Problem 29 Medium Difficulty

(a) If the wavelength of an electron is $5.00 \times 10^{-7} \mathrm{m},$ how fast is it moving? (b) If the electron has a speed equal to $1.00 \times$ $10^{7} \mathrm{m} / \mathrm{s},$ what is its wavelength?

Answer

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Video Transcript

Okay, So for this problem, we're told that the wavelength of an electron is 500 Nanami interest. So that's in the visible light range. Of course, we wouldn't be able to see it cause it's not radiation. It's Ah, particle. Um and so way want to get how fast it's moving. So what we would do is use the abruptly wavelength formula H overpay and P S M V. So V is equal to H over, um, Lambda and you, just like everything in a massive electron 9.11 ton of minus 31. Um, come through the minus nine h over amd h m lambda Great. And then without we got it's going, Uh um who December seems a little bit too big. So this has it going at? Well, maybe not this. How's it going? At 1.45 times 10 of the three, So yeah, 1.45 times. 10 to the three. I know, like normally moving particles. I mean, they have pretty small, differently way blanks, but those air particles and then these air electrons and these were much smaller. So I kind of forgot about that shit when I was surprised at the speed. So this is pretty fast, but doesn't have an extremely small way, like because it's an electron. And then we want to get its wavelength given the speed. So we want to just plug everything into here. So then, in that case, um, using wth e. So this is a and then for B. If we use B is equal to one times 10 of the seven blue, it's almost relativistic. Probably gonna be small way blink. So we just want to take a JJ divided by M V. 1 10 to the seven. And with that I got 7.27 kinds, 10 to the minus 11. Wow, It's pretty small if it's like, almost like an X ray, but for an electron.