Concept explainers
(a)
Wavelength of the Compton scattered photon and the kinetic energy of the scattered electron if the scattering angle is
Answer to Problem 55QAP
Wavelength of the Compton scattered photon is 0.140 nm and the kinetic energy of the scattered electron is 0 if the scattering angle is
Explanation of Solution
Given:
Initial wavelength
Formula used:
According to Compton scattering the change in wavelength of the incident photon is given by
Now the energy of the scattered photon is
Kinetic energy of the scattered electron is given by
Calculation:
For
So,
And using the value of
K = 0.
Conclusion:
So the wavelength of the Compton scattered photon is 0.140 nm and the kinetic energy of the scattered electron is 0
(b)
Wavelength of the Compton scattered photon and the kinetic energy of the scattered electron if the scattering angle is
Answer to Problem 55QAP
Wavelength of the Compton scattered photon is 0.140325 nm and the kinetic energy of the scattered electron is 20.5 eV
Explanation of Solution
Given:
Initial wavelength
Formula used:
According to Compton scattering the change in wavelength of the incident photon is given by
Now the energy of the scattered photon is
Kinetic energy of the scattered electron is given by
Calculation:
For
Now using the values of
[Above we have used 1 nm = 10-9 m and
Conclusion:
So the wavelength of the Compton scattered photon is 0.140325 nm and the kinetic energy of the scattered electron is 20.5 eV.
(c)
Wavelength of the Compton scattered photon and the kinetic energy of the scattered electron if the scattering angle is
Answer to Problem 55QAP
Wavelength of the Compton scattered photon is 0.140712 nm and the kinetic energy of the scattered electron is 44.9 eV
Explanation of Solution
Given:
Initial wavelength
Formula used:
According to Compton scattering the change in wavelength of the incident photon is given by
Now the energy of the scattered photon is
Kinetic energy of the scattered electron is given by,
Calculation:
For
Now using the values of
Conclusion:
Wavelength of the Compton scattered photon is 0.140712 nm and the kinetic energy of the scattered electron is 44.9 eV
(d)
Wavelength of the Compton scattered photon and the kinetic energy of the scattered electron if the scattering angle is
Answer to Problem 55QAP
Wavelength of the Compton scattered photon is 0.141215 nm and the kinetic energy of the scattered electron is 75.32 eV if the scattering angle is
Explanation of Solution
Given:
Initial wavelength
Formula used:
According to Compton scattering the change in wavelength of the incident photon is given by
Now the energy of the scattered photon is
Kinetic energy of the scattered electron is given by,
Calculation:
For
Now using the values of
Conclusion:
Wavelength of the Compton scattered photon is 0.141215 nm and the kinetic energy of the scattered electron is 75.32 eV
(e)
Wavelength of the Compton scattered photon and the kinetic energy of the scattered electron if the scattering angle is
Answer to Problem 55QAP
Wavelength of the Compton scattered photon is 0.14243 nm and the kinetic energy of the scattered electron is 151.32 eV
Explanation of Solution
Given:
Initial wavelength
Formula used:
According to Compton scattering the change in wavelength of the incident photon is given by
Now the energy of the scattered photon is
Kinetic energy of the scattered electron is given by,
Calculation:
For θ = 900 using Eq. (1.1)
Now using the values of
Conclusion:
Wavelength of the Compton scattered photon is 0.14243 nm and the kinetic energy of the scattered electron is 151.32 eV.
(f)
Wavelength of the Compton scattered photon and the kinetic energy of the scattered electron if the scattering angle is
Answer to Problem 55QAP
Wavelength of the Compton scattered photon is 0.14486 nm and the kinetic energy of the scattered electron is 297.43 eV
Explanation of Solution
Given:
Initial wavelength
Formula used:
According to Compton scattering the change in wavelength of the incident photon is given by
Now the energy of the scattered photon is
Kinetic energy of the scattered electron is given by,
Calculation:
For θ = 1800 using Eq. (1.1)
Now using the values of
Conclusion:
Wavelength of the Compton scattered photon is 0.14486 nm and the kinetic energy of the scattered electron is 297.43 eV
Want to see more full solutions like this?
Chapter 26 Solutions
COLLEGE PHYSICS
- Nuclear fusion reactions at the center of the sun produce gamma-ray photons with energies of about 1 MeV (106 eV). By contrast, what we see emanating from the sun’s surface are visiblelight photons with wavelengths of about 500 nm. A simple model that explains this difference in wavelength is that a photon undergoes Compton scattering many times—in fact, about 1026 times, as suggested by models of the solar interior—as it travels from the center of the sun to its surface. (a) Estimate the increase in wavelength of a photon in an average Compton-scattering event. (b) Find the angle in degrees through which the photon is scattered in the scattering event described in part (a). (Hint: A useful approximation is cosf ≈ 1 - f2/2, which is valid for f V1. Note that f is in radians in this expression.) (c) It is estimated that a photon takes about 106 years to travel from the core to the surface of the sun. Find the average distance that light can travel within the interior of the sun without…arrow_forwardPhotons that have a wavelength of 0.00226 nm are Compton scattered off stationary electrons at 33.0 degrees. What is the energy E of the scattered photons? E = ? Jarrow_forwardA photon undergoes Compton scattering off a stationary free electron. The photon scatters at 90.0° from its initial direction; its initial wavelength is 3.00*10-12 m. What is the electron’s kinetic energy?arrow_forward
- In a Compton scattering experiment, an x-ray photon scatters through an angle of 22.6° from a free electron that is initially at rest. The electron recoils with a speed of 1,720 km/s. (a) Calculate the wavelength of the incident photon. nm (b) Calculate the angle through which the electron scatters. Oarrow_forwardA photon has a collision with a stationary electron (h/mc = 2.43 × 10–12 m) and loses 5.0% of its energy. The photon scattering angle is 180°. What is the wavelength of the incident photon in this scattering process?arrow_forwardWhen a photon has an energy of E and a wavelength of l prior to scattering from a free electron, determine the photon's a) initial wavelength and b) initial energy. The wavelength has risen by 10% after scattering at a 135 degree angle.arrow_forward
- Problem 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_forward1. a) What are the energy and momentum of a photon of red light of wavelength 650 nm? (b) What is the wavelength of a photon of energy 2.40 eV?arrow_forwardYou use 0.124 nm x-ray photons in a Compton-scattering experiment. (a) At what angle is the wavelength of the scattered x rays 1.0% longer than that of the incident x rays? (b) At what angle is it 0.050% longer?arrow_forward
- X-rays of wavelength 1.450 Angstroms (10-10 m) incident on an aluminum target undergo Compton scattering. (a) For a photon scattered at 83° relative to the incident beam, what is the wavelength of the scattered photon? m (b) What are the magnitude of the momentum and the energy of this scattered photon at this angle? momentum kg-m/s energyarrow_forwardYou use 0.124 nm x-ray photons in a Compton-scattering experiment. At what angle is the wavelength of the scattered x rays 1.0% longer than that of the incident x rays? O 70.6° 56.5° 67.0° 60.7°arrow_forwardFresh out of university you've been hired to do some photoelectron spectroscopy. You have a lamp that outputs an unknown wavelength of light. When the light is incident on a metal with a work function of 6.31 eV, you observe a stopping voltage equal to 4.21 V. What is the wavelength of the light? (unit in nm).arrow_forward
- Modern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage LearningPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning