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$\bullet$ (a) In an electron microscope, what accelerating voltage is needed to produce electrons with wavelength 0.0600 nm? (b) If protons are used instead of electrons, what accelerating voltage is needed to produce protons with wavelength 0.0600 nm? (Hint: In each case the initial kinetic energy is negligible.)

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A) 419 $\mathrm{V}$B) 0.229 $\mathrm{V}$

Physics 102 Electricity and Magnetism

Physics 103

Chapter 28

Photons, Electrons, and Atoms

Electromagnetic Waves

Atomic Physics

Rutgers, The State University of New Jersey

Hope College

University of Sheffield

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) In an electron microsc…

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$\bullet$ (a) In an electr…

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What accelerating voltage …

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(a) What accelerating pote…

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$\bullet$ (a) What acceler…

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In a certain electron micr…

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What voltage is needed to …

02:35

In an electron microscope,…

01:23

Electrons in an electron m…

05:33

The electrons that are use…

Hey, so in this problem we have an electron microscope and we want to get the voltage needed to produce electrons. Um, with the wavelength of 0.6 nanometers. So Lamda equals 0.6 and then I'll add all the sig figs, Nano meters. So that's three sink figs. And, um so we need to figure out their velocity. Or from from this, we can get their velocity through. Lambda is equal to each over p and P S M V. So V is equal to h over. Um um Lambda. And then we know that kinetic energy is equal to 1/2 on B squared. So instead of e, I'm gonna write this whole thing, so it's gonna be a TSH over m lambda quantity squared. So that's gonna be one over to, um, each squared or Lambda squared. So when I go ahead and plug that into a calculator, let's see what I got. It's quite over to him. Lambda Squared Action. Linda's Point. 06 centimeters. 12 times 9.11 times 10 from minus 31. Problem applied by that being good. I everything in my too and I'm gonna get me up And with that, I got the was like homing for Oh, yeah, the kinetic energy. And then maybe I should convert it to electron folds. Let's go ahead and convert it to electron folds. So I'm gonna divide by 1.60 times 10 minus 19 to do that conversion. And then I got 418 TV. 00 that's perfect, actually. So this would be the kinetic energy, um, for 18 evey and then in general. So that's equal to Q times V. And so, um therefore of as we've seen in other problems, that means the voltage is 418. You be, ah, 418 holes. Excuse me, and we want to go next. What the? Let's see. Protons are used in wide voltage is needed if protons are used than what we need is just to change the mass so massive a pro time. I think it's 1.67 times 10 to the minus 27. So that's how I would change it. Double check that number s O fine. 167 Come. Let me something y'all comes right, So that, um, you would just need 0.2 0.228 year olds. So I guess so. This is my answer for a And then my answer is no label that a And then my answer would be would just be, you know, modify this with changing your M. And then I got was 0.2 to 8. Wants. Yeah. And then So, um, so, Yeah, I'm kind of taking into account already. Sort of did approximation. The initial kinetic energy is, um, negligible. It's home. So it's really all, uh, So you would say the change in energy is equal to the kinetic energy and in a kinetic energy comes through here. Um, so, yeah, hopefully that's clear. I think there's examples.

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