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A pesky 1.5 mg mosquito is annoying you as you attempt to study physics in your room, which is 5.0 $\mathrm{m}$ wide and 2.5 $\mathrm{m}$ high. You decide to swat the bothersome insect as it flies toward you, but you need to estimate its speed to make a successful hit. (a) What is the maximum uncertainty in the horizontal position of the mosquito? (b) What limit does the Heisenberg uncertainty principle place on your ability to know the horizontal velocity of this mosquito? Is this limitation a serious impediment to your attempt to swat it?

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$0.070 \times 10^{-28} \mathrm{m} / \mathrm{s}$

Physics 102 Electricity and Magnetism

Physics 103

Chapter 28

Photons, Electrons, and Atoms

Electromagnetic Waves

Atomic Physics

Rutgers, The State University of New Jersey

University of Sheffield

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.

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all right. The Heisenberg Uncertainty Relations says that the uncertainty in that position times the uncertainty in the mo mentum is greater than or equal to plants constant, led by two pi thie uncertainty, no momentum can be re written as m times the uncertainty in the velocity and in this case, the mass of our mosquito is 1.5 times 10 to the negative six kilograms. In part A were asked about the maximum uncertainty in the position of the mosquito, and that just comes from the dimensions of the room. So we have no idea where the mosquito is. Then it's maximum. Uncertainty is just five meters, which again comes from the dimensions of the room in part B. We want to know what is the minimum uncertainty in the velocity that comes from the uncertainty in the position. So using this equation, I have appear the minimum uncertainty will be Delta V is equal to H over too high and Delta X, where the Delta X his five meters ages 6.63 times 10 to the negative 30 for jules dot seconds and them, of course, is 1.5 times since the negative six and this comes out toe one point for times 10 to the negative, 29 meters per second, which is an extremely small number and it doesn't impose any riel impediment swatting mosquitoes.

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