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~LSlev" = 23,0e~3.6eVAn excited bound hydrogen eiectron IS in Stale n = 2 Afree electron witn 2.60 ev collides with Ihe bound electron Which of the following I...

Question

~LSlev" = 23,0e~3.6eVAn excited bound hydrogen eiectron IS in Stale n = 2 Afree electron witn 2.60 ev collides with Ihe bound electron Which of the following I5 true? The bound electron jumps Up to n = 3 and the free etectron leaves with evThe (ree electron does not transfer any energy I0 the bound electron Both Ihe bound electron jumping Up t0 n = 3 and the free electron leav with 0.71 eV AND the bound electron jumping up (0 n = 4 and the free electron leaving with 0.05 ev are possibleThe

~LSlev " = 2 3,0e ~3.6eV An excited bound hydrogen eiectron IS in Stale n = 2 Afree electron witn 2.60 ev collides with Ihe bound electron Which of the following I5 true? The bound electron jumps Up to n = 3 and the free etectron leaves with ev The (ree electron does not transfer any energy I0 the bound electron Both Ihe bound electron jumping Up t0 n = 3 and the free electron leav with 0.71 eV AND the bound electron jumping up (0 n = 4 and the free electron leaving with 0.05 ev are possible The bound electron jumps up i0 n = 4 and the free electron leaves with In order ior a bound electron In n = 4 t0 transition t0 n 5 the atoin would photon with frequency 0f The statement above IS best completed by the answers in rOw: Row absorb 7.39x 1013 absorb 1.31 X 1014 emit 2 05 X 1014 emi 7. 39 X1013



Answers

$\bullet$ The energy-level scheme for the hypothetical one-electron element searsium is shown in Fig. $28.24 .$ The potential energy is taken to be zero for an electron at an infinite distance from the nucleus. (a) How much energy (in electron volts) does it take to ionize an electron from the ground level? (b) An 18 eV photon is absorbed by a searsium atom in its ground level. As the atom returns to its ground level, what possible energies can the emitted photons have? Assume that there can be transitions between all pairs of levels. (c) What will happen if a photon with an energy of 8 $\mathrm{eV}$ strikes a searsium atom in its ground level? Why? (d) Photons emitted in the searsium transitions $n=3 \rightarrow n=2$ and $n=3 \rightarrow n=1$ will eject photoelectrons from an unknown metal, but the photon emitted from the transition $n=4 \rightarrow n=3$ will not. What are the limits (maximum and minimum possible values) of the work function of the metal?

In this problem. We'll talk about atomic transition. Consider that we have an atom. It has several possible energy lines. Energy level is, um eso I'm going to just write to energy levels here, you one and two. But this can be extended to mawr energy levels. And let's say that the atom is initially in the ground state. That is the smallest energy. And that is you want now. Transition occurs in the atom when the atom observed absorbs a fordham. And with that, the energy is increased. Okay, so the the atom must absorb a fulton that has an energy. Yeah, that is equal to the difference between 200 levels in two minutes. You want, in this case, mhm on. In order to transition back to the ground state, the Adam must emit a photon that has this same energy here as before. Eat guns. Also, in order to completely ionized the Adam, we need the final energy off the election. The electron that is ionized, that is thrown out of the atom to be at least equal to zero. So the final energy of the atom is equal to the initial energy that C one plus the energy of the incoming Fulton. This must be greater than zero. So e gamma must be greater than minus you want? So now we can move on to your exercise. What we have is an atom that has these energy levels here, mhm and in question A. We have to find what must be the energy of a off Fulton search that an Adam initially at the ground state is ionized. I noticed that since the government must be greater than minus E one greater or equal than actually than gamma must be greater than the ground state energy level. That's 20 electoral votes. So the minimum energy is 20 electoral votes. That's the answer to question eight in question be we have ah, Fulton. Ah, a photon that has an energy off 18 electoral votes and the atom is initially in the ground state. So we one is in which, minus 20 like in this case, notice that's the final Energy is equal to the initial energy. E one was the energy Fulton, and this is equal to minus 20 plus 18. This is minus two electoral votes. Electoral votes, now minus the electric votes, corresponds to end equals four. So this is a four. So the atom is now at the end, equals four. Enter your level and we want the atom to transition back to the ground state. So from and people before we want the atom to go to n equals one. And we want to know what energies can be emitted by the Fulton in this transition. So notice that for the atom to go from n equals four training calls one there are several are possible steps can go from 4 to 3 to 2 to 1 can go from 4 to 3 to one from 4 to 2 to one or from four directly to one. Um so notice. That's the energies. The possible energies emitted by the sultan. I'm sorry. The possible energies off the photon emitted by the atom is equal to four minus three. This is the first one. The second one is Ah, he four miners. You too. Instead of yeah, writing like this, I'm gonna write it for three for two. Then we have 41 This is the energy from four you want, and we have 32 31 and finally, 21 mhm and Now we can calculate the energies. So if four minus the three is minus two minus minus five, that's three electoral votes before minus E chew is minus two minus minus 10. That's eight electoral votes. E 41 is minus two uh minus minus 20. There is 18 electoral votes. Minute E 32 is minus five minus 10. It's five electoral votes, and the three one is I'm sorry. Yeah, 31 is minus five minus minus for any That's 15 electoral votes. And each year we won is minus 10 minus minus 20. That's 10 electoral votes. So these are the possible values of the energy. Okay, any questions? See, you have to say what would happen if, uh, a photon within energy off eight electoral votes was to strike the atom? Um, given that the atom is initially in the ground state. Well, um, in the ground state is minus two. Any electrical notice that, uh, if the atom waas to transition to a higher energy level, the final energy would be E Girma Lazy one. That's minus 20 my plus eight. So this is minus 12 electron volts. But notice that there are There is no state with an energy of minus 12 electrical s. So this means that the atom will not be absorbed. I'm sorry the fulton will not be absorbed. And hence the atom will not transition to a higher state. Okay, then, in question D, we have to consider that when the atom transitions from n equals 32 n equals one and equal. So I'm sorry. And when it transitions from n equals three to an equal one, the Fulton in admits will be able to, uh, reject Ah Fulton Ejected Electron. I'm sorry. From a certain metal. Yeah. Now, when the photon traditions remain equals 4 20 equals three, when the atom traditions from n equals 14 equals three, then three. Adam, the Fulton admitted, will not be able to inject such an election and are going to find more. What are the minimum and maximum possible values of the work function of the matter? Remember, First, that the work functional motto is the energy necessary in order to eject and lack from from that matter, the energy off the end equals 3 20. Close to transition is equal to five electoral votes. We've already calculated it. It's this one here from three 21 is this one here. 15 electoral votes from 4 to 3. Its three electoral votes. No notice that an energy of five electoral votes is able to eject an electron while an urge of three electoral votes is not so. The minimum value of the energy is three electoral votes, while the maximum value of the work function is five electoral votes. And this concludes your exercise.

My discussion. We have a hypothetical eto I call c s. Um, this is the energy level scheme. So given this energy that we're gonna find ho mush Energy's quiet toe ionized electron from the ground level, that is, if the Etame Cynthia growing states over. Sure. And it was the one. Well, the energy would just be taking energy Infinity minus away the energy Oregon State. And as we know, because the various given here are negative. Instead, it is with respect over a friend's studi organization, energy to the ionization. And you must be Syria. Levy therefore, the amount of energy required specie il minus negative 20. Just do nt v nobody export. We are told that it actually Stutts ABS ops and 18 TV full time. Right? So from the Garden state, absolute a TV goes up. Pottery two d n equals two forced it, right, because negative trend he plus 18 gives us native too easy. So it must be a d. And it goes to fall and you're fine. You ask ourselves why the possible energies that the meter photons can't half right as it returns to the ground state. So they're quite a few of possible transitions gonna go through over here first is a single emission orbital directly. This would be 18. The TV. We have another possible transition that goes half down. So just any question to this will be negative. Two minus native 10. She gives us a TV, and then we have from many close to two down to just one. We just had a baby. Do we have from four down to only tree? It would be she e v. And then from tree Don't to to which is five TV and then from two really have one day structure to one so that transition is ready accounted for. And I possible what would be for tree or the way too one can't disobey, eat to any minus five, which is 15. Even so, this should be should cover or possible energies that he falls once Can't have cause it covers all the possible transitions. Know what would happen if a full tone if it TV off energy hits? Oh, go on, States here when there is a TV default on Well, the thing is, there is no energy that is just a TV higher than our becasue one state, right? The closest is intercourse, two to which is 10 TV away. So as such, this is no enough energy to excite the atom and therefore actually doesn't get up stopped for us. But you're given that. Ah, some of the photons emitters from 70 transitions will reject for the restaurants from some unknown metal. Right? But the transition from any coastal for Nico's tree that's not goes to forge an industry. We're not in no e checked the full it actually from the metal. So this energy get. What we hear is tree E v. So the energy only four twenties tree V But for the rest off the transitions night from tree to to treated two is five TV treat a one IHS 15 TV. So he highest. I'm sorry. The minimum possible value 40 for the function of the metal unify wife, the smallest possible value that will fit, or destry quite hear that it doesn't emit any full electronics tree V, but it does. At 5 15 the smallest possible would be for right Oh, actually, somewhere above tree evey any value days above TV. Just call ISTEA. Function cannot be a TV, but any very desert buff TV. And for the maximum value, you can have be five. Because this fire TV was to eject for the electron when you were function. Is that five?

Here, we're going to look at an example of an energy level diagram with just for energy levels notice that they are all negative energies, which means that this is a bound system. So our electron is bound inside of the material. And the first question is, how much energy would it take to lionize this adam, pretend it's an atom. And the idea is what you're doing is liberating the electron so it no longer has negative energy. So you're asking how much energy do you have to add to get the electron from minus 20 electron volts all the way up to zero electron volts. And of course the answer is add 20 electron volts. So that would be your ionization energy. Um the next thing to think about is I suppose someone added 18 electron volts to the electron in the ground state. Okay, so clearly what will happen is the electron will get boosted up to the and equals four state. And the question is, what will that electron do? Well, it will fall back down to the ground state in many different ways. And we want to calculate all the energies that the electron could potentially emit. So that involves all pairs of energy levels starting with N equals for It can go to three or two or one initially. And we'll call those 1, 2 and three. Well, if we don't have to number them, that could get confusing and then it could Wind up in the n equals three state and that it will have two possible transitions. Or it could have fallen down to the an equal to state and there's one possible transition. So let's just figure out all those possible energies. Um and there's also two electron volt emission if the atom was ionized. But here we're assuming it just got and equals four. So and equals 4-3 Is a difference of three electron volts. Um 342, two is eight electron volts And for 2, 1 directly Is the full 18V of emissions. Then we've got n equals three going quips wrong color. So we have three going to two is five electron volts and three going to one is 15 electron volts and only one more possibility and equals two. Going to back to one is 10 electron volts. Okay, so, um the next question is supposed that the particle, the electron is in the ground state and along comes um An eight electron volt photon. What will it do? Um so the electron is in n equals one. And if we look at all the potential transitions, 12 Takes 10 electoral votes. And then there's some higher ones. Um what we see is there's not enough energy for that photon to do anything. And so the photon will go through the material. Um photon does not interact and go on its merry way. Mm. Okay. And finally, uh let's see the next thing is um we are going to look at photons that come out of certain transitions in this material and we will see what they do to another material. So this is kind of the photo electric effect idea. Um so we're going to take the photons that come from this atom and we can find their wavelengths. But we know that um The 3-2 transition, Which is a five electron volt does create a photoelectric effect And 321, Which is the 15 electron volts. Both of these cause photoelectric effect In some other material. We don't know what it is but some other material, however, we find out that the 4-3 transition does not, and that's a three electron hold, no photo electric effect. And of course this gives us some information about the work function of the material, recall that the work function is the minimum amount of energy or potential, depending on what units you want to use. Minimum amount of energy. Two liberate, just barely liberate electrons from your material. Um And we see that uh whatever the work function is, let's call it, w it has to be greater than three electron volts because three electron volts does not work. And it has to be less than or equal to five electron volts. Because five electron volts is the first energy we see for which it works. It may be a little bit less than that. So we'd have to have more data between three electron volts and five electron volts to identify that work function.

So just so this exercise, we have to recall just a few things regarding atomic transition. So here I drew a energy diagram for a random eight. Um, and I'm showing you in green the absorption dynamics that this aid, um can have. So the Adam we can go from the ground state to any of these higher energy states by absorbing a photo that has an energy that is equal to the energy gap between the ground and the excited state. And in blue, I'm showing you the emissions that this item can have. So basically, if the item is in a higher state, this item can decay to any other state towards the the ground state. So, for instance, the eight, um, can go for the from the highest state directly to the ground state and emits a photon that has an energy again equal to the energy gap. And likely the eight, um, can go from the highest state to an equal to two and then from any country to to go to an equal to one. Okay, so, uh, the energy of the photon that is going to be involved with the atomic transitions is going to be equal to the final energy of data minus the initial energy. This is roughly you can see a but in the magnitude here, uh, this has to be cultural definition to the the importance energy, which is age C, divided by Lambda, on which ages plank blinks constant that I wrote. The value that I'm going to use here and see is the light speed, which again I wrote here in green develop that I'm going to use throughout the exercise, so please check it out. Okay, so in this exercise, we are going to suppose that we have this item is a random eight. Um and this Adam has these four energy levels on which the ground state is an equal. Chuan has the energy of minus 20 electoral votes. Um, in question a, we are asked, how much energy does it take to ionized this item? So to iron is an item you have basically you need to remove the electron from the nucleus belt. So in this case, we generally define the ionized energy level as being the energy level of zero e V. So the amount of energy required to ionized is going to be, uh, iron minus the ground state. So the ground state is this minus 20 e v and the e i 00 So the amount of energy that we need to organize this item is trying to e v. Hi. Okay. Now, um, question be we want to find the energies for the emitted photons F d A. To make the transition from any culture one to, uh, a higher state on which the difference between you won and yen is going to be equal to 18 electoral votes. So you can notice here that the transition that the data is going to have is from the ground state to an equal to four. So this is going to be the absorption. Now we want to calculate what is going to be the energy of the emitted photons during the emission. So you can see if that the emission starts from any culture for and go to any lower state. But it has always should go towards any cultura. So first we can have the transition 4 to 1. Here. We can also have a transition. 4 to 2 and then 2 to 1. We can have a transition for 23 and then 3 to 2. And of course, we can have the transition for for a long three, 21 So all we have to do is to calculate the energies between all these atomic transitions. So let's right here. Um, so starting with 4 to 1? Yeah. So for this particular transition, the energy of the emitted photo, as you can see here, is going to be the magnitude of, uh, minus two e v plus 20 evening, which is equal to 18 electoral books. So this is one of the possible, uh, emitted photons. So for the Fulton, from transition 42 we have, uh, minus to my, uh, minus minus. Stan Oh, which is equal to eight election books. Okay, Mhm. Now, from the for the transition 4 to 3, which is this one we're going to have. So a level three has an energy of five. I'm sorry. So, um, when Stevie blows five v b, which is three e v. Yeah. Now for three to chew, we're going to have Yeah, um I understand TV. Yes. Five vb magnitude. So five vv no. For 321 Keep. We're going to have 20 e v. Bliss 10 e v. Notice that here. I'm not bothering much about the order of the final and initial states because I'm using the magnitude so it doesn't really matter, Tony v. And finally, I think we have from two to the ground state. Um, actually, there's a mistake here. This is five. So this must be 15. And here. So for the ground state, we have this energy for the first excited state we have. This sorry is actually 10 mhm. Okay, so these are the answers for questions. Be Let me put here all these values. Um okay, So now questions see questions, See asks us to suppose what happens if we have a photo of Let me draw here in red. We have a photo that is going to collide with the atoms, and we know that the photons energy is eight e. V. So the exercise asks us what is going to happen with the ADA after these photons, you know, collides with the ADA. So in this case, you can see that, uh, the only type of dynamics that can happen since we have an incoming photons is absorption. But you can see here that the shortest amount of energy required for a absorption dynamics for this aid, um, has to be 10 electoral votes, which is the energy gap between the two and the one. But since the photons energy is much smaller than the required energy, then nothing happens. The item is not going through any type of transition. Nothing happens if the item is in the ground state, because the energy of the item is not enough to make the transition. So sorry. The energy of a photon. It's not enough. The energy of the photo, remember, has to be equal to the energy gap. No question, the finally, um Okay, So question details is that for this particular eight? Um uh, the ejected photons from the transition Street two and 31 Yeah. So let me highlight these transitions here. So the photons emitted from three to and 31 uh, are enough to, um, make a are enough to eject photo electrons from an random metal. But the photon emitted from this transition here, in the other hand, is not going to do anything to this same random metal. So the exercise asks us. Then what are the limits of the work function of this random, um, metal. So remembering that for the photo electric effect, um, we have that the kinetic energy of the photo that gets the attached from the metal is going to be equal to Sorry. The the the kinetic energy of the election that gets the attachment from the atom is going to be the energy of the photon that collided with the medal minus the work function. Mhm. And here we can see that the work function is, in fact, the minimal energy required to remove the, uh, the elections from the the the metal. Okay, so in this case is this is the definition of, uh, f zero. Okay, so, uh, for transitions three, 22 We know that the energy of the emitted photons where it should be five e v. And for 321 we know that the energy is going to be 15 e v. No. So we know that these two energies are going to make the photoelectric effect happened in the meadow. So these two energies works, but the energy from 4 to 3 Yeah, that we calculated to be equal to three election votes is not going to be enough. Okay, Okay. So in the sense we can define a range for the work function. So the work function? Uh, well, we can see that the maximum value for the work function can be roughly five e V. But the work function must never, ever be less or equal to three election votes. And with this, we conclude the exercise.


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