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An incident $x$ -ray photon is scattered from a free electron that is initially at rest. The photon is scattered straight back at an angle of $180^{\circ}$ from its initial direction. The wavelength of the scattered photon is 0.0830 $\mathrm{nm.}$ (a) What is the wavelength of the incident photon? (b) What is the magnitude of the momentum of the electron after the collision? (c) What is the kinetic energy of the electron after the collision?

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A) 0.0780 $\mathrm{nm}$B) $1.65 \times 10^{-23} \mathrm{kg} \cdot \mathrm{m} / \mathrm{s}$C) 928 $\mathrm{eV}$

Physics 102 Electricity and Magnetism

Physics 103

Chapter 28

Photons, Electrons, and Atoms

Electromagnetic Waves

Atomic Physics

Simon Fraser University

University of Sheffield

McMaster University

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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An incident X-ray photon i…

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An incident x-ray photon o…

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An incident $x$ -ray photo…

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A photon with wavelength 0…

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A photon with wavelength o…

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An X-ray photon scatters f…

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A photon with wavelength …

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An X-ray photon with a wav…

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All right. So this is the formula that relates on the change in wave length to the scattering angle. And we're told that the wavelength after scattering is 0.830 Nana meters, Um, we're told that the photon is sent back in the same direction that it started in, so the scattering angle is 180 degrees or pie pi ratings. So one minus co sign pi equals one minus negative one, which is too. Okay. So if we want to know the original wavelength we have land is equal to land the prime minus two h over M C and his 9.11 times 10 to the negative 31 kilograms h is 6.63 10. Send the negative 30 for Jules Doc seconds and C is three times entity meters per second. So if we plug everything in what we get is that the new or sorry that the original wavelength is 0.781 Nana meters pretend to the negative nine medals in part B. We want to know what Mo mentum is imparted by the electron. Sorry, what moments was imparted to the electron by the scattering of the photons. So basically, by momentum conservation, the mo mentum change of the photons has to be compensated for by the moment and change with the electron. So using the grubbly relation we have adult pee is equal to each overland minus negative h over land of crime. And we have the negative in here because Momenta me's a vector. Quantity is we need to be careful about signs so plugging everything in What we get is that this is 1.65 times 10 to the negative 23 killer grounds. Times means per second. Now, if we want to know their kinetic energy of the electron that's given by p squared over to m plugging in the value of P that we got in part B and the value of M for an electron that I've written up here. What this comes out toe 1.49 times 10 to the negative 16 Jules

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