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$\bullet$ (a) What is the de Broglie wavelength of an electron accelerated through 800 $\mathrm{V} ?$ (b) What is the de Broglie wavelength of a proton accelerated through the same potential difference?

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0.001013 $\mathrm{nm}$

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.

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all right. So if a particle with a charge equal to the electron electron charge on is accelerated through 800 volts, then by definition, and has an energy of 800 electron volts, that is, by definition of an electron. If we want to convert this to Jules, thank you. That's going to be 800 times 1.6 times 10 to the negative 19 Jules. And that's that comes out to 1.28 times Center. The negative 16. So now if we want to know the wavelength of a particle that has this kinetic energy, then we use the Debra Ugly relation here, combined with the relationship between the mo mentum and the kinetic energy. So we have a chew over to I mean, in the first part we used the mass of an electron, and the second part we use the mass of a proton, so plugin planks constant and divide by the square root of two times 1.28 times in the negative 16 in part a. Them that you want to use the mass of an electron just a 9.11 on the night of 31 and in part B the mass that you want to use the mass of a proton, which is 1.67 times in the negative twice.

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