The hydrogen atom is in the six Ju ST. Okay, In this question, there are four parts on part A. What's the principal? Quantum number. Okay, so the principal quantum number is he going to six, then the energy. Hey, energy is equal to minus 13.6 e v. Divide by N square. So this is equal to minus 13.6 e V. Divided by 36 which is minus 0.378 e V. Okay, then in part C, you want to find a popular, angular momentum quantum number. So G state, which means that our is equal to four. So they just highlight the answers or the previous parts a party. Okay. And then I see the popular, angular momentum content number is four. And then, ah, magnitude, Okay, is equal to square our times out last one times each bar. So this is equal to square 20 times 1.55 times 10 to the minus 34. So this is equal to, uh, 4.72 times 10 to the minus 34 two seconds. Okay, so this is the answer for policy. Okay. Then in Park City, while the possible values off many of the quantum number for each value we need to find her. Ah, the component. Um, And then we also need to find out, uh, electron orbital. The angle. That's the orbital angular momentum vector mixed with the Z axis. Mhm. So Okay, so the possible ah, values off, nl. Hey, things are how is he always equal to fall? So you have. And now it goes to zero. Last night s one as minus two as ministry and plus minus four. Okay, so we call that l m l ah, m l is between minus l two l in steps off one day. So the, um the corresponding Z component. Okay, so, for, uh, now it goes to zero. Okay, so this are lousy if you go toe zero each by zero. Okay, then. Lousy. Okay than for America's one. Ah, plus minus one. Okay, I will see. It goes toe class minus H bar, which is plus minus, Uh, 1.55 times 10 to the minus. 34 2 seconds. Yes. I didn't think that The Apprentice is okay. Then we have, uh And now it goes through last minus two. So l Z is equal to last. Minus two is far. This is equal toe past minus 3.11 times 10 to the minus 34 two seconds. And for M l, it goes to plus minus three. How easy it goes to cause my nose. Three H bar. This is equal to Okay, that's minus. Uh, this is 2.11 Sorry, it's 2.11 Okay, Um, right. M l equals two plus minus tree. We have l Z equals 23.17 times. 10 to the minus 34 2 seconds and then amount goes through. Class minus four. Elsie goes through class minus four. H bar is this equal to okay? Plus minus 4.22 times 10 to the minus. 34 two seconds. Okay, Okay. So, just to highlight some of the answers Yeah. Zero plus minus. H bar last minus two. Each bar last minus tree H bar, then pass minus four. H bar. Hey, this is a manitou, then next year, going to look for the angle. Okay, So for the angle, um, we'll be looking at this like driver. He recalled that as us. Yeah. Okay. So, um, services. Ah. Okay, So this is when, uh, I was He goes to zero, right? And then you have Elsie goes toe one to when l z equals when Americans to to and to make it clearer, e m l. Okay. And then you have, Ah, America's three. Just a rough sketch, okay? And then you have americans to fall, and then you also have the corresponding negative, the job, and l Okay, so the angle that we're interested in is the angle that Ah, okay. The angular, the orbital angular momentum vector makes with the positive Z axis. Okay, so, um okay, then. Well, just do it, uh, systematically for Americans to zero. So the angle is, uh, co sign. Ah. 1/0 over 20. Okay, so this is 90 degrees, okay? And then amount goes to one. The the angle is equal to, uh, cause I won over 20. So this is, um, 77.1 degrees. Okay, so for MLB goes to minus one, So the angle I z go through, I 80 degrees minus 77.1, So you get 10 2.9 degrees. Okay, so the angle again. Is the angle, uh, from all right. Strong, positive Z axis. Okay, this is how I'm going to define my angle. So on. Yeah, Than for Americans to to you have angle, because to cause I to over 20. Okay, so this is equal to 63.4 degrees. So no ml it goes to my s two. Your angle the 180 degrees minus 63.4 degrees. So this is 116.6 degrees. Okay, so next we have ML request to three. The angle is equal to cause I 3/20 and you get, um, 47.9 degrees. And for m l. It goes to ministry the angle. Yes. Hurry in 80 degrees, minus 47.9 degrees. So you have 12.1 degrees. Okay, then ml goes to four. The angle is equal to, uh, cause I for 20. Okay, so you get 26.6 degrees, and for americans to minus four, the angle is equal to find 80 degrees minus 26.6 degrees. So you have 153.4 degrees Mhm. So you know the answer. Okay. These are the angles for each M l. Okay. The anger is measured from the Was this, uh, the axis? Okay. All right. So that's all for this question.