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$\bullet$ The photoelectric work function of potassium is 2.3 $\mathrm{eV}$ . If light having a wavelength of 250 $\mathrm{nm}$ falls on potassium, find (a) the stopping potential in volts; (b) the kinetic energy, in electron volts, of the most energetic electrons ejected; (c) the speeds of these electrons.

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Physics 102 Electricity and Magnetism

Physics 103

Chapter 28

Photons, Electrons, and Atoms

Electromagnetic Waves

Atomic Physics

Cornell University

Rutgers, The State University of New Jersey

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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The photoelectric work fun…

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When light of wavelength $…

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In a photoelectric-effect …

okay. And this problem? We're told that, um for potassium, the foot electric work function is 2.3 evey. So let's go ahead. Write that down. Bye as 2.3 e feet. And undo that. And we are concerned with light with hazard, which has a wavelength of 250 nanometers, and we want to get the stopping potential. So Lamda is 250 nanometers. So we want to use this equation, which is from the text. You may not is equal to the energy of the photons, so that's gonna be HC over lambda eyes that minus for polos. Give me one second one. A pause. The video. I'm sure I could think through it, but I'm just gonna look Okay, so we want to subtract the work function. And so for trying to solve for this stopping voltage and faults, we just wanna, um we can evaluate this side and then divide by e. So if I plug this all into a calculator, um, So, yeah, h I'm gonna use the one that is in units of electron volts. So that's 4.14 times that of the minus 15. Cuz it's pure light three times eight. And I'm gonna go ahead of posit video. I plug that into a calculator. Okay, so this is equal to 2.7 bebe 70 And so, uh, to get, and then that's in electron volts. And so to convert this to Jules, you would divide it by, um, are Yeah, you were divided by E. Um, And so that's exactly what. So, actually, let me rewind and explain that differently. If you um it's all for every night you're taking your dividing by e on both sides, right? And then But if you divide by e ah, number an electron volts, then you get it in S I u nits and so, um like And so therefore, um, be not is just equal to 2.70 votes. And then the question that asks what's the kinetic energy? And then, um, again. So if you're converting this thing to Jules, you're dividing it by e. And so, um, you'll get the same thing the same value for the kinetic energy that it's 2.7, um, jewels. It might be nice to kind of think through it yourself If that didn't seem convincing to just imagine to yourself how you would convert this number two jewels. And then how? Because, like, this is equal to Katie. So in either case, you're riding by you great. And then for see what we want to D'oh! Oh, wait. Actually, let me pause. Actually, I take that back. It is not in jewels. It's, um, TVs. I'm gonna think through that, um, this well, so yeah, so let's just kind of think through So they're kinetic energy is gonna be just equal to 2.7 TV, Um, s so you don't have to worry about dividing by E in the case that you're calculating the kinetic energy. So then the kinetic energy would have units of Phoebe Great. And then you want to convert it to Jules to get the speed for the next one so you can do 1/2 on B squared equals que es. And then, uh, V is equal to the square root of the kinetic energy. Times two divided by the mass. And so you want to take this 2.7 and converted to Jules by dividing it by E. Um, so I'll just write that down 2.7 provided by ae. You don't have to do anything to two. And then the mass of potassium. Let's look at that, huh? Mmm. At 6.492 times 10 to the minus 26 kilograms. So I'm gonna posit video while I calculate with the speed is and I guess I'll just still write this. I'm here, actually. Sorry about I mean, one small mistake. It's not divided by E, but multiplied by ye. I just remember it by the jewels are always much smaller than e b. So it's actually multiplied by E. And then when I made that correction, I got 3650 meters per second groups three green.

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