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When an electron drops from the M shell $(n=3)$ to a vacancy in the $\mathrm{K}$ shell $(n=1),$ the measured wavelength of the emitted $\mathrm{x}$ -ray is found to be 0.101 $\mathrm{nm} .$ Identify the element.

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Menna G.

February 2, 2021

An electron in a hydrogen atom jumps from some initial Bohr orbit n¡ to some final Bohr orbit n, as in the figure (a) If the photon emitted in the process is capable of ejecting a photoelectron from tungsten (work function = 4.58 eV), determine n. (b) If

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In this exercise, we have an electric on a certain Adam transitions from the M shell that is from the N equals three energy level to the K shell, which is The animals want energy level, and in the process, it emits a fulton that has a wavelength. People, too, is your point ones. You're one No, no meters and we want to find what element this is. And in order to do that, what we need to do is to calculate the atomic number Z of the elements. Uh, so let's start first by calculating the energy of the immediate fortune just a gum and that's a C over London. HC is 240 and I from vote nine millimeters, divided by girl. Bye. I'm sort of Linda, which is is your 0.101 and the meters and this is equal to 12.3 killer electoral votes. This is the energy of a photon. But another way of writing it by conservation of energy is that the energy of the immediate photon is equal to the energy off the M shell. That is the third energy level, minus the energy off the Keisha that is the first energy level. So what we need to do is to calculate the energy of these levels. So remember that the energy when Adam maybe reading s minus the effective atomic number Z f squared times 13.6 electoral votes divided by and square where the effective atomic number is the atomic number Z of the element minus the number of electrons that are shooting the the shell that we're interested in. Okay, so in our case, you can call Kate E three. That's gonna be minus the effective at the number, which is Z minus the number of electrons that are shooting the third energy level. Ah, In this case, there are eight electrons in the in the Al shell in the second interview level. And there is one election in the decay shell because the case show that there is one vacancy there. That's why three electricity is transitioning from the third to the first. So, in total, there are eight plus one elected in shooting the third energy level for that reason, Uh, the effective atomic number. Easy. Mine is not square times 13 0.6 electoral votes divided by night. Okay, I'm gonna expend this. So have that. E three is equal to minus 13.6 times. Is he squared over nine minus two Z plus night in electoral votes. Okay. And I'm gonna highlight this because this is gonna be useful. Also, we can calculate the energy of the first energy level. So the energy of the first energy level is minus Z minus one. Because there's in the first energy level, there is only one election shooting. Ah, and the shell times 13.6 electron volt. And this if we expand Yes, minus 13.6. Is he squared? Minus two Z Bliss. What? Okay. Oh, no. I'm also gonna high like this so you can go back and start. This is e wa 93. So you can go back to the Gamma here and apply what we found for the energy of the of the shells. So I have that Girma is people to be three minus you want. And this is 13.6 times eight is he square over nine minus eight. Okay. And this is equal to We have found the energy of the Fulton before. It's up here. It's 12.3. Killer like from vote. So the energy of the fall tennis 12.3 times sent to the third in electoral votes. Okay, so we have 13.6 times eight is he squared over nine minus one. This is equal to 12 0.3 times into the third. So Z square over nine minus one is able to 12.3 times 10 to the third, divided by 13.6 times eight. So Z squared minus nine at over nine minutes. One is 113.1. So Z square is 113.1 times nine, which is 1000 and 26 point 46 and z is able to 32. Okay, it's actually a little bigger than 32 but that's only due to the approximations that we did when making the calculations. Okay, so if we look up in the periodic table what? What element corresponds to the atomic number 32. We're gonna find that the answer is Jermaine iam

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