42. Derive the Compton shift equation, Equation 39.13, by applying conservation principles for energy and momentum the collision shown in Figure 39.13. Assume that the elec- tron is free and initially at rest. X-rays are scattered at various angles by electrons in a target. In such a scattering event, a shift in waveleng th is observed for the scattered x-rays, a phenomenon known as the Compton effect. Classical physics does not predict the correct behavior in this effect. If the x-ray is treated as a photon, conservation of energy and linear momen- tum applied to the photon-electron collisions yields, for the Compton shift, h (1- cos 0) тс (39.13) where m, is the mass of the electron, c is the speed of light, and 0 is the scattering angle.

42. Derive the Compton shift equation, Equation 39.13, by applying conservation principles for energy and momentum the collision shown in Figure 39.13. Assume that the elec- tron is free and initially at rest. X-rays are scattered at various angles by electrons in a target. In such a scattering event, a shift in waveleng th is observed for the scattered x-rays, a phenomenon known as the Compton effect. Classical physics does not predict the correct behavior in this effect. If the x-ray is treated as a photon, conservation of energy and linear momen- tum applied to the photon-electron collisions yields, for the Compton shift, h (1- cos 0) тс (39.13) where m, is the mass of the electron, c is the speed of light, and 0 is the scattering angle.

College Physics

1st Edition

ISBN:9781938168000

Author:Paul Peter Urone, Roger Hinrichs

Publisher:Paul Peter Urone, Roger Hinrichs

Chapter29: Introduction To Quantum Physics

Section: Chapter Questions

Problem 68PE: The decay energy of a short-lived particle has an uncertainty of 1.0 MeV due to its short lifetime....

See similar textbooks

Related questions

Q: X-rays of wavelength 0.120 nm are scattered from a block of carbon. If the scattered radiation is…

A: Given data The wavelength of the X rays is given as λ=0.120 nm. The scattering angle is given as…

Q: Find the typical de Broglie wavelength associated with a He atom in helium gas at room temperature…

Q: Under ideal conditions, a visual sensation can occur in the human visual system if light of…

Q: Through what angle must a 200 keV photon be scattered by a free electron so that the photon loses…

Q: The wavelength of the X-ray photons is 0.02480 nm, the photons collide with a target and experience…

Q: When radiation of frequency 8 x 10^14 Hz is incident to Calcium which has 4.3x10^-19 J work…

A: Given that Incidence frequency f = 8 X 1014 Hz Work function w = 4.3 X 10-19 J

Q: A photon of initial energy E, undergoes Compton scatter- ing at an angle 0 from a free electron…

A: From the Crompton effect, the expression for the change in wavelength of the scattered photon is:

Q: Show that the wavelength of electromagnetic radiation is equal to the de Broglie wavelength of its…

A: The De-Broglie wavelength of a photon is,

Q: Ajani is trying to experimentally measure Planck's constant h. He does this by shining different…

Q: When a metal surface, in a photoelectric effect apparatus, is illuminated with monochromatic light…

Q: Consider the Compton scattering of a photon of wavelength Xo by a free electron moving with a…

Q: What should be the minimum applied potential for complete stoppage of photocurrent in an…

Q: Draw a plot showing the variation of de Broglie wavelength of electron as a function of its K.E.

A: The de Broglie wavelength is given by λ =hp where, p is the momentum

Q: A 245 W bulb produces monochromatic U-V light of frequency 1.34x1015 Hz. If the efficiency of the…

A: Power = 245 efficiency = 24% Thus , effective power = 0.24 * 245 = 58.8 W

Q: In the Compton scattering event, the kinetic energy of an electron recoiled by an x-ray is 264 eV.…

A: The energy of the incident photon can be calculated as,

Q: Light of wavelength 400 nm bombards a surface with work function 2.46 eV. What is the maximum…

A: Given data :- Wavelength λ = 400 nm Work function W = 2.46 eV

Q: A Proton Of Energy 250keV is scattered at an angle 120° by a stationary free electron,Then Find The…

A: Given : Proton's energy→Einitial =250 KeV=4.005×10-14J Scattering angle →θ=120° Standard Data Used :…

Q: What is the de Broglie wavelength of (a) an electron accelerated from rest by a potential difference…

A: a) The kinetic energy of the electron which is accelerated is given by K=eV=pe22me…

Q: In the Compton scattering, the photon of energy 8.7 MeV is scattered free electron of mass 9.1 x…

A: GivenInitial energy of photon (E)=8.7 MeV=1.394×10-12 Jmass of free electron (m)=9.1×10-31…

Q: What speed must a neutron have if its de Broglie wavelength is to be equal to the interionic spacing…

Q: Problem 4: a. For Compton scattering, what photon scattering angle provides the maximum possible…

A: Given, A Compton scattering gives max K.E to electron To find photon scattering angle, K.E value…

Q: A beam having photon of energy 480 k eV is incident on a foil of aluminum. If the photon is…

Q: What is the recoil velocity of an electron (in m/s), if a 17 keV photon strikes the electron…

A: Energy of photon =17 kev Photon is scattered through an angle (θ)= 92.8o The energy of scattered…

Q: It is stated without proof with respect to Bragg’s law that when the atoms are not sym- metrically…

A: Write the equation of Bragg’s law. Draw the schematic diagram of the system.

Q: It is desired to produce x-ray radiation with a wavelength of 1 A. (a) Through what potential…

A: Energy of a photon is given by E = hc⋋ Where, h = Planks constant, c = speed of light, ⋋= Wavelength

Q: In the Compton scattering, the photon of energy 8,4 MeV is scattered from a free electron of mass…

Q: What is the work function for the metal (in eV), if the maximum wavelength of light to produce…

Q: In a photoelectric effect experiment you illuminate a metal with light of wavelength 240 nm and…

Q: What are (a) the Compton shift Δλ, (b) the fractional Compton shift Δλ/λ, and (c) the change…

A: Hello. Since your question has multiple sub-parts, we will solve the first three sub-parts for you.…

Q: Show that the ratio of the Compton wavelength A, to the de Broglie wavelength A = h/pfor a…

A: The expression for the de-Broglie wavelength, The expression for the Compton wavelength,

Q: In the Compton scattering, the photon of energy 8.4 MeV is scattered from a free electron of mass…

Q: Light of wavelength 327 nm is incident on an uncharged metal sphere of diameter 14.2 cm. If the work…

Q: Consider the Compton sca - of a by ehtem dire ctron Show bree eleton moing urth a mom of magnilude p…

Q: In a particular photoelectric experiment, a stoppingpotential of 2.10 V is measured when ultraviolet…

A: The expression for energy of a photon in terms of its wavelength is, E=hcλ Here, h is Planck’s…

Q: For photons of energy 8.00 eV, what stopping potential would be required to arrest the current of…

A: The stopping potential is defined as the voltage difference necessary during the photoelectric…

Q: What (a) frequency, (b) photon energy, and (c) photon momentum magnitude (in keV/c) are associated…

A: a) To determine the frequency,

Q: Light of wavelength 277 nm is incident on an uncharged metal sphere of diameter 16.2 cm. If the work…

A: The charge induced on the sphere due to photoelectric effect is 7.2×10-12C.

Q: Find the maximum Compton wave shift corresponding to a collision between a photon and a proton at…

Q: A 0.7 MeV photon scatters from an electron initially at rest. If the photon scatters at an angle of…

Q: An electron and a proton, each initially at rest, are accelerated across the same voltage. Assuming…

A: Heisenberg's uncertainty principle states that it is impossible to measure the position and momentum…

Question

100%

42. Derive the Compton shift equation, Equation 39.13, by
applying conservation principles for energy and momentum
the collision shown in Figure 39.13. Assume that the elec-
tron is free and initially at rest.

X-rays are scattered at various angles by electrons in a target. In such a scattering
event, a shift in waveleng th is observed for the scattered x-rays, a phenomenon known
as the Compton effect. Classical physics does not predict the correct behavior in this
effect. If the x-ray is treated as a photon, conservation of energy and linear momen-
tum applied to the photon-electron collisions yields, for the Compton shift,
h
(1- cos 0)
тс
(39.13)
where m, is the mass of the electron, c is the speed of light, and 0 is the scattering
angle.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step 7

Step 8

Trending now

This is a popular solution!

Step by step

Solved in 8 steps with 7 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Note that a thermal neutron is a neutron whose most probable kinetic energy is ~ 0.025 eV. What is the de Broglie wavelength of a thermal neutron? (Hint: Neutrons in a nuclear reactor are thermalized in order to enhance their probability of fissioning 235U.)
The decay energy of a short-lived particle has an uncertainty of 1.0 MeV due to its short lifetime. What is the smallest lifetime it can have?
(a) What is the uncertainty in the energy released in the decay of a due to its short lifetime? (b) What traction of the decay energy is this, noting that the decay mode is (so that all the mass is destroyed)?
A virtual particle having an approximate mass of may be associated with the uni?cation of the strong and electroweak forces. For what length of time could this virtual particle exist (in temporary violation of the conservation of mass-energy as allowed by the Heisenberg uncertainty principle)?
Why does the energy of characteristic x rays become increasingly greater for heavier atoms?
What is the ratio of the velocity of a 5.00-MeV β ray to that of an α particle with the same kinetic energy? This should confirm that β s travel much faster than α s even when relativity is taken into consideration.
Photoelectron from a material with binding energy of 2.71ev are ejected by 420nm photons. Once ejected , how long does it take these electrons to travel 2.50cm to a detection device?
A muon, or mu meson, has the same charge as an electron, but is 207 times as massive. a) Compared with electron-positron pair production, the pair production of a muon and antimuon requires a photon of what energy? E = _____ MeV b) What would be the minimum frequency for such a photon? f = _________ Hz
Calculate the energy of a 511 keV annihilation photon after Compton has been scattered at one angle of 90° and another at 180°. The kinetic energy of the Compton electron is given by KE = hν − hν'. Calculate the kinetic energy of the Compton electron in each case. (please type answer not write by hend)
Wave-particle duality of light extends to matter particles by the de Broglie hypothesis. If an electron in free space is in thermal equilibrium with Cosmic Microwave Background (CMB) photons at 2.725K, and assuming electron motion can be modeled as an ‘ideal gas’ point particle, (a) What is the electron’s de Broglie wavelength? (me = 9.11 x 10-31 kg) (Hint: (3/2) kBT = (1/2) meVavg2)
At what speed must a beam of neutrons travel so that its associated wavelength is 2 Amstrongs?
An electron and a positron, each moving at 3.0 x105 m/scollide head on, disappear, and producetwo photons, each with the same energy and momentummoving in opposite directions. Determine the energy andmomentum of each photon.