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$\bullet$ (a) The uncertainty in the $x$ component of the position of a proton is $2.0 \times 10^{-12} \mathrm{m}$ . What is the minimum uncertainty in the $x$ component of the velocity of the proton? (b) The uncertainty in the $x$ component of the velocity of an electron is 0.250 $\mathrm{m} / \mathrm{s} .$ What is the minimum uncertainty in the $x$ coordinate of the electron?

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0.4628 $\mathrm{mm}$

Physics 102 Electricity and Magnetism

Physics 103

Chapter 28

Photons, Electrons, and Atoms

Electromagnetic Waves

Atomic Physics

University of Washington

Simon Fraser University

Hope College

University of Winnipeg

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.

03:49

(a) The uncertainty in the…

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00:55

04:57

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(a) The x-coordinate of an…

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(a) The $x$ -coordinate of…

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If the uncertainty in th…

03:20

In a nonrelativistic exper…

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What is the minimum uncert…

all right. In part, they were given uncertainty in the position of a proton. Um is two times 10 to the negative 12 meters and the mass of a proton is 1.67 Him send the negative 27 kilograms and the Heisenberg Uncertainty Relation says that the uncertainty and X times the uncertainty in the mo mentum is greater than or equal to things constant divided by two pi. And we can translate the uncertainty in the mo mentum toe uncertainty in the velocity using that p e is equal to envy. So adult API becomes m guilty, so the minimum uncertainty will be given at the lower bound of this inequality. So we have Delta V the minimum uncertainty. Envy is equal to H Over to Pie and Delta X, where adult access the two temps into the negative 12 and M is the 1.67 times into the negative 27. And H, of course, is 6.63 times and the negative 34. Jules got seconds in Part B. We now have an electron and instead of given instead of being given the uncertainty in the position, we're given the uncertainty in the velocity. We just rearrange the formula for part A. You have Delta X is h over to pie M Delta V and them that we use this time is the mass of an electron, which is 9.11 times 10 to the negative 31 kilograms.

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