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When sodium is bombarded with electrons accelerated through a potential difference $\Delta V,$ its $x$ -ray spectrum contains emission peaks at 1.04 $\mathrm{keV}$ and 1.07 $\mathrm{keV}$ . Find the minimum value of $\Delta V$ required to produce both of these peaks.

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Okay, so in this problem, you know, sodium miss bombarding electrons through different delta bees, and then we know there's peaks in the spectrum at these particular energies. We want to get the adult to be that produces thes peak. So let's write out the general formula. That would kind of bring all these variables together. So for the photoelectric effect, we have equals e time still to be equals the energy of the photons, Um, minus the work function. So we're told that we can apply this twice. So for the first time, our goal is to get Dell to be actually let me rewind. Um, I'm just gonna take this equation and then manipulated and salt for adult bees that's gonna be won over e dividing both sides by literally that's one over easy times e minus phi. And so let's get the, um, sodium find the sodium work function. I think it should be in the tax was gonna look it up online, so it looks like it should be That looks like it should be around two point. So there's two different values I'm seeing online. Lem. Let me look through the tax agency. If, um if there's, like, a nice table or something that we could use. Um, just to be consistent, if a cz consistent as possible with the book. Um 22 Mmm. Okay. I'm not seeing Oh, there's a nice table. Um, but it doesn't have sodium. Oh, it does have sodium. Okay, great. So that's 2.46 and I'm looking at table 27.1. So five is equal to 2.46 What kind of a little arrow Bye is two point for six you be And what we want to do solved for it all to be in each case. But of course, we want this in terms. I don't know, actually do have the energy. So for one were given that the peak is at 1.4 Can you be so we can say E I almost wrote Lambda is equal to one point off four e. B. So then you can get that, um Delta Bi is there for just gonna plug bad in here. So said what must be killing you be I must have missed Written that? Oh, yeah, baby. So Okay, I guess you can kind of see in this place, you can very basically just neglect this 2.4 because it's 100. So it's one point for you, B. So then that's gonna be so basically 1040 so you could do 1040 minus 2.4, derided by E. And then you got that, Um, see what that is? 1040 minutes. 2.4, um, and then divided by one of six. Extend to the minus 19. And so with that Oh, wow. This seems like a really big number. So 1040? Oh, yeah, that's a TV already. And then So you had converted to Jules by multiplying by 1.6 and then converted back to TV by dividing by 1.6. And so you actually just gotta just come for you to bite minus 10.2. So that's, um, how many sig figs do we have? And then we're subtracting. So we want to just keep the same number after the decimal, so you can only have two after two after the decimal. Um, and so see, so 10. 40? Oh, I guess that's fine. So I'm just gonna write down the full number. So that's 10. 10 37.6. And then for two. Problem the same rule. It's one point of seven. Katie, which is 10. 70 e v. And then you subtract Gonna work function 2.46 and then you got one. So let's see. 1067 points. Sex, um, thoughts.

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