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$\cdot$ An x ray with a wavelength of 0.100 nm collides with a electron that is initially at rest. The $x$ ray's final wavelength 0.110 nm. What is the final kinetic energy of the electron?

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1.13 $\mathrm{keV}$

Physics 102 Electricity and Magnetism

Physics 103

Chapter 28

Photons, Electrons, and Atoms

Electromagnetic Waves

Atomic Physics

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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.

02:41

An x ray with a wavelength…

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02:32

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An $x$ ray with a waveleng…

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$\cdot$ An x ray with a wa…

01:56

An x ray with wavelength o…

03:35

An xx ray with a wavelengt…

05:30

A photon with wavelength 0…

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04:39

An x-ray photon with wavel…

08:46

A photon with wavelength …

03:02

A photon with wavelength o…

03:07

All right. So for this problem, we're talking about an X ray question, like trying on and its wavelength than increases. And so that means it's lower energy. We want to get the final kinetic energy of the electron so we won't use energy conservation. So we can say Lambda initial is 0.1 nanometers groups nano meters. Lambda Final is equal to 0.11 nano meters, and that changing energy is gonna go to the electron. And so we just want to get the kinetic energy of the electron. So, um, so the kinetic energy is just gonna be the energy difference between the final and initial state and then energy for photons HC over Lando's who it's gonna be HC overland of Final my S H C over Manda initial and then plugging that into a calculator. E get went over point when one minus one over 10.1. Oh, shrinking me new ones. Second, getting an answer that I do not expect. Okay, I realized I just need to focus on the sign. So this is the kinetic energy change in the the X rays. And then the positive of that is gonna go to the electrons so took sort of modified Alex just do magnitudes. And I guess I didn't need a magnitude here. Whatever. Um And then if I like, I got a set number I got And then I converting it to electron volts. What I get is 1.13 k e v.

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