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$\bullet$ (a) Calculate the maximum increase in photon wavelength that can occur during Compton scattering. (b) What is the energy (in electron volts) of the smallest-energy x-ray photon for which Compton scattering could result in doubling the original wavelength?

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$2.56 \times 10^{5} \mathrm{eV}$

Physics 102 Electricity and Magnetism

Physics 103

Chapter 28

Photons, Electrons, and Atoms

Electromagnetic Waves

Atomic Physics

University of Michigan - Ann Arbor

Hope College

University of Winnipeg

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.

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(a) Calculate the maximum …

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03:56

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(a) Compute the Compton wa…

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In Compton scattering, cal…

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(a) Find the Compton wavel…

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Calculate the Compton wave…

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(II) Determine the Compton…

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A photon with a wavelength…

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Determine the maximum wave…

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The high-energy photons ca…

All right. So I've written here the formula for the wavelength change associative Compton scattering. And if we want to know what the biggest change in wavelength is possible, we want to make the right side of this equation as large as possible. And the coastline function varies between negative one and one. And so it's pretty clear that this quantity will be biggest when co sign is equal to negative one. And this all comes out too. So the biggest we can get is two H over and see, which is two times 6.63 times 10 to the negative, 34 over the mass of an electron, which is 9.11 times 10 to the negative, 31 kilograms times the speed of light. And this comes out 4.85 times 10 to the negative 12 meters in part B. We want to know what wavelength is capable of getting doubled. So if it gets doubled, then Lambda Prime is equal to two landa. So if we substitute that into the scattering equation, we have to land minus land. Chico's land equals to H u M C. And so the starting wave length is the same. Value is in part a. Now if we want to know the energy of the sky, we take calm is equal to H C. Over Lambda. Okay, okay. And if we want to express this in electron volts, then we have 4.14 tens tens and negative 15. Yeah, And this comes out to 2.56 times 10 to the five you owe me.

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