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Suppose that the uncertainty in position of an electron is equal to the radius of the $n=1$ Bohr orbit, about $0.5 \times 10^{-10} \mathrm{m} .$ Calculate the minimum uncertainty in the cor- responding momentum the minimum uncertainty in the cor- magnitude of the momentum of the electron in the $n=1$ Bohr orbit.

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Physics 102 Electricity and Magnetism

Physics 103

Chapter 28

Photons, Electrons, and Atoms

Electromagnetic Waves

Atomic Physics

Cornell University

University of Winnipeg

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.

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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 in this problem, we have uncertainty in position of the electron for an equal one about 10.5 times 10 to the minus 10 meters. So Delta Axe 100.5 times 10 minus 10. And not really what it is. That's almost the size of the radius. So I'm experimenting with new ways. Toe, hold the pen. That's 10 to the minus 10. And yeah, I guess that's right. And then, of course, uncertainty and corresponding mo mentum. So we want to use felt to saturate the uncertainty we have. Delta peed on himself the access h over to pie. So Delta P is equal to age over to pie times. Delta eggs. Um and so let's go ahead and live all of this into a calculator. Introvert. You. Hi. The X is five times 10 to the minus 10 crates of the answering P. The momentum is two point 11 times 10 to the minus 24. Double check. Two on one ton of minus 24 meters for a second. You Oh, it's, um, three units of momentum. So it's kilogram meter per second. And then actually, so they want the velocity of their momentum. Oh, yeah, I was momentum. Yeah. So that's what I got for that

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