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$\bullet($ a) What is the energy of a photon that has wavelength 0.10$\mu m ?$ (b) Through approximately what potential difference must electrons be accelerated so that they will exhibit wave nature in passing through a pinhole 0.10$\mu m$ in diameter? What is the speed of these electrons? (c) If protons rather than electrons were used, through what potential difference would protons have to be accelerated so they would exhibit wave nature in passing through this pinhole? What would be the speed of these protons?

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4.0 $\mathrm{m} / \mathrm{s}$

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 Washington

Simon Fraser 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.

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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If the de Broglie waveleng…

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In an electron microscope,…

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In a supercollider at CERN…

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(a) What accelerating pote…

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$\bullet$ (a) What acceler…

Okay, so in this question, we're talking about photons on the wavelength of 0.1 micrometer. So, um, let's see where this problem goes. He is equal to HC over lambda. And then we were told, Lambda is 0.1 micrometers. That's 0.1 times 10 to the minus six meters. And what we want to do is do h crimes point at any time since two days and then goodbye to buy 0.1 times 10 to the minus six. Um, it's not really what they asked for. What is the energy of the photo? And I guess I didn't even you, you be so 1.62 times 10 to the minus 19. And so I divided it by either charge of the electron. And I got, um how many sick think? Should I do it, too, to Sig Figs. So then I get 12 uh, 12 evey for a and then for B. We want to know, um, that if we're accelerating electrons through some potential difference, um, and we want them to exhibit wave their wave nature if they're gonna pass through, um, a pinhole of that size, and then what's the speed of the electrons. Oh, that's kind of interesting. And so, um, we want they're so basically weather to royally way like to be on scale with the size of this pin hole. So we, um Because in general, whenever the whatever dimensions that abruptly wavelength is, um that's where you'll see the wave of facts. And so, for normal matter, that becomes very, very small. Um, so we don't generally see the wave effects. So what we're gonna do then, um, is do Lambda is used this for a lambda and then set that equal age overpay and okay, and then Okay, we want to know, um, the potential difference. Okay, so we have landed. We have aged so we can get P so you can get that p is equal to age over lambda. And then, um P But then we eso thinking about sending a car. Bola let me back up. So this is the pea that we need to get so we can calculate that. Why? Just dividing this number by the river dividing age by this number. Um, but then to associate that with the voltage, we need to figure out how many, um, what potential difference would get an electron to that potential difference or excuse me to that moment. Um And so basically, through energy conservation, you can say you could turn Theo energy gain through being accelerated through potential difference, which is e delta V into kinetic energy. And that's p squared over two m. So then, if you take this equation and sulfur V, you just want to take this whole thing and divided by E sold out to be a sequel to P squared over two m I wonder if they will end up connecting Find out. So P is plugging in this for P. Then we got h squared over Lambda squared. Um, yeah. Oh, and then times two can't forget this too. And so far, I'm not quite seeing the connection. But that's okay. My go ahead and start calculating and then a guy, and I'm gonna use this for my Lambda apostle video while I do this calculation. I got a 0.1 villa folds and double check. I didn't forget that factor of two to limit squared m e Great. So now what I want to do is, um, get their speed. So, getting this speed, um, that's just Let's see. That's just calculating M V. And so, um, so I guess loving start labeling this, actually. So this is all for B? Oh, I didn't leave with them. Um, so P is m b fee is P over AM P is equal to H over Lambda. So that's H over lambda m. Something to go ahead and calculate that h divided by point line. Extent of the minus, um, six. And then, Well, Piper, the mask times 9.1 own. I'm kind of 10 to the minus 31. I mean, I got, um, 7.3 times 10 to the three. And next, if protons were used, um, me. So we just basically need to review these calculations, but changing the mass to 1.67 times 10 to the minus 27. So I'll go ahead and do that, and maybe I'll put it on a separate page. So, um, so then so that we'll call this see so Delta V is equal to six seat with. That's 1.67 times come to the minus 27. It's me 8.2 times 10 to the minus eight. But we're swapping for a 0.2 times out of my face. That's really not that much kind. Reflect on these numbers, sort of at the end here. Okay? Fools. And then for the speed, that's just plain B. I can just redoing the calculation. I got 1.67 times kind of the minus, um, 27 and then I get four readers per second. So maybe the idea is they like you. Um that is possible. Thio. See the interference effects of electrons through reasonably sized on pinholes, which is probably more the principal along, huh? For, um, excuse me, The principles behind tm microscopes is that you can really see this wave behavior. Um, but getting electrons protons to go to a sort of reasonable speed, so four meters per second and then for the block for the protons and then the boss of the electrons is actually much higher. Um, yeah, that's so interesting. And doesn't doesn't really make sense that the velocity for electrons has to be much bigger. So I guess for so I guess this really specifies the mo mentum in either case, like given that we want a certain Lambda. And so because the masses smaller, the bee has to be a lot bigger or for the electrons interesting

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