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A photon with wavelength of 0.1100 nm collides with a free electron that is initially at rest. After the collision, the photon's wavelength is 0.132 $\mathrm{nm}$ . (a) What is the kinetic energy of the electron after the collision? What is its speed? (b) If the electron is suddenly stopped (for example, in a solid target), all of its kinetic energy is used to create a photon. What is the wavelength of this photon?

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3.89 $\mathrm{nm}$

Physics 102 Electricity and Magnetism

Physics 103

Chapter 28

Photons, Electrons, and Atoms

Electromagnetic Waves

Atomic Physics

Cornell University

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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A photon with wavelength o…

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A photon with wavelength 0…

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A photon with wavelength …

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An incident $x$ -ray photo…

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An incident x-ray photon o…

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A photon of wavelength 4.5…

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A 0.110-nm photon collides…

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A 0.110 -nm photon collide…

All right. So the energy change of a photon is given by Excuse me. The energy of a photon is given by H C over Lambda. So if we want to know how much energy eyes imparted to an electron when a photon scatters off of it, we just need to look at the change in energy of the photon. Um, every arranged the values here so that the energy gained by the electron is positive. But, you know, you could write this in either order and just be mindful of the sign. So land ah starts out at 0.11 night up X unit, 0.11 Nanna meters and after scattering has a wavelength of 0.113 to Nana meters. So we plugged this in and we can factor our tend to the nine. That's common to both terms. And this comes out to 319 evey that's passed to the electron. Now, if the Elektron is brought to rest all this 319 electron volts, um gets past two the photo on that it creates. So if we want to know the wavelength of that photon weaken just take Lam the equal to H C. Over E. So this is 4.14 attend Send the negative 15 evey that seconds times three times. 10 to the eight meters per second. Yeah, divided by 319. And this comes out to 3.89 nano meters. Yeah.

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