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.