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The behavior of the Tr-electrons in a Ceo molecule can be approximated using the particle in a sphere model: Using reasonable approximations for the diameter of the...

Question

The behavior of the Tr-electrons in a Ceo molecule can be approximated using the particle in a sphere model: Using reasonable approximations for the diameter of the molecule, calculate the energy required to promote an lectron from the highest occupied Tr orbital to the lowest unoccupied orbital: Recall that there are 60 7 electrons in a Cwo molecule and that we can make the assumption that you can place two electrons per orbital, What are the frequency and wavelength of the light required to ex

The behavior of the Tr-electrons in a Ceo molecule can be approximated using the particle in a sphere model: Using reasonable approximations for the diameter of the molecule, calculate the energy required to promote an lectron from the highest occupied Tr orbital to the lowest unoccupied orbital: Recall that there are 60 7 electrons in a Cwo molecule and that we can make the assumption that you can place two electrons per orbital, What are the frequency and wavelength of the light required to excite the electron from the highest occupied to the lowest unoccupied T orbital?



Answers

For fixed electron energy, the orbital quantum number $\ell$ is limited to $n-1 .$ We can obtain this result from a semiclassical argument using the fact that the largest angular momentum describes circular orbits, where all the kinetic energy is in orbital form. For hydrogen-like atoms, $U(r)=-Z k e^{2} / r,$ and the energy in circular orbits becomes $$E=\frac{|\mathbf{L}|^{2}}{2 m r^{2}}-\frac{Z k e^{2}}{r}$$ Quantize this relation using the rules of Equations 8.16 and $8.38,$ together with the Bohr result for the allowed values of $r,$ to show that the largest integer value of $\ell$ consistent with the total energy is $\ell_{\max }=n-1.$

The monocle er orbital's for and can really for them to us sick mother in this sick mast our wellness Sigmar Clueless sick Mark stop you piss! Then comes the by and doctors by b y And why don't be sit After this comes the Sigmar little actors Sigma We'll be X Then comes the and demanding my aunt does That is by stuff be way and by stop and the sick masters sick Ma star do b s so there are a total 14 victims total 14 electric There we started feeling it delivers that does dream full steak it Dan good and 40. So this is that I just occupy animal interrupted which we come This is the highest occupied month These are the lowest unoccupied molecule So on expectations electrons will go Any of the two orbits? No. For the be part, we are required to calculate the bond or off the normal nitrogen molecules and the excited state excite You stated that he presented it Stop So the number of bonding electrons is 10 in case of nitrogen and the number off and take bonding electrons up for these other bonding electrons to for 68 10 These urban number on antimony electrons that is to and do four. So according to the farmer, 10 minus four by two gives six battle That is no in case off Enstar One electron for there goes to the and they wanted one. So the number of one being electrons becomes nine. Where s the anti warning electrons becomes by and the border. Therefore I'm so too. Therefore, Anto is more civil. The barn lint off and two is small. There s the bomb went off and to start is more the Borglum. Oh, and is less than the bomb went off. And do start No, regarding the magnetic director. The end to stop. Is there a magnetic in nature? It this bad magnetic in nature whereas nitrogen laws No, The Victoria Waveland in party is 470. No, no meters. That is 470. My particular ever tenders for minus nine meters. This is the Vaillant, which is a material vendor. Electron comes back a little. We have can't learn the energy. So he is goingto etching where it is. A constant plants constant. Its real loose explained 6 to 6 multi level minus septic for into a new candidate. Tennessee. Remember, new is C there see is three in pretenders are eight Mika capacity and speed off light, and the new the lender is 470 in attendance were minus nine meters. When we can clear this, so we'll get the answers. E is the portal. The energy released is before 4.3 tenders to the hour minus use minus name jokes so we can sum up. He actually was a formula. New is a core to see upon Linda. That's when we use this here and we get even knew four fine through three into tennis from my understand Joe's.

In the first part of this problem. Magnitude off orbital angular momentum is given Andi, we wantto find our little quantum number. So we have a magnitude off our little quantum number is Can you do homes? So good old off 57 in tow. Japon Go away! SB hill The religion for magnitude Off our little angry woman Dome is you, Goto and into helpless one dimes age upon Goodbye. So there is equal to I didn't do. Sigurd rode off into seven times a job on why here s Japan. Dubai will be concerned from Mozart. So we have Ellen toe l plus one hearts curb physical too. I didn't do so good of love pisser nobody taking some girl on both sides of the region. We have Ellen to l plus one physical true 100 into 57 are you can write This expression is else a girl plus l physical toe 57 100 else girl plus l minus 5700 is equal to zero. No compare by comparing this accordion with the sea gender form off quadratic equation. There did execute a plus. Be explicit. See easy car zero we have here a sickle toe one basically 21 and C is equal to minus 57 double zero iss. We hear the religion farm roofs off. Quadratic equation is X equal to minus B, but let's minus. It's a good, although be sicker minus for a C upon do it. Nobody Putting the values off A, B and C we held L. A is equal to minus B, but let's minus. It's a good old off once again, minus four in tow. Here is one and the seas minus 57 100 upon Go indoors A's one Here we have Well, you off bees one. So l is equal to minus one less minus one protector off foreign food for seven 100 is to do and noma zero upon do so political toe minus one plus minus The some off one engine Do any drew and 100 is so do I and 01 upon Go. So l is equal to minus one. But that's minus. It's a girdle graph, Toto. Engine one is 1 51 Upon from here we held you were yourself and there l physical toe minus one plus 1 51 divided by two and second where you is minus one minus 1 51 dried by two. So we have a musical too 75 and the other value off, please. Minus so under six. But we know that our little quantum number Well, in two days positive values. So the required Well, you off Ellis 70 five. No, in the people off this problem we want to find minimum Will you off peaceful quantum number off there. Adam s video. The values off l that l takes the values from zero toe and minus one here. And he's peaceful quantum number. Ask me how already concluded in part. You have this problem that the maximum weight you off our little call our little quantum memories. 75. Yes, we have the relation between maximum our little quantum number and principal quantum memories. And maximum is it Kal toh and minus one. Here we have l'm maximum is 7 to 5. Is it going toe and minus one? From here we help. And is it going toe? Seven to fire people as one. So we have a musical do 76. So this is the minimum value. A principal quantum number for political too. 75 now in the last quarter off this problem we want to calculate. And now do ya go Adam for a physical toe tending to secure a draft number seven dimes Japon, Dubai We held maximum. Our little England momentum is 7 to 5 and far dared. We have minimum principal Quantum. Nobody's 76. Now we want to find energy of their dome. Yes, we heard the relation for in our job Bottom is equal to minus 13. Fire six Ella gone world upon and sugar which is a goto minus 13 fired six Ladan world upon here and he's 76. So after computing, we have energy equal to minus zero point 00 Cruelty five alert down world Which is it going? Toe minus two Part 35 times Tendered of our ministry Celadon world There's the end of the problem. Thanks for watching

In the first part of this problem. And Angie Officer Don in a hydrogen atom is given and we want to pull Glade principal Quantum number for this Adam. So here we heal Energy Equal toe minus zero point 55 Little buying five, 44 Electron world as we hold the relation for energy far anymore are good use equal toe minus 13 Fired six l adorn world upon and secure No for in we hear the relation and is you Goto girl Oh, minus 13.6 Electron world upon energy Nowhere put in the value off And are you here? And is it could do so good to go minus 13 Fired six Celadon World upon and RG art dealer Don is minus little point five 44 Electron world So the hell and physical drew body wedding two numbers in the inside the square root He's 25 so we hear and physical Do what living the second part of this problem we want to calculate maximum possible orbital angular moment after Adam Yes, we heard the religion for Are we will maximum are brutal. I want a number. He's l mix is eagle do and minus one here. And his principal quantum number. So we have L. Max Physical too. Five minus one. Is it gonna do for nobody using the relation for magnitude off our little Anglin momentum? And is it going toe so good a graph, Ellen. Do l plus one times, eh? Japon? Dubai By substituting the value of orbital quantum number the hell and a little window musical room for in tow four plus one and the willow Planck's constant ese. 6 to 5 or 6 to 3 times 10 to the power minus 34. You'll induce again upon. Go into here buys three point 14 So we have the video off our little angular momentum. Equal toe four point seven room 56 times genital power minus 34. Jule sicken. Now, in the last part of this problem, we want to calculate number upstairs in the subtitles. With the mud with the next lovers will you off l So here we heal the next lovers to reel you off and he's four minus one here for is the well you, which we have calculated in part be up this problem so that next lowest value is four minus one. The physical do three. So far a given. Were you up in? There are through l plus one. Radios off. Emily, hear Emily's Maggie want, remember And for you And will you off and Mel we heal through values off Emmis here a Mrs Sutphin quantum number. So quite a given. Well, you off and not possible where youse off and this are doing toe do l bolos one. So for a given well, you off sup shell and well, number off sitters equal toe do in tow. Well, plus one here. Analytical room three. So remember, after dares for and equal to Is it going toe to toe in tow too Well, plus one. Here are the three bless one which is a call to go into 60 plus one Is it gold toe going to seven Musical do 40 So there are 46 years for political too three

This list here is the orbital's that are involved in the excitation of diatonic nitrogen. These were also the orbital's you would see in a molecular orbital diagram. We'll have a Sigma and Sigma anti bonding for our one and two s orbital's. We'll have a pie bonding for R two p or middle. We'll have another pie bombing for two pz orbital laugh signal bonding for a two p x orbital and pie anti bonding for two p. Why orbital as well as pie anti bonding for two pz orbital. So in our excitation of die atomic nitrogen, the electrons in transition will take place from the Sigma two p x orbital. Going into the pie anti bonding to pee wipe, I enter biting two p x orbital. The next that we need to do is find the bond order in order to find the bond order will take 1/2 times this entire quantity of the electrons involved in the bonding of molecular orbital's minus the electrons involved in anti bonding like their orbital's. And when we do that, we'll find that the bond order for just regular diatonic nitrogen is three, and then the bond order order for excited die. Time of nitrogen is, too, and we can also deduce from from the molecular or burr orbital diagram or the very simplified transition image that I showed you before is that the excited version of Diatonic Nation is dying magnetic. And that's because doesn't have any unpaid electrons, or the only unimpaired electrons that are present in this diagram have opposite spins. The next thing that we should know is how to find the energy of a photon energy of a photon is equal to H C over Lambda, where ages Plank's constant C is the speed of light and Lambda is our wave length in meters. So to find the energy of the photon will take Plank's constant 6.626 times, 10 to the negative 34th Jules time seconds. Multiply that by the speed of light three times 10 to the eighth meters per second and will divide that by our wave length in meters, which will be 470 times 10 to the negative ninth meters. And we'll find that the energy is 4.23 times 10 to the negative 19th jewels


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