow_forward15.(a)What is the frequency of an x-ray photon whose momentum is 1.1x 1023 kg m/s? (b) How much energy must a photon have if it is to have the momentum of a 10-MeV proton?arrow_forward
- An electron and a photon each have a wavelength of 2.0. What are their (a) momenta and (b) total energies? (c) Compare the kinetic energies of the electron and the photon.arrow_forwardWhat is the wavelength of (a) a photon with energy 1.00 eV, (b) an electron with energy 1.00 eV, (c) a photon of energy 1.00 GeV, and (d) an electron with energy 1.00 GeV?arrow_forward
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