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$\bullet$ A photon with a wavelength of 0.1800 nm is Compton scattered through an angle of $180^{\circ} .$ (a) What is the wavelength of the scattered photon? (b) How much energy is given to the electron? (c) What is the recoil speed of the electron? Is it necessary to use the relativistic kinetic-energy relationship?

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$8 \times 10^{6} \mathrm{m} / \mathrm{s}$

Physics 102 Electricity and Magnetism

Physics 103

Chapter 28

Photons, Electrons, and Atoms

Electromagnetic Waves

Atomic Physics

University of Michigan - Ann Arbor

University of Washington

Simon Fraser University

University of Sheffield

Lectures

02:42

Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. It is primarily concerned with the arrangement of electrons around the nucleus and the processes by which these arrangements change. The theory of quantum mechanics, a set of mathematical rules that describe the behaviour of matter and its interactions, provides a good model for the description of atomic structure and properties.

03:50

In atomic physics, the Rutherford-Bohr model or Bohr model or Bohr model of the atom was first proposed by Niels Bohr in 1913. It was the first quantum theory of the atomic structure, applying the principles of quantum mechanics to the hydrogen atom. The Rutherford-Bohr model is a planetary model in which the electron is assumed to revolve around the nucleus in circular orbits. The Rutherford-Bohr model of the atom was based on Max Planck's quantum theory of radiation, which explained the spectrum of blackbody radiation, and Albert Einstein's theory of the photoelectric effect, which explained the origin of the spectrum of line emission from atoms. The Bohr model of the atom was the first to explain the discrete spectrum of hydrogen and how the spectral lines of the hydrogen atom were split into multiple spectral lines in a phenomenon called the fine structure. It introduced the Bohr radius and the concept of quantum levels to explain the discrete nature of the spectrum of the hydrogen atom. The Bohr model of the atom had a significant influence on the development of quantum mechanics, and was instrumental in the development and validation of quantum mechanics.

03:17

A photon with a wavelength…

01:38

Compton used photons of wa…

02:27

02:50

A photon of initial energy…

03:23

An X-ray photon scatters f…

05:46

02:33

A 0.75-nm photon is scatte…

07:17

In a Compton scattering ex…

02:30

Okay, so for this problem, it's about classic Compton scattering one. We know that the photons starts out with a lambda of 10.18 so I'll go ahead. Write that down. That it's Santa initial is 0.1800 nana meters and then our goals to cut with the photons that scattered if given that angle is 180 degrees. So we want to use the usual Formula Lambda final minus Lambda Initial is equal to H over M. C. Times one minus co. Sign of fei and then you can get Lambda Final is equal to Lambda initial plus each over M C. And then times one maestro signed five so that if I was 1 80 this whole thing becomes too, Um, and so you can go ahead and plug in the numbers and I So for this problem, it's about classic Compton scattering one. We know that the photons starts out with a lambda of 10.18 so I'll go ahead. Write that down. That it's Santa initial is 0.1800 nana meters and then our goals to cut with the photons that scattered. Um, if given that the actually to the calculation have time. Um, And I got 0.1849 centimeters, 0.18 for nine nano meters. And the next we want I got the energy is so we can use energy is equal to magnitude of age. See, um so over So the final mighty So they're okay. Let me remind a little bit. Um whatever energy is lost from the photons is gained by the electron by kinetic energy. So we want to get the energy lost. Um, from goal is 180 degrees. So we want to use the usual formula Lambda final minus Lambda Initial is equal to H over M C. Times one minus co. Sign of fei, and then you can get Lambda Final is equal to Lambda initial plus each over M C. And then times one maestro signed five so that if I was 1 80 this whole thing becomes too. Um and so you can go ahead and plug in the numbers. And I actually did that from the from the photons. So it's gonna be the final initial energy, my see initial energy, and then you should take the magnitude because this is gonna come out of negative number. Um And so in that case, we would got 1 82.80 b and next What we have is he's one happened b squared. And so, um, what we can do is say is equaled calculation. Have time. Um, And I got 10.1849 centimeters, 0.18 for nine nano meters. And the next we want I got the energy is so we can use energy is equal to magnitude of h. C. Um, so over. So the final mighty So they're okay. Let me remind a little bit. Um, whatever energy is lost from the photons is gained by the electron by kinetic energy. So we want to get the energy lost. Um, from 1/2 on b squared, gonna get the velocity of sulfur BVs screwed of to be over em. And when I plug that into a calculator gonna into this beforehand, I got a point 1018 time meters per second. And, um yeah. Oh, sorry. Not Tom the from the proton. So it's gonna be the final initial energy, my see initial energy, and then you should take the magnitude because this is gonna come out of negative number. Um, And so in that case, we would got 1 82 point a TV and next, What we have is he's 1/2 and b squared. And so, um, what we can do is say, is equal to times 10 of those six. My bad. I made that mistake last time. Um and so that's near the speed of light. It's almost a little more than 1/100 of it. So, yeah, I would say that you should use relativity corrections at this point because the what the strength of it kind of goes is was be oversee.

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