Problem 16 Easy Difficulty

Calculate the minimum-wavelength $\mathrm{x}$ -ray that can be produced when a target is struck by an electron that has been accelerated through a potential difference of (a) 15.0 $\mathrm{kV}$ and (b) $1.00 \times 10^{2} \mathrm{kV}$ . (c) What happens to the minimum wavelength as the potential difference increases?

Answer

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Video Transcript

Okay, So for this problem, we want to get the minimum wavelength X ray. If a target is struck by an electron that's have been accelerated through uproot certain potential. Um And so, uh, let's see. So we want to assume for this one that we've accelerated the electron in its head of material on the material's very giving. And it'll easily give up, um, photons with no work function. So I wrote down the general formula describing the photo electric effect. And so we just want to set this fi equal to zero to get the maximum, um, the Macs, the minimum wage playing through the maximum energy. So let's put this in terms of wavelength, kinetic energy is equal to HC over Lambda Lambda is equal to HC over kinetic energy. Oh, and then I forgot to say on the kinetic energy of an electron if it has stopped, who would take a voltage, uh, v or taken energy of e times V to stop it? Use the charge of the electron B is the voltage. And then perhaps we Yeah, so we want to replace Katie bye, baby, and then plugging that into a calculator. Take this age time. See by 1.600 times I'm starting to the minus 19. Um, times V and then, we were told, is 1.5 kill or 15 kilovolts? So that's 15 123 So that gives 8.27 times 10 to the minus 11. Yeah, um, eaters soldiers ready like that. 8.2. So it's pretty small, um, 8.27 times seven minus 11. And then we want to evaluate that for, um ah, 100 kilovolts. So? So this would be our land of one. And then I'll just call the one for 100 kill Bold slammed a two. Um, almost no thought b is equal to, uh, 15,000. It's a B one b Ron, just to be totally clear, you want to do h C over e be too, and envy to is equal to 100 1000. And so we'd expect a lower wavelength. Um, so let's see what we get. But I got 1.24 times 10 to the minus 11 meters, and we want to get what happens to the minimum wavelength as a potential increases so much. Label this a be, um it decreases so the photons get more energetic